Add Spark 1.6.0 docs

author: Michael Armbrust <marmbrus@apache.org> 2016-01-04 17:53:21 +0000
committer: Michael Armbrust <marmbrus@apache.org> 2016-01-04 17:53:21 +0000
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+                    
+                        <h1 class="title">Classification and regression - spark.ml</h1>
+                    
+
+                    <p><code>\[
+\newcommand{\R}{\mathbb{R}}
+\newcommand{\E}{\mathbb{E}}
+\newcommand{\x}{\mathbf{x}}
+\newcommand{\y}{\mathbf{y}}
+\newcommand{\wv}{\mathbf{w}}
+\newcommand{\av}{\mathbf{\alpha}}
+\newcommand{\bv}{\mathbf{b}}
+\newcommand{\N}{\mathbb{N}}
+\newcommand{\id}{\mathbf{I}}
+\newcommand{\ind}{\mathbf{1}}
+\newcommand{\0}{\mathbf{0}}
+\newcommand{\unit}{\mathbf{e}}
+\newcommand{\one}{\mathbf{1}}
+\newcommand{\zero}{\mathbf{0}}
+\]</code></p>
+
+<p><strong>Table of Contents</strong></p>
+
+<ul id="markdown-toc">
+  <li><a href="#classification" id="markdown-toc-classification">Classification</a>    <ul>
+      <li><a href="#logistic-regression" id="markdown-toc-logistic-regression">Logistic regression</a></li>
+      <li><a href="#decision-tree-classifier" id="markdown-toc-decision-tree-classifier">Decision tree classifier</a></li>
+      <li><a href="#random-forest-classifier" id="markdown-toc-random-forest-classifier">Random forest classifier</a></li>
+      <li><a href="#gradient-boosted-tree-classifier" id="markdown-toc-gradient-boosted-tree-classifier">Gradient-boosted tree classifier</a></li>
+      <li><a href="#multilayer-perceptron-classifier" id="markdown-toc-multilayer-perceptron-classifier">Multilayer perceptron classifier</a></li>
+      <li><a href="#one-vs-rest-classifier-aka-one-vs-all" id="markdown-toc-one-vs-rest-classifier-aka-one-vs-all">One-vs-Rest classifier (a.k.a. One-vs-All)</a></li>
+    </ul>
+  </li>
+  <li><a href="#regression" id="markdown-toc-regression">Regression</a>    <ul>
+      <li><a href="#linear-regression" id="markdown-toc-linear-regression">Linear regression</a></li>
+      <li><a href="#decision-tree-regression" id="markdown-toc-decision-tree-regression">Decision tree regression</a></li>
+      <li><a href="#random-forest-regression" id="markdown-toc-random-forest-regression">Random forest regression</a></li>
+      <li><a href="#gradient-boosted-tree-regression" id="markdown-toc-gradient-boosted-tree-regression">Gradient-boosted tree regression</a></li>
+      <li><a href="#survival-regression" id="markdown-toc-survival-regression">Survival regression</a></li>
+    </ul>
+  </li>
+  <li><a href="#decision-trees" id="markdown-toc-decision-trees">Decision trees</a>    <ul>
+      <li><a href="#inputs-and-outputs" id="markdown-toc-inputs-and-outputs">Inputs and Outputs</a>        <ul>
+          <li><a href="#input-columns" id="markdown-toc-input-columns">Input Columns</a></li>
+          <li><a href="#output-columns" id="markdown-toc-output-columns">Output Columns</a></li>
+        </ul>
+      </li>
+    </ul>
+  </li>
+  <li><a href="#tree-ensembles" id="markdown-toc-tree-ensembles">Tree Ensembles</a>    <ul>
+      <li><a href="#random-forests" id="markdown-toc-random-forests">Random Forests</a>        <ul>
+          <li><a href="#inputs-and-outputs-1" id="markdown-toc-inputs-and-outputs-1">Inputs and Outputs</a>            <ul>
+              <li><a href="#input-columns-1" id="markdown-toc-input-columns-1">Input Columns</a></li>
+              <li><a href="#output-columns-predictions" id="markdown-toc-output-columns-predictions">Output Columns (Predictions)</a></li>
+            </ul>
+          </li>
+        </ul>
+      </li>
+      <li><a href="#gradient-boosted-trees-gbts" id="markdown-toc-gradient-boosted-trees-gbts">Gradient-Boosted Trees (GBTs)</a>        <ul>
+          <li><a href="#inputs-and-outputs-2" id="markdown-toc-inputs-and-outputs-2">Inputs and Outputs</a>            <ul>
+              <li><a href="#input-columns-2" id="markdown-toc-input-columns-2">Input Columns</a></li>
+              <li><a href="#output-columns-predictions-1" id="markdown-toc-output-columns-predictions-1">Output Columns (Predictions)</a></li>
+            </ul>
+          </li>
+        </ul>
+      </li>
+    </ul>
+  </li>
+</ul>
+
+<p>In <code>spark.ml</code>, we implement popular linear methods such as logistic
+regression and linear least squares with $L_1$ or $L_2$ regularization.
+Refer to <a href="mllib-linear-methods.html">the linear methods in mllib</a> for
+details about implementation and tuning.  We also include a DataFrame API for <a href="http://en.wikipedia.org/wiki/Elastic_net_regularization">Elastic
+net</a>, a hybrid
+of $L_1$ and $L_2$ regularization proposed in <a href="http://users.stat.umn.edu/~zouxx019/Papers/elasticnet.pdf">Zou et al, Regularization
+and variable selection via the elastic
+net</a>.
+Mathematically, it is defined as a convex combination of the $L_1$ and
+the $L_2$ regularization terms:
+<code>\[
+\alpha \left( \lambda \|\wv\|_1 \right) + (1-\alpha) \left( \frac{\lambda}{2}\|\wv\|_2^2 \right) , \alpha \in [0, 1], \lambda \geq 0
+\]</code>
+By setting $\alpha$ properly, elastic net contains both $L_1$ and $L_2$
+regularization as special cases. For example, if a <a href="https://en.wikipedia.org/wiki/Linear_regression">linear
+regression</a> model is
+trained with the elastic net parameter $\alpha$ set to $1$, it is
+equivalent to a
+<a href="http://en.wikipedia.org/wiki/Least_squares#Lasso_method">Lasso</a> model.
+On the other hand, if $\alpha$ is set to $0$, the trained model reduces
+to a <a href="http://en.wikipedia.org/wiki/Tikhonov_regularization">ridge
+regression</a> model.
+We implement Pipelines API for both linear regression and logistic
+regression with elastic net regularization.</p>
+
+<h1 id="classification">Classification</h1>
+
+<h2 id="logistic-regression">Logistic regression</h2>
+
+<p>Logistic regression is a popular method to predict a binary response. It is a special case of <a href="https://en.wikipedia.org/wiki/Generalized_linear_model">Generalized Linear models</a> that predicts the probability of the outcome.
+For more background and more details about the implementation, refer to the documentation of the <a href="mllib-linear-methods.html#logistic-regression">logistic regression in <code>spark.mllib</code></a>.</p>
+
+<blockquote>
+  <p>The current implementation of logistic regression in <code>spark.ml</code> only supports binary classes. Support for multiclass regression will be added in the future.</p>
+</blockquote>
+
+<p><strong>Example</strong></p>
+
+<p>The following example shows how to train a logistic regression model
+with elastic net regularization. <code>elasticNetParam</code> corresponds to
+$\alpha$ and <code>regParam</code> corresponds to $\lambda$.</p>
+
+<div class="codetabs">
+
+<div data-lang="scala">
+    <div class="highlight"><pre><span class="k">import</span> <span class="nn">org.apache.spark.ml.classification.LogisticRegression</span>
+
+<span class="c1">// Load training data</span>
+<span class="k">val</span> <span class="n">training</span> <span class="k">=</span> <span class="n">sqlCtx</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">).</span><span class="n">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="o">)</span>
+
+<span class="k">val</span> <span class="n">lr</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">LogisticRegression</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setMaxIter</span><span class="o">(</span><span class="mi">10</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setRegParam</span><span class="o">(</span><span class="mf">0.3</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setElasticNetParam</span><span class="o">(</span><span class="mf">0.8</span><span class="o">)</span>
+
+<span class="c1">// Fit the model</span>
+<span class="k">val</span> <span class="n">lrModel</span> <span class="k">=</span> <span class="n">lr</span><span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">training</span><span class="o">)</span>
+
+<span class="c1">// Print the coefficients and intercept for logistic regression</span>
+<span class="n">println</span><span class="o">(</span><span class="n">s</span><span class="s">&quot;Coefficients: ${lrModel.coefficients} Intercept: ${lrModel.intercept}&quot;</span><span class="o">)</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/LogisticRegressionWithElasticNetExample.scala" in the Spark repo.</small></div>
+  </div>
+
+<div data-lang="java">
+    <div class="highlight"><pre><span class="kn">import</span> <span class="nn">org.apache.spark.ml.classification.LogisticRegression</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.classification.LogisticRegressionModel</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.DataFrame</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.SQLContext</span><span class="o">;</span>
+
+<span class="c1">// Load training data</span>
+<span class="n">DataFrame</span> <span class="n">training</span> <span class="o">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="na">read</span><span class="o">().</span><span class="na">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="o">);</span>
+
+<span class="n">LogisticRegression</span> <span class="n">lr</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">LogisticRegression</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setMaxIter</span><span class="o">(</span><span class="mi">10</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setRegParam</span><span class="o">(</span><span class="mf">0.3</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setElasticNetParam</span><span class="o">(</span><span class="mf">0.8</span><span class="o">);</span>
+
+<span class="c1">// Fit the model</span>
+<span class="n">LogisticRegressionModel</span> <span class="n">lrModel</span> <span class="o">=</span> <span class="n">lr</span><span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">training</span><span class="o">);</span>
+
+<span class="c1">// Print the coefficients and intercept for logistic regression</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;Coefficients: &quot;</span>
+  <span class="o">+</span> <span class="n">lrModel</span><span class="o">.</span><span class="na">coefficients</span><span class="o">()</span> <span class="o">+</span> <span class="s">&quot; Intercept: &quot;</span> <span class="o">+</span> <span class="n">lrModel</span><span class="o">.</span><span class="na">intercept</span><span class="o">());</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaLogisticRegressionWithElasticNetExample.java" in the Spark repo.</small></div>
+  </div>
+
+<div data-lang="python">
+    <div class="highlight"><pre><span class="kn">from</span> <span class="nn">pyspark.ml.classification</span> <span class="kn">import</span> <span class="n">LogisticRegression</span>
+
+<span class="c"># Load training data</span>
+<span class="n">training</span> <span class="o">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="s">&quot;libsvm&quot;</span><span class="p">)</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="p">)</span>
+
+<span class="n">lr</span> <span class="o">=</span> <span class="n">LogisticRegression</span><span class="p">(</span><span class="n">maxIter</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">regParam</span><span class="o">=</span><span class="mf">0.3</span><span class="p">,</span> <span class="n">elasticNetParam</span><span class="o">=</span><span class="mf">0.8</span><span class="p">)</span>
+
+<span class="c"># Fit the model</span>
+<span class="n">lrModel</span> <span class="o">=</span> <span class="n">lr</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">training</span><span class="p">)</span>
+
+<span class="c"># Print the coefficients and intercept for logistic regression</span>
+<span class="k">print</span><span class="p">(</span><span class="s">&quot;Coefficients: &quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">lrModel</span><span class="o">.</span><span class="n">coefficients</span><span class="p">))</span>
+<span class="k">print</span><span class="p">(</span><span class="s">&quot;Intercept: &quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">lrModel</span><span class="o">.</span><span class="n">intercept</span><span class="p">))</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/python/ml/logistic_regression_with_elastic_net.py" in the Spark repo.</small></div>
+  </div>
+
+</div>
+
+<p>The <code>spark.ml</code> implementation of logistic regression also supports
+extracting a summary of the model over the training set. Note that the
+predictions and metrics which are stored as <code>DataFrame</code> in
+<code>BinaryLogisticRegressionSummary</code> are annotated <code>@transient</code> and hence
+only available on the driver.</p>
+
+<div class="codetabs">
+
+<div data-lang="scala">
+
+    <p><a href="api/scala/index.html#org.apache.spark.ml.classification.LogisticRegressionTrainingSummary"><code>LogisticRegressionTrainingSummary</code></a>
+provides a summary for a
+<a href="api/scala/index.html#org.apache.spark.ml.classification.LogisticRegressionModel"><code>LogisticRegressionModel</code></a>.
+Currently, only binary classification is supported and the
+summary must be explicitly cast to
+<a href="api/scala/index.html#org.apache.spark.ml.classification.BinaryLogisticRegressionTrainingSummary"><code>BinaryLogisticRegressionTrainingSummary</code></a>.
+This will likely change when multiclass classification is supported.</p>
+
+    <p>Continuing the earlier example:</p>
+
+    <div class="highlight"><pre><span class="k">import</span> <span class="nn">org.apache.spark.ml.classification.</span><span class="o">{</span><span class="nc">BinaryLogisticRegressionSummary</span><span class="o">,</span> <span class="nc">LogisticRegression</span><span class="o">}</span>
+
+<span class="c1">// Extract the summary from the returned LogisticRegressionModel instance trained in the earlier</span>
+<span class="c1">// example</span>
+<span class="k">val</span> <span class="n">trainingSummary</span> <span class="k">=</span> <span class="n">lrModel</span><span class="o">.</span><span class="n">summary</span>
+
+<span class="c1">// Obtain the objective per iteration.</span>
+<span class="k">val</span> <span class="n">objectiveHistory</span> <span class="k">=</span> <span class="n">trainingSummary</span><span class="o">.</span><span class="n">objectiveHistory</span>
+<span class="n">objectiveHistory</span><span class="o">.</span><span class="n">foreach</span><span class="o">(</span><span class="n">loss</span> <span class="k">=&gt;</span> <span class="n">println</span><span class="o">(</span><span class="n">loss</span><span class="o">))</span>
+
+<span class="c1">// Obtain the metrics useful to judge performance on test data.</span>
+<span class="c1">// We cast the summary to a BinaryLogisticRegressionSummary since the problem is a</span>
+<span class="c1">// binary classification problem.</span>
+<span class="k">val</span> <span class="n">binarySummary</span> <span class="k">=</span> <span class="n">trainingSummary</span><span class="o">.</span><span class="n">asInstanceOf</span><span class="o">[</span><span class="kt">BinaryLogisticRegressionSummary</span><span class="o">]</span>
+
+<span class="c1">// Obtain the receiver-operating characteristic as a dataframe and areaUnderROC.</span>
+<span class="k">val</span> <span class="n">roc</span> <span class="k">=</span> <span class="n">binarySummary</span><span class="o">.</span><span class="n">roc</span>
+<span class="n">roc</span><span class="o">.</span><span class="n">show</span><span class="o">()</span>
+<span class="n">println</span><span class="o">(</span><span class="n">binarySummary</span><span class="o">.</span><span class="n">areaUnderROC</span><span class="o">)</span>
+
+<span class="c1">// Set the model threshold to maximize F-Measure</span>
+<span class="k">val</span> <span class="n">fMeasure</span> <span class="k">=</span> <span class="n">binarySummary</span><span class="o">.</span><span class="n">fMeasureByThreshold</span>
+<span class="k">val</span> <span class="n">maxFMeasure</span> <span class="k">=</span> <span class="n">fMeasure</span><span class="o">.</span><span class="n">select</span><span class="o">(</span><span class="n">max</span><span class="o">(</span><span class="s">&quot;F-Measure&quot;</span><span class="o">)).</span><span class="n">head</span><span class="o">().</span><span class="n">getDouble</span><span class="o">(</span><span class="mi">0</span><span class="o">)</span>
+<span class="k">val</span> <span class="n">bestThreshold</span> <span class="k">=</span> <span class="n">fMeasure</span><span class="o">.</span><span class="n">where</span><span class="o">(</span><span class="n">$</span><span class="s">&quot;F-Measure&quot;</span> <span class="o">===</span> <span class="n">maxFMeasure</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">select</span><span class="o">(</span><span class="s">&quot;threshold&quot;</span><span class="o">).</span><span class="n">head</span><span class="o">().</span><span class="n">getDouble</span><span class="o">(</span><span class="mi">0</span><span class="o">)</span>
+<span class="n">lrModel</span><span class="o">.</span><span class="n">setThreshold</span><span class="o">(</span><span class="n">bestThreshold</span><span class="o">)</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/LogisticRegressionSummaryExample.scala" in the Spark repo.</small></div>
+  </div>
+
+<div data-lang="java">
+    <p><a href="api/java/org/apache/spark/ml/classification/LogisticRegressionTrainingSummary.html"><code>LogisticRegressionTrainingSummary</code></a>
+provides a summary for a
+<a href="api/java/org/apache/spark/ml/classification/LogisticRegressionModel.html"><code>LogisticRegressionModel</code></a>.
+Currently, only binary classification is supported and the
+summary must be explicitly cast to
+<a href="api/java/org/apache/spark/ml/classification/BinaryLogisticRegressionTrainingSummary.html"><code>BinaryLogisticRegressionTrainingSummary</code></a>.
+This will likely change when multiclass classification is supported.</p>
+
+    <p>Continuing the earlier example:</p>
+
+    <div class="highlight"><pre><span class="kn">import</span> <span class="nn">org.apache.spark.ml.classification.BinaryLogisticRegressionSummary</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.classification.LogisticRegression</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.classification.LogisticRegressionModel</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.classification.LogisticRegressionTrainingSummary</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.DataFrame</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.SQLContext</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.functions</span><span class="o">;</span>
+
+<span class="c1">// Extract the summary from the returned LogisticRegressionModel instance trained in the earlier</span>
+<span class="c1">// example</span>
+<span class="n">LogisticRegressionTrainingSummary</span> <span class="n">trainingSummary</span> <span class="o">=</span> <span class="n">lrModel</span><span class="o">.</span><span class="na">summary</span><span class="o">();</span>
+
+<span class="c1">// Obtain the loss per iteration.</span>
+<span class="kt">double</span><span class="o">[]</span> <span class="n">objectiveHistory</span> <span class="o">=</span> <span class="n">trainingSummary</span><span class="o">.</span><span class="na">objectiveHistory</span><span class="o">();</span>
+<span class="k">for</span> <span class="o">(</span><span class="kt">double</span> <span class="n">lossPerIteration</span> <span class="o">:</span> <span class="n">objectiveHistory</span><span class="o">)</span> <span class="o">{</span>
+  <span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="n">lossPerIteration</span><span class="o">);</span>
+<span class="o">}</span>
+
+<span class="c1">// Obtain the metrics useful to judge performance on test data.</span>
+<span class="c1">// We cast the summary to a BinaryLogisticRegressionSummary since the problem is a binary</span>
+<span class="c1">// classification problem.</span>
+<span class="n">BinaryLogisticRegressionSummary</span> <span class="n">binarySummary</span> <span class="o">=</span>
+  <span class="o">(</span><span class="n">BinaryLogisticRegressionSummary</span><span class="o">)</span> <span class="n">trainingSummary</span><span class="o">;</span>
+
+<span class="c1">// Obtain the receiver-operating characteristic as a dataframe and areaUnderROC.</span>
+<span class="n">DataFrame</span> <span class="n">roc</span> <span class="o">=</span> <span class="n">binarySummary</span><span class="o">.</span><span class="na">roc</span><span class="o">();</span>
+<span class="n">roc</span><span class="o">.</span><span class="na">show</span><span class="o">();</span>
+<span class="n">roc</span><span class="o">.</span><span class="na">select</span><span class="o">(</span><span class="s">&quot;FPR&quot;</span><span class="o">).</span><span class="na">show</span><span class="o">();</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="n">binarySummary</span><span class="o">.</span><span class="na">areaUnderROC</span><span class="o">());</span>
+
+<span class="c1">// Get the threshold corresponding to the maximum F-Measure and rerun LogisticRegression with</span>
+<span class="c1">// this selected threshold.</span>
+<span class="n">DataFrame</span> <span class="n">fMeasure</span> <span class="o">=</span> <span class="n">binarySummary</span><span class="o">.</span><span class="na">fMeasureByThreshold</span><span class="o">();</span>
+<span class="kt">double</span> <span class="n">maxFMeasure</span> <span class="o">=</span> <span class="n">fMeasure</span><span class="o">.</span><span class="na">select</span><span class="o">(</span><span class="n">functions</span><span class="o">.</span><span class="na">max</span><span class="o">(</span><span class="s">&quot;F-Measure&quot;</span><span class="o">)).</span><span class="na">head</span><span class="o">().</span><span class="na">getDouble</span><span class="o">(</span><span class="mi">0</span><span class="o">);</span>
+<span class="kt">double</span> <span class="n">bestThreshold</span> <span class="o">=</span> <span class="n">fMeasure</span><span class="o">.</span><span class="na">where</span><span class="o">(</span><span class="n">fMeasure</span><span class="o">.</span><span class="na">col</span><span class="o">(</span><span class="s">&quot;F-Measure&quot;</span><span class="o">).</span><span class="na">equalTo</span><span class="o">(</span><span class="n">maxFMeasure</span><span class="o">))</span>
+  <span class="o">.</span><span class="na">select</span><span class="o">(</span><span class="s">&quot;threshold&quot;</span><span class="o">).</span><span class="na">head</span><span class="o">().</span><span class="na">getDouble</span><span class="o">(</span><span class="mi">0</span><span class="o">);</span>
+<span class="n">lrModel</span><span class="o">.</span><span class="na">setThreshold</span><span class="o">(</span><span class="n">bestThreshold</span><span class="o">);</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaLogisticRegressionSummaryExample.java" in the Spark repo.</small></div>
+  </div>
+
+<!--- TODO: Add python model summaries once implemented -->
+<div data-lang="python">
+    <p>Logistic regression model summary is not yet supported in Python.</p>
+  </div>
+
+</div>
+
+<h2 id="decision-tree-classifier">Decision tree classifier</h2>
+
+<p>Decision trees are a popular family of classification and regression methods.
+More information about the <code>spark.ml</code> implementation can be found further in the <a href="#decision-trees">section on decision trees</a>.</p>
+
+<p><strong>Example</strong></p>
+
+<p>The following examples load a dataset in LibSVM format, split it into training and test sets, train on the first dataset, and then evaluate on the held-out test set.
+We use two feature transformers to prepare the data; these help index categories for the label and categorical features, adding metadata to the <code>DataFrame</code> which the Decision Tree algorithm can recognize.</p>
+
+<div class="codetabs">
+<div data-lang="scala">
+
+    <p>More details on parameters can be found in the <a href="api/scala/index.html#org.apache.spark.ml.classification.DecisionTreeClassifier">Scala API documentation</a>.</p>
+
+    <div class="highlight"><pre><span class="k">import</span> <span class="nn">org.apache.spark.ml.Pipeline</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.ml.classification.DecisionTreeClassifier</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.ml.classification.DecisionTreeClassificationModel</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.ml.feature.</span><span class="o">{</span><span class="nc">StringIndexer</span><span class="o">,</span> <span class="nc">IndexToString</span><span class="o">,</span> <span class="nc">VectorIndexer</span><span class="o">}</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator</span>
+
+<span class="c1">// Load the data stored in LIBSVM format as a DataFrame.</span>
+<span class="k">val</span> <span class="n">data</span> <span class="k">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">).</span><span class="n">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="o">)</span>
+
+<span class="c1">// Index labels, adding metadata to the label column.</span>
+<span class="c1">// Fit on whole dataset to include all labels in index.</span>
+<span class="k">val</span> <span class="n">labelIndexer</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">StringIndexer</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setInputCol</span><span class="o">(</span><span class="s">&quot;label&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setOutputCol</span><span class="o">(</span><span class="s">&quot;indexedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">data</span><span class="o">)</span>
+<span class="c1">// Automatically identify categorical features, and index them.</span>
+<span class="k">val</span> <span class="n">featureIndexer</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">VectorIndexer</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setInputCol</span><span class="o">(</span><span class="s">&quot;features&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setOutputCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setMaxCategories</span><span class="o">(</span><span class="mi">4</span><span class="o">)</span> <span class="c1">// features with &gt; 4 distinct values are treated as continuous</span>
+  <span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">data</span><span class="o">)</span>
+
+<span class="c1">// Split the data into training and test sets (30% held out for testing)</span>
+<span class="k">val</span> <span class="nc">Array</span><span class="o">(</span><span class="n">trainingData</span><span class="o">,</span> <span class="n">testData</span><span class="o">)</span> <span class="k">=</span> <span class="n">data</span><span class="o">.</span><span class="n">randomSplit</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="mf">0.7</span><span class="o">,</span> <span class="mf">0.3</span><span class="o">))</span>
+
+<span class="c1">// Train a DecisionTree model.</span>
+<span class="k">val</span> <span class="n">dt</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">DecisionTreeClassifier</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setLabelCol</span><span class="o">(</span><span class="s">&quot;indexedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setFeaturesCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">)</span>
+
+<span class="c1">// Convert indexed labels back to original labels.</span>
+<span class="k">val</span> <span class="n">labelConverter</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">IndexToString</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setInputCol</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setOutputCol</span><span class="o">(</span><span class="s">&quot;predictedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setLabels</span><span class="o">(</span><span class="n">labelIndexer</span><span class="o">.</span><span class="n">labels</span><span class="o">)</span>
+
+<span class="c1">// Chain indexers and tree in a Pipeline</span>
+<span class="k">val</span> <span class="n">pipeline</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">Pipeline</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setStages</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="n">labelIndexer</span><span class="o">,</span> <span class="n">featureIndexer</span><span class="o">,</span> <span class="n">dt</span><span class="o">,</span> <span class="n">labelConverter</span><span class="o">))</span>
+
+<span class="c1">// Train model.  This also runs the indexers.</span>
+<span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="n">pipeline</span><span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">trainingData</span><span class="o">)</span>
+
+<span class="c1">// Make predictions.</span>
+<span class="k">val</span> <span class="n">predictions</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">transform</span><span class="o">(</span><span class="n">testData</span><span class="o">)</span>
+
+<span class="c1">// Select example rows to display.</span>
+<span class="n">predictions</span><span class="o">.</span><span class="n">select</span><span class="o">(</span><span class="s">&quot;predictedLabel&quot;</span><span class="o">,</span> <span class="s">&quot;label&quot;</span><span class="o">,</span> <span class="s">&quot;features&quot;</span><span class="o">).</span><span class="n">show</span><span class="o">(</span><span class="mi">5</span><span class="o">)</span>
+
+<span class="c1">// Select (prediction, true label) and compute test error</span>
+<span class="k">val</span> <span class="n">evaluator</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">MulticlassClassificationEvaluator</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setLabelCol</span><span class="o">(</span><span class="s">&quot;indexedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setPredictionCol</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setMetricName</span><span class="o">(</span><span class="s">&quot;precision&quot;</span><span class="o">)</span>
+<span class="k">val</span> <span class="n">accuracy</span> <span class="k">=</span> <span class="n">evaluator</span><span class="o">.</span><span class="n">evaluate</span><span class="o">(</span><span class="n">predictions</span><span class="o">)</span>
+<span class="n">println</span><span class="o">(</span><span class="s">&quot;Test Error = &quot;</span> <span class="o">+</span> <span class="o">(</span><span class="mf">1.0</span> <span class="o">-</span> <span class="n">accuracy</span><span class="o">))</span>
+
+<span class="k">val</span> <span class="n">treeModel</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">stages</span><span class="o">(</span><span class="mi">2</span><span class="o">).</span><span class="n">asInstanceOf</span><span class="o">[</span><span class="kt">DecisionTreeClassificationModel</span><span class="o">]</span>
+<span class="n">println</span><span class="o">(</span><span class="s">&quot;Learned classification tree model:\n&quot;</span> <span class="o">+</span> <span class="n">treeModel</span><span class="o">.</span><span class="n">toDebugString</span><span class="o">)</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/DecisionTreeClassificationExample.scala" in the Spark repo.</small></div>
+
+  </div>
+
+<div data-lang="java">
+
+    <p>More details on parameters can be found in the <a href="api/java/org/apache/spark/ml/classification/DecisionTreeClassifier.html">Java API documentation</a>.</p>
+
+    <div class="highlight"><pre><span class="kn">import</span> <span class="nn">org.apache.spark.SparkConf</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaSparkContext</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.Pipeline</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.PipelineModel</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.PipelineStage</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.classification.DecisionTreeClassifier</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.classification.DecisionTreeClassificationModel</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.feature.*</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.DataFrame</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.SQLContext</span><span class="o">;</span>
+
+<span class="c1">// Load the data stored in LIBSVM format as a DataFrame.</span>
+<span class="n">DataFrame</span> <span class="n">data</span> <span class="o">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="na">read</span><span class="o">().</span><span class="na">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">).</span><span class="na">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="o">);</span>
+
+<span class="c1">// Index labels, adding metadata to the label column.</span>
+<span class="c1">// Fit on whole dataset to include all labels in index.</span>
+<span class="n">StringIndexerModel</span> <span class="n">labelIndexer</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">StringIndexer</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setInputCol</span><span class="o">(</span><span class="s">&quot;label&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setOutputCol</span><span class="o">(</span><span class="s">&quot;indexedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">data</span><span class="o">);</span>
+
+<span class="c1">// Automatically identify categorical features, and index them.</span>
+<span class="n">VectorIndexerModel</span> <span class="n">featureIndexer</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">VectorIndexer</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setInputCol</span><span class="o">(</span><span class="s">&quot;features&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setOutputCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setMaxCategories</span><span class="o">(</span><span class="mi">4</span><span class="o">)</span> <span class="c1">// features with &gt; 4 distinct values are treated as continuous</span>
+  <span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">data</span><span class="o">);</span>
+
+<span class="c1">// Split the data into training and test sets (30% held out for testing)</span>
+<span class="n">DataFrame</span><span class="o">[]</span> <span class="n">splits</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="na">randomSplit</span><span class="o">(</span><span class="k">new</span> <span class="kt">double</span><span class="o">[]{</span><span class="mf">0.7</span><span class="o">,</span> <span class="mf">0.3</span><span class="o">});</span>
+<span class="n">DataFrame</span> <span class="n">trainingData</span> <span class="o">=</span> <span class="n">splits</span><span class="o">[</span><span class="mi">0</span><span class="o">];</span>
+<span class="n">DataFrame</span> <span class="n">testData</span> <span class="o">=</span> <span class="n">splits</span><span class="o">[</span><span class="mi">1</span><span class="o">];</span>
+
+<span class="c1">// Train a DecisionTree model.</span>
+<span class="n">DecisionTreeClassifier</span> <span class="n">dt</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">DecisionTreeClassifier</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setLabelCol</span><span class="o">(</span><span class="s">&quot;indexedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setFeaturesCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">);</span>
+
+<span class="c1">// Convert indexed labels back to original labels.</span>
+<span class="n">IndexToString</span> <span class="n">labelConverter</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">IndexToString</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setInputCol</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setOutputCol</span><span class="o">(</span><span class="s">&quot;predictedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setLabels</span><span class="o">(</span><span class="n">labelIndexer</span><span class="o">.</span><span class="na">labels</span><span class="o">());</span>
+
+<span class="c1">// Chain indexers and tree in a Pipeline</span>
+<span class="n">Pipeline</span> <span class="n">pipeline</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">Pipeline</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setStages</span><span class="o">(</span><span class="k">new</span> <span class="n">PipelineStage</span><span class="o">[]{</span><span class="n">labelIndexer</span><span class="o">,</span> <span class="n">featureIndexer</span><span class="o">,</span> <span class="n">dt</span><span class="o">,</span> <span class="n">labelConverter</span><span class="o">});</span>
+
+<span class="c1">// Train model.  This also runs the indexers.</span>
+<span class="n">PipelineModel</span> <span class="n">model</span> <span class="o">=</span> <span class="n">pipeline</span><span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">trainingData</span><span class="o">);</span>
+
+<span class="c1">// Make predictions.</span>
+<span class="n">DataFrame</span> <span class="n">predictions</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="na">transform</span><span class="o">(</span><span class="n">testData</span><span class="o">);</span>
+
+<span class="c1">// Select example rows to display.</span>
+<span class="n">predictions</span><span class="o">.</span><span class="na">select</span><span class="o">(</span><span class="s">&quot;predictedLabel&quot;</span><span class="o">,</span> <span class="s">&quot;label&quot;</span><span class="o">,</span> <span class="s">&quot;features&quot;</span><span class="o">).</span><span class="na">show</span><span class="o">(</span><span class="mi">5</span><span class="o">);</span>
+
+<span class="c1">// Select (prediction, true label) and compute test error</span>
+<span class="n">MulticlassClassificationEvaluator</span> <span class="n">evaluator</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">MulticlassClassificationEvaluator</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setLabelCol</span><span class="o">(</span><span class="s">&quot;indexedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setPredictionCol</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setMetricName</span><span class="o">(</span><span class="s">&quot;precision&quot;</span><span class="o">);</span>
+<span class="kt">double</span> <span class="n">accuracy</span> <span class="o">=</span> <span class="n">evaluator</span><span class="o">.</span><span class="na">evaluate</span><span class="o">(</span><span class="n">predictions</span><span class="o">);</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;Test Error = &quot;</span> <span class="o">+</span> <span class="o">(</span><span class="mf">1.0</span> <span class="o">-</span> <span class="n">accuracy</span><span class="o">));</span>
+
+<span class="n">DecisionTreeClassificationModel</span> <span class="n">treeModel</span> <span class="o">=</span>
+  <span class="o">(</span><span class="n">DecisionTreeClassificationModel</span><span class="o">)</span> <span class="o">(</span><span class="n">model</span><span class="o">.</span><span class="na">stages</span><span class="o">()[</span><span class="mi">2</span><span class="o">]);</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;Learned classification tree model:\n&quot;</span> <span class="o">+</span> <span class="n">treeModel</span><span class="o">.</span><span class="na">toDebugString</span><span class="o">());</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaDecisionTreeClassificationExample.java" in the Spark repo.</small></div>
+
+  </div>
+
+<div data-lang="python">
+
+    <p>More details on parameters can be found in the <a href="api/python/pyspark.ml.html#pyspark.ml.classification.DecisionTreeClassifier">Python API documentation</a>.</p>
+
+    <div class="highlight"><pre><span class="kn">from</span> <span class="nn">pyspark</span> <span class="kn">import</span> <span class="n">SparkContext</span><span class="p">,</span> <span class="n">SQLContext</span>
+<span class="kn">from</span> <span class="nn">pyspark.ml</span> <span class="kn">import</span> <span class="n">Pipeline</span>
+<span class="kn">from</span> <span class="nn">pyspark.ml.classification</span> <span class="kn">import</span> <span class="n">DecisionTreeClassifier</span>
+<span class="kn">from</span> <span class="nn">pyspark.ml.feature</span> <span class="kn">import</span> <span class="n">StringIndexer</span><span class="p">,</span> <span class="n">VectorIndexer</span>
+<span class="kn">from</span> <span class="nn">pyspark.ml.evaluation</span> <span class="kn">import</span> <span class="n">MulticlassClassificationEvaluator</span>
+
+<span class="c"># Load the data stored in LIBSVM format as a DataFrame.</span>
+<span class="n">data</span> <span class="o">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="s">&quot;libsvm&quot;</span><span class="p">)</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="p">)</span>
+
+<span class="c"># Index labels, adding metadata to the label column.</span>
+<span class="c"># Fit on whole dataset to include all labels in index.</span>
+<span class="n">labelIndexer</span> <span class="o">=</span> <span class="n">StringIndexer</span><span class="p">(</span><span class="n">inputCol</span><span class="o">=</span><span class="s">&quot;label&quot;</span><span class="p">,</span> <span class="n">outputCol</span><span class="o">=</span><span class="s">&quot;indexedLabel&quot;</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
+<span class="c"># Automatically identify categorical features, and index them.</span>
+<span class="c"># We specify maxCategories so features with &gt; 4 distinct values are treated as continuous.</span>
+<span class="n">featureIndexer</span> <span class="o">=</span>\
+    <span class="n">VectorIndexer</span><span class="p">(</span><span class="n">inputCol</span><span class="o">=</span><span class="s">&quot;features&quot;</span><span class="p">,</span> <span class="n">outputCol</span><span class="o">=</span><span class="s">&quot;indexedFeatures&quot;</span><span class="p">,</span> <span class="n">maxCategories</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
+
+<span class="c"># Split the data into training and test sets (30% held out for testing)</span>
+<span class="p">(</span><span class="n">trainingData</span><span class="p">,</span> <span class="n">testData</span><span class="p">)</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">randomSplit</span><span class="p">([</span><span class="mf">0.7</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">])</span>
+
+<span class="c"># Train a DecisionTree model.</span>
+<span class="n">dt</span> <span class="o">=</span> <span class="n">DecisionTreeClassifier</span><span class="p">(</span><span class="n">labelCol</span><span class="o">=</span><span class="s">&quot;indexedLabel&quot;</span><span class="p">,</span> <span class="n">featuresCol</span><span class="o">=</span><span class="s">&quot;indexedFeatures&quot;</span><span class="p">)</span>
+
+<span class="c"># Chain indexers and tree in a Pipeline</span>
+<span class="n">pipeline</span> <span class="o">=</span> <span class="n">Pipeline</span><span class="p">(</span><span class="n">stages</span><span class="o">=</span><span class="p">[</span><span class="n">labelIndexer</span><span class="p">,</span> <span class="n">featureIndexer</span><span class="p">,</span> <span class="n">dt</span><span class="p">])</span>
+
+<span class="c"># Train model.  This also runs the indexers.</span>
+<span class="n">model</span> <span class="o">=</span> <span class="n">pipeline</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">trainingData</span><span class="p">)</span>
+
+<span class="c"># Make predictions.</span>
+<span class="n">predictions</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">testData</span><span class="p">)</span>
+
+<span class="c"># Select example rows to display.</span>
+<span class="n">predictions</span><span class="o">.</span><span class="n">select</span><span class="p">(</span><span class="s">&quot;prediction&quot;</span><span class="p">,</span> <span class="s">&quot;indexedLabel&quot;</span><span class="p">,</span> <span class="s">&quot;features&quot;</span><span class="p">)</span><span class="o">.</span><span class="n">show</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+
+<span class="c"># Select (prediction, true label) and compute test error</span>
+<span class="n">evaluator</span> <span class="o">=</span> <span class="n">MulticlassClassificationEvaluator</span><span class="p">(</span>
+    <span class="n">labelCol</span><span class="o">=</span><span class="s">&quot;indexedLabel&quot;</span><span class="p">,</span> <span class="n">predictionCol</span><span class="o">=</span><span class="s">&quot;prediction&quot;</span><span class="p">,</span> <span class="n">metricName</span><span class="o">=</span><span class="s">&quot;precision&quot;</span><span class="p">)</span>
+<span class="n">accuracy</span> <span class="o">=</span> <span class="n">evaluator</span><span class="o">.</span><span class="n">evaluate</span><span class="p">(</span><span class="n">predictions</span><span class="p">)</span>
+<span class="k">print</span><span class="p">(</span><span class="s">&quot;Test Error = </span><span class="si">%g</span><span class="s"> &quot;</span> <span class="o">%</span> <span class="p">(</span><span class="mf">1.0</span> <span class="o">-</span> <span class="n">accuracy</span><span class="p">))</span>
+
+<span class="n">treeModel</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">stages</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
+<span class="c"># summary only</span>
+<span class="k">print</span><span class="p">(</span><span class="n">treeModel</span><span class="p">)</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/python/ml/decision_tree_classification_example.py" in the Spark repo.</small></div>
+
+  </div>
+
+</div>
+
+<h2 id="random-forest-classifier">Random forest classifier</h2>
+
+<p>Random forests are a popular family of classification and regression methods.
+More information about the <code>spark.ml</code> implementation can be found further in the <a href="#random-forests">section on random forests</a>.</p>
+
+<p><strong>Example</strong></p>
+
+<p>The following examples load a dataset in LibSVM format, split it into training and test sets, train on the first dataset, and then evaluate on the held-out test set.
+We use two feature transformers to prepare the data; these help index categories for the label and categorical features, adding metadata to the <code>DataFrame</code> which the tree-based algorithms can recognize.</p>
+
+<div class="codetabs">
+<div data-lang="scala">
+
+    <p>Refer to the <a href="api/scala/index.html#org.apache.spark.ml.classification.RandomForestClassifier">Scala API docs</a> for more details.</p>
+
+    <div class="highlight"><pre><span class="k">import</span> <span class="nn">org.apache.spark.ml.Pipeline</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.ml.classification.</span><span class="o">{</span><span class="nc">RandomForestClassificationModel</span><span class="o">,</span> <span class="nc">RandomForestClassifier</span><span class="o">}</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.ml.feature.</span><span class="o">{</span><span class="nc">IndexToString</span><span class="o">,</span> <span class="nc">StringIndexer</span><span class="o">,</span> <span class="nc">VectorIndexer</span><span class="o">}</span>
+
+<span class="c1">// Load and parse the data file, converting it to a DataFrame.</span>
+<span class="k">val</span> <span class="n">data</span> <span class="k">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">).</span><span class="n">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="o">)</span>
+
+<span class="c1">// Index labels, adding metadata to the label column.</span>
+<span class="c1">// Fit on whole dataset to include all labels in index.</span>
+<span class="k">val</span> <span class="n">labelIndexer</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">StringIndexer</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setInputCol</span><span class="o">(</span><span class="s">&quot;label&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setOutputCol</span><span class="o">(</span><span class="s">&quot;indexedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">data</span><span class="o">)</span>
+<span class="c1">// Automatically identify categorical features, and index them.</span>
+<span class="c1">// Set maxCategories so features with &gt; 4 distinct values are treated as continuous.</span>
+<span class="k">val</span> <span class="n">featureIndexer</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">VectorIndexer</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setInputCol</span><span class="o">(</span><span class="s">&quot;features&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setOutputCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setMaxCategories</span><span class="o">(</span><span class="mi">4</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">data</span><span class="o">)</span>
+
+<span class="c1">// Split the data into training and test sets (30% held out for testing)</span>
+<span class="k">val</span> <span class="nc">Array</span><span class="o">(</span><span class="n">trainingData</span><span class="o">,</span> <span class="n">testData</span><span class="o">)</span> <span class="k">=</span> <span class="n">data</span><span class="o">.</span><span class="n">randomSplit</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="mf">0.7</span><span class="o">,</span> <span class="mf">0.3</span><span class="o">))</span>
+
+<span class="c1">// Train a RandomForest model.</span>
+<span class="k">val</span> <span class="n">rf</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">RandomForestClassifier</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setLabelCol</span><span class="o">(</span><span class="s">&quot;indexedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setFeaturesCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setNumTrees</span><span class="o">(</span><span class="mi">10</span><span class="o">)</span>
+
+<span class="c1">// Convert indexed labels back to original labels.</span>
+<span class="k">val</span> <span class="n">labelConverter</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">IndexToString</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setInputCol</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setOutputCol</span><span class="o">(</span><span class="s">&quot;predictedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setLabels</span><span class="o">(</span><span class="n">labelIndexer</span><span class="o">.</span><span class="n">labels</span><span class="o">)</span>
+
+<span class="c1">// Chain indexers and forest in a Pipeline</span>
+<span class="k">val</span> <span class="n">pipeline</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">Pipeline</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setStages</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="n">labelIndexer</span><span class="o">,</span> <span class="n">featureIndexer</span><span class="o">,</span> <span class="n">rf</span><span class="o">,</span> <span class="n">labelConverter</span><span class="o">))</span>
+
+<span class="c1">// Train model.  This also runs the indexers.</span>
+<span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="n">pipeline</span><span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">trainingData</span><span class="o">)</span>
+
+<span class="c1">// Make predictions.</span>
+<span class="k">val</span> <span class="n">predictions</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">transform</span><span class="o">(</span><span class="n">testData</span><span class="o">)</span>
+
+<span class="c1">// Select example rows to display.</span>
+<span class="n">predictions</span><span class="o">.</span><span class="n">select</span><span class="o">(</span><span class="s">&quot;predictedLabel&quot;</span><span class="o">,</span> <span class="s">&quot;label&quot;</span><span class="o">,</span> <span class="s">&quot;features&quot;</span><span class="o">).</span><span class="n">show</span><span class="o">(</span><span class="mi">5</span><span class="o">)</span>
+
+<span class="c1">// Select (prediction, true label) and compute test error</span>
+<span class="k">val</span> <span class="n">evaluator</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">MulticlassClassificationEvaluator</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setLabelCol</span><span class="o">(</span><span class="s">&quot;indexedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setPredictionCol</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setMetricName</span><span class="o">(</span><span class="s">&quot;precision&quot;</span><span class="o">)</span>
+<span class="k">val</span> <span class="n">accuracy</span> <span class="k">=</span> <span class="n">evaluator</span><span class="o">.</span><span class="n">evaluate</span><span class="o">(</span><span class="n">predictions</span><span class="o">)</span>
+<span class="n">println</span><span class="o">(</span><span class="s">&quot;Test Error = &quot;</span> <span class="o">+</span> <span class="o">(</span><span class="mf">1.0</span> <span class="o">-</span> <span class="n">accuracy</span><span class="o">))</span>
+
+<span class="k">val</span> <span class="n">rfModel</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">stages</span><span class="o">(</span><span class="mi">2</span><span class="o">).</span><span class="n">asInstanceOf</span><span class="o">[</span><span class="kt">RandomForestClassificationModel</span><span class="o">]</span>
+<span class="n">println</span><span class="o">(</span><span class="s">&quot;Learned classification forest model:\n&quot;</span> <span class="o">+</span> <span class="n">rfModel</span><span class="o">.</span><span class="n">toDebugString</span><span class="o">)</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/RandomForestClassifierExample.scala" in the Spark repo.</small></div>
+  </div>
+
+<div data-lang="java">
+
+    <p>Refer to the <a href="api/java/org/apache/spark/ml/classification/RandomForestClassifier.html">Java API docs</a> for more details.</p>
+
+    <div class="highlight"><pre><span class="kn">import</span> <span class="nn">org.apache.spark.ml.Pipeline</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.PipelineModel</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.PipelineStage</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.classification.RandomForestClassificationModel</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.classification.RandomForestClassifier</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.feature.*</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.DataFrame</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.SQLContext</span><span class="o">;</span>
+
+<span class="c1">// Load and parse the data file, converting it to a DataFrame.</span>
+<span class="n">DataFrame</span> <span class="n">data</span> <span class="o">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="na">read</span><span class="o">().</span><span class="na">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">).</span><span class="na">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="o">);</span>
+
+<span class="c1">// Index labels, adding metadata to the label column.</span>
+<span class="c1">// Fit on whole dataset to include all labels in index.</span>
+<span class="n">StringIndexerModel</span> <span class="n">labelIndexer</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">StringIndexer</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setInputCol</span><span class="o">(</span><span class="s">&quot;label&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setOutputCol</span><span class="o">(</span><span class="s">&quot;indexedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">data</span><span class="o">);</span>
+<span class="c1">// Automatically identify categorical features, and index them.</span>
+<span class="c1">// Set maxCategories so features with &gt; 4 distinct values are treated as continuous.</span>
+<span class="n">VectorIndexerModel</span> <span class="n">featureIndexer</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">VectorIndexer</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setInputCol</span><span class="o">(</span><span class="s">&quot;features&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setOutputCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setMaxCategories</span><span class="o">(</span><span class="mi">4</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">data</span><span class="o">);</span>
+
+<span class="c1">// Split the data into training and test sets (30% held out for testing)</span>
+<span class="n">DataFrame</span><span class="o">[]</span> <span class="n">splits</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="na">randomSplit</span><span class="o">(</span><span class="k">new</span> <span class="kt">double</span><span class="o">[]</span> <span class="o">{</span><span class="mf">0.7</span><span class="o">,</span> <span class="mf">0.3</span><span class="o">});</span>
+<span class="n">DataFrame</span> <span class="n">trainingData</span> <span class="o">=</span> <span class="n">splits</span><span class="o">[</span><span class="mi">0</span><span class="o">];</span>
+<span class="n">DataFrame</span> <span class="n">testData</span> <span class="o">=</span> <span class="n">splits</span><span class="o">[</span><span class="mi">1</span><span class="o">];</span>
+
+<span class="c1">// Train a RandomForest model.</span>
+<span class="n">RandomForestClassifier</span> <span class="n">rf</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">RandomForestClassifier</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setLabelCol</span><span class="o">(</span><span class="s">&quot;indexedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setFeaturesCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">);</span>
+
+<span class="c1">// Convert indexed labels back to original labels.</span>
+<span class="n">IndexToString</span> <span class="n">labelConverter</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">IndexToString</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setInputCol</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setOutputCol</span><span class="o">(</span><span class="s">&quot;predictedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setLabels</span><span class="o">(</span><span class="n">labelIndexer</span><span class="o">.</span><span class="na">labels</span><span class="o">());</span>
+
+<span class="c1">// Chain indexers and forest in a Pipeline</span>
+<span class="n">Pipeline</span> <span class="n">pipeline</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">Pipeline</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setStages</span><span class="o">(</span><span class="k">new</span> <span class="n">PipelineStage</span><span class="o">[]</span> <span class="o">{</span><span class="n">labelIndexer</span><span class="o">,</span> <span class="n">featureIndexer</span><span class="o">,</span> <span class="n">rf</span><span class="o">,</span> <span class="n">labelConverter</span><span class="o">});</span>
+
+<span class="c1">// Train model. This also runs the indexers.</span>
+<span class="n">PipelineModel</span> <span class="n">model</span> <span class="o">=</span> <span class="n">pipeline</span><span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">trainingData</span><span class="o">);</span>
+
+<span class="c1">// Make predictions.</span>
+<span class="n">DataFrame</span> <span class="n">predictions</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="na">transform</span><span class="o">(</span><span class="n">testData</span><span class="o">);</span>
+
+<span class="c1">// Select example rows to display.</span>
+<span class="n">predictions</span><span class="o">.</span><span class="na">select</span><span class="o">(</span><span class="s">&quot;predictedLabel&quot;</span><span class="o">,</span> <span class="s">&quot;label&quot;</span><span class="o">,</span> <span class="s">&quot;features&quot;</span><span class="o">).</span><span class="na">show</span><span class="o">(</span><span class="mi">5</span><span class="o">);</span>
+
+<span class="c1">// Select (prediction, true label) and compute test error</span>
+<span class="n">MulticlassClassificationEvaluator</span> <span class="n">evaluator</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">MulticlassClassificationEvaluator</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setLabelCol</span><span class="o">(</span><span class="s">&quot;indexedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setPredictionCol</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setMetricName</span><span class="o">(</span><span class="s">&quot;precision&quot;</span><span class="o">);</span>
+<span class="kt">double</span> <span class="n">accuracy</span> <span class="o">=</span> <span class="n">evaluator</span><span class="o">.</span><span class="na">evaluate</span><span class="o">(</span><span class="n">predictions</span><span class="o">);</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;Test Error = &quot;</span> <span class="o">+</span> <span class="o">(</span><span class="mf">1.0</span> <span class="o">-</span> <span class="n">accuracy</span><span class="o">));</span>
+
+<span class="n">RandomForestClassificationModel</span> <span class="n">rfModel</span> <span class="o">=</span> <span class="o">(</span><span class="n">RandomForestClassificationModel</span><span class="o">)(</span><span class="n">model</span><span class="o">.</span><span class="na">stages</span><span class="o">()[</span><span class="mi">2</span><span class="o">]);</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;Learned classification forest model:\n&quot;</span> <span class="o">+</span> <span class="n">rfModel</span><span class="o">.</span><span class="na">toDebugString</span><span class="o">());</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaRandomForestClassifierExample.java" in the Spark repo.</small></div>
+  </div>
+
+<div data-lang="python">
+
+    <p>Refer to the <a href="api/python/pyspark.ml.html#pyspark.ml.classification.RandomForestClassifier">Python API docs</a> for more details.</p>
+
+    <div class="highlight"><pre><span class="kn">from</span> <span class="nn">pyspark.ml</span> <span class="kn">import</span> <span class="n">Pipeline</span>
+<span class="kn">from</span> <span class="nn">pyspark.ml.classification</span> <span class="kn">import</span> <span class="n">RandomForestClassifier</span>
+<span class="kn">from</span> <span class="nn">pyspark.ml.feature</span> <span class="kn">import</span> <span class="n">StringIndexer</span><span class="p">,</span> <span class="n">VectorIndexer</span>
+<span class="kn">from</span> <span class="nn">pyspark.ml.evaluation</span> <span class="kn">import</span> <span class="n">MulticlassClassificationEvaluator</span>
+
+<span class="c"># Load and parse the data file, converting it to a DataFrame.</span>
+<span class="n">data</span> <span class="o">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="s">&quot;libsvm&quot;</span><span class="p">)</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="p">)</span>
+
+<span class="c"># Index labels, adding metadata to the label column.</span>
+<span class="c"># Fit on whole dataset to include all labels in index.</span>
+<span class="n">labelIndexer</span> <span class="o">=</span> <span class="n">StringIndexer</span><span class="p">(</span><span class="n">inputCol</span><span class="o">=</span><span class="s">&quot;label&quot;</span><span class="p">,</span> <span class="n">outputCol</span><span class="o">=</span><span class="s">&quot;indexedLabel&quot;</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
+<span class="c"># Automatically identify categorical features, and index them.</span>
+<span class="c"># Set maxCategories so features with &gt; 4 distinct values are treated as continuous.</span>
+<span class="n">featureIndexer</span> <span class="o">=</span>\
+    <span class="n">VectorIndexer</span><span class="p">(</span><span class="n">inputCol</span><span class="o">=</span><span class="s">&quot;features&quot;</span><span class="p">,</span> <span class="n">outputCol</span><span class="o">=</span><span class="s">&quot;indexedFeatures&quot;</span><span class="p">,</span> <span class="n">maxCategories</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
+
+<span class="c"># Split the data into training and test sets (30% held out for testing)</span>
+<span class="p">(</span><span class="n">trainingData</span><span class="p">,</span> <span class="n">testData</span><span class="p">)</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">randomSplit</span><span class="p">([</span><span class="mf">0.7</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">])</span>
+
+<span class="c"># Train a RandomForest model.</span>
+<span class="n">rf</span> <span class="o">=</span> <span class="n">RandomForestClassifier</span><span class="p">(</span><span class="n">labelCol</span><span class="o">=</span><span class="s">&quot;indexedLabel&quot;</span><span class="p">,</span> <span class="n">featuresCol</span><span class="o">=</span><span class="s">&quot;indexedFeatures&quot;</span><span class="p">)</span>
+
+<span class="c"># Chain indexers and forest in a Pipeline</span>
+<span class="n">pipeline</span> <span class="o">=</span> <span class="n">Pipeline</span><span class="p">(</span><span class="n">stages</span><span class="o">=</span><span class="p">[</span><span class="n">labelIndexer</span><span class="p">,</span> <span class="n">featureIndexer</span><span class="p">,</span> <span class="n">rf</span><span class="p">])</span>
+
+<span class="c"># Train model.  This also runs the indexers.</span>
+<span class="n">model</span> <span class="o">=</span> <span class="n">pipeline</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">trainingData</span><span class="p">)</span>
+
+<span class="c"># Make predictions.</span>
+<span class="n">predictions</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">testData</span><span class="p">)</span>
+
+<span class="c"># Select example rows to display.</span>
+<span class="n">predictions</span><span class="o">.</span><span class="n">select</span><span class="p">(</span><span class="s">&quot;prediction&quot;</span><span class="p">,</span> <span class="s">&quot;indexedLabel&quot;</span><span class="p">,</span> <span class="s">&quot;features&quot;</span><span class="p">)</span><span class="o">.</span><span class="n">show</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+
+<span class="c"># Select (prediction, true label) and compute test error</span>
+<span class="n">evaluator</span> <span class="o">=</span> <span class="n">MulticlassClassificationEvaluator</span><span class="p">(</span>
+    <span class="n">labelCol</span><span class="o">=</span><span class="s">&quot;indexedLabel&quot;</span><span class="p">,</span> <span class="n">predictionCol</span><span class="o">=</span><span class="s">&quot;prediction&quot;</span><span class="p">,</span> <span class="n">metricName</span><span class="o">=</span><span class="s">&quot;precision&quot;</span><span class="p">)</span>
+<span class="n">accuracy</span> <span class="o">=</span> <span class="n">evaluator</span><span class="o">.</span><span class="n">evaluate</span><span class="p">(</span><span class="n">predictions</span><span class="p">)</span>
+<span class="k">print</span><span class="p">(</span><span class="s">&quot;Test Error = </span><span class="si">%g</span><span class="s">&quot;</span> <span class="o">%</span> <span class="p">(</span><span class="mf">1.0</span> <span class="o">-</span> <span class="n">accuracy</span><span class="p">))</span>
+
+<span class="n">rfModel</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">stages</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
+<span class="k">print</span><span class="p">(</span><span class="n">rfModel</span><span class="p">)</span>  <span class="c"># summary only</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/python/ml/random_forest_classifier_example.py" in the Spark repo.</small></div>
+  </div>
+</div>
+
+<h2 id="gradient-boosted-tree-classifier">Gradient-boosted tree classifier</h2>
+
+<p>Gradient-boosted trees (GBTs) are a popular classification and regression method using ensembles of decision trees. 
+More information about the <code>spark.ml</code> implementation can be found further in the <a href="#gradient-boosted-trees-gbts">section on GBTs</a>.</p>
+
+<p><strong>Example</strong></p>
+
+<p>The following examples load a dataset in LibSVM format, split it into training and test sets, train on the first dataset, and then evaluate on the held-out test set.
+We use two feature transformers to prepare the data; these help index categories for the label and categorical features, adding metadata to the <code>DataFrame</code> which the tree-based algorithms can recognize.</p>
+
+<div class="codetabs">
+<div data-lang="scala">
+
+    <p>Refer to the <a href="api/scala/index.html#org.apache.spark.ml.classification.GBTClassifier">Scala API docs</a> for more details.</p>
+
+    <div class="highlight"><pre><span class="k">import</span> <span class="nn">org.apache.spark.ml.Pipeline</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.ml.classification.</span><span class="o">{</span><span class="nc">GBTClassificationModel</span><span class="o">,</span> <span class="nc">GBTClassifier</span><span class="o">}</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.ml.feature.</span><span class="o">{</span><span class="nc">IndexToString</span><span class="o">,</span> <span class="nc">StringIndexer</span><span class="o">,</span> <span class="nc">VectorIndexer</span><span class="o">}</span>
+
+<span class="c1">// Load and parse the data file, converting it to a DataFrame.</span>
+<span class="k">val</span> <span class="n">data</span> <span class="k">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">).</span><span class="n">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="o">)</span>
+
+<span class="c1">// Index labels, adding metadata to the label column.</span>
+<span class="c1">// Fit on whole dataset to include all labels in index.</span>
+<span class="k">val</span> <span class="n">labelIndexer</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">StringIndexer</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setInputCol</span><span class="o">(</span><span class="s">&quot;label&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setOutputCol</span><span class="o">(</span><span class="s">&quot;indexedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">data</span><span class="o">)</span>
+<span class="c1">// Automatically identify categorical features, and index them.</span>
+<span class="c1">// Set maxCategories so features with &gt; 4 distinct values are treated as continuous.</span>
+<span class="k">val</span> <span class="n">featureIndexer</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">VectorIndexer</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setInputCol</span><span class="o">(</span><span class="s">&quot;features&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setOutputCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setMaxCategories</span><span class="o">(</span><span class="mi">4</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">data</span><span class="o">)</span>
+
+<span class="c1">// Split the data into training and test sets (30% held out for testing)</span>
+<span class="k">val</span> <span class="nc">Array</span><span class="o">(</span><span class="n">trainingData</span><span class="o">,</span> <span class="n">testData</span><span class="o">)</span> <span class="k">=</span> <span class="n">data</span><span class="o">.</span><span class="n">randomSplit</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="mf">0.7</span><span class="o">,</span> <span class="mf">0.3</span><span class="o">))</span>
+
+<span class="c1">// Train a GBT model.</span>
+<span class="k">val</span> <span class="n">gbt</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">GBTClassifier</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setLabelCol</span><span class="o">(</span><span class="s">&quot;indexedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setFeaturesCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setMaxIter</span><span class="o">(</span><span class="mi">10</span><span class="o">)</span>
+
+<span class="c1">// Convert indexed labels back to original labels.</span>
+<span class="k">val</span> <span class="n">labelConverter</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">IndexToString</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setInputCol</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setOutputCol</span><span class="o">(</span><span class="s">&quot;predictedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setLabels</span><span class="o">(</span><span class="n">labelIndexer</span><span class="o">.</span><span class="n">labels</span><span class="o">)</span>
+
+<span class="c1">// Chain indexers and GBT in a Pipeline</span>
+<span class="k">val</span> <span class="n">pipeline</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">Pipeline</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setStages</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="n">labelIndexer</span><span class="o">,</span> <span class="n">featureIndexer</span><span class="o">,</span> <span class="n">gbt</span><span class="o">,</span> <span class="n">labelConverter</span><span class="o">))</span>
+
+<span class="c1">// Train model.  This also runs the indexers.</span>
+<span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="n">pipeline</span><span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">trainingData</span><span class="o">)</span>
+
+<span class="c1">// Make predictions.</span>
+<span class="k">val</span> <span class="n">predictions</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">transform</span><span class="o">(</span><span class="n">testData</span><span class="o">)</span>
+
+<span class="c1">// Select example rows to display.</span>
+<span class="n">predictions</span><span class="o">.</span><span class="n">select</span><span class="o">(</span><span class="s">&quot;predictedLabel&quot;</span><span class="o">,</span> <span class="s">&quot;label&quot;</span><span class="o">,</span> <span class="s">&quot;features&quot;</span><span class="o">).</span><span class="n">show</span><span class="o">(</span><span class="mi">5</span><span class="o">)</span>
+
+<span class="c1">// Select (prediction, true label) and compute test error</span>
+<span class="k">val</span> <span class="n">evaluator</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">MulticlassClassificationEvaluator</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setLabelCol</span><span class="o">(</span><span class="s">&quot;indexedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setPredictionCol</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setMetricName</span><span class="o">(</span><span class="s">&quot;precision&quot;</span><span class="o">)</span>
+<span class="k">val</span> <span class="n">accuracy</span> <span class="k">=</span> <span class="n">evaluator</span><span class="o">.</span><span class="n">evaluate</span><span class="o">(</span><span class="n">predictions</span><span class="o">)</span>
+<span class="n">println</span><span class="o">(</span><span class="s">&quot;Test Error = &quot;</span> <span class="o">+</span> <span class="o">(</span><span class="mf">1.0</span> <span class="o">-</span> <span class="n">accuracy</span><span class="o">))</span>
+
+<span class="k">val</span> <span class="n">gbtModel</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">stages</span><span class="o">(</span><span class="mi">2</span><span class="o">).</span><span class="n">asInstanceOf</span><span class="o">[</span><span class="kt">GBTClassificationModel</span><span class="o">]</span>
+<span class="n">println</span><span class="o">(</span><span class="s">&quot;Learned classification GBT model:\n&quot;</span> <span class="o">+</span> <span class="n">gbtModel</span><span class="o">.</span><span class="n">toDebugString</span><span class="o">)</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/GradientBoostedTreeClassifierExample.scala" in the Spark repo.</small></div>
+  </div>
+
+<div data-lang="java">
+
+    <p>Refer to the <a href="api/java/org/apache/spark/ml/classification/GBTClassifier.html">Java API docs</a> for more details.</p>
+
+    <div class="highlight"><pre><span class="kn">import</span> <span class="nn">org.apache.spark.ml.Pipeline</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.PipelineModel</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.PipelineStage</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.classification.GBTClassificationModel</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.classification.GBTClassifier</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.feature.*</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.DataFrame</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.SQLContext</span><span class="o">;</span>
+
+<span class="c1">// Load and parse the data file, converting it to a DataFrame.</span>
+<span class="n">DataFrame</span> <span class="n">data</span> <span class="o">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="na">read</span><span class="o">().</span><span class="na">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">).</span><span class="na">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="o">);</span>
+
+<span class="c1">// Index labels, adding metadata to the label column.</span>
+<span class="c1">// Fit on whole dataset to include all labels in index.</span>
+<span class="n">StringIndexerModel</span> <span class="n">labelIndexer</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">StringIndexer</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setInputCol</span><span class="o">(</span><span class="s">&quot;label&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setOutputCol</span><span class="o">(</span><span class="s">&quot;indexedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">data</span><span class="o">);</span>
+<span class="c1">// Automatically identify categorical features, and index them.</span>
+<span class="c1">// Set maxCategories so features with &gt; 4 distinct values are treated as continuous.</span>
+<span class="n">VectorIndexerModel</span> <span class="n">featureIndexer</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">VectorIndexer</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setInputCol</span><span class="o">(</span><span class="s">&quot;features&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setOutputCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setMaxCategories</span><span class="o">(</span><span class="mi">4</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">data</span><span class="o">);</span>
+
+<span class="c1">// Split the data into training and test sets (30% held out for testing)</span>
+<span class="n">DataFrame</span><span class="o">[]</span> <span class="n">splits</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="na">randomSplit</span><span class="o">(</span><span class="k">new</span> <span class="kt">double</span><span class="o">[]</span> <span class="o">{</span><span class="mf">0.7</span><span class="o">,</span> <span class="mf">0.3</span><span class="o">});</span>
+<span class="n">DataFrame</span> <span class="n">trainingData</span> <span class="o">=</span> <span class="n">splits</span><span class="o">[</span><span class="mi">0</span><span class="o">];</span>
+<span class="n">DataFrame</span> <span class="n">testData</span> <span class="o">=</span> <span class="n">splits</span><span class="o">[</span><span class="mi">1</span><span class="o">];</span>
+
+<span class="c1">// Train a GBT model.</span>
+<span class="n">GBTClassifier</span> <span class="n">gbt</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">GBTClassifier</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setLabelCol</span><span class="o">(</span><span class="s">&quot;indexedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setFeaturesCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setMaxIter</span><span class="o">(</span><span class="mi">10</span><span class="o">);</span>
+
+<span class="c1">// Convert indexed labels back to original labels.</span>
+<span class="n">IndexToString</span> <span class="n">labelConverter</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">IndexToString</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setInputCol</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setOutputCol</span><span class="o">(</span><span class="s">&quot;predictedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setLabels</span><span class="o">(</span><span class="n">labelIndexer</span><span class="o">.</span><span class="na">labels</span><span class="o">());</span>
+
+<span class="c1">// Chain indexers and GBT in a Pipeline</span>
+<span class="n">Pipeline</span> <span class="n">pipeline</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">Pipeline</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setStages</span><span class="o">(</span><span class="k">new</span> <span class="n">PipelineStage</span><span class="o">[]</span> <span class="o">{</span><span class="n">labelIndexer</span><span class="o">,</span> <span class="n">featureIndexer</span><span class="o">,</span> <span class="n">gbt</span><span class="o">,</span> <span class="n">labelConverter</span><span class="o">});</span>
+
+<span class="c1">// Train model.  This also runs the indexers.</span>
+<span class="n">PipelineModel</span> <span class="n">model</span> <span class="o">=</span> <span class="n">pipeline</span><span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">trainingData</span><span class="o">);</span>
+
+<span class="c1">// Make predictions.</span>
+<span class="n">DataFrame</span> <span class="n">predictions</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="na">transform</span><span class="o">(</span><span class="n">testData</span><span class="o">);</span>
+
+<span class="c1">// Select example rows to display.</span>
+<span class="n">predictions</span><span class="o">.</span><span class="na">select</span><span class="o">(</span><span class="s">&quot;predictedLabel&quot;</span><span class="o">,</span> <span class="s">&quot;label&quot;</span><span class="o">,</span> <span class="s">&quot;features&quot;</span><span class="o">).</span><span class="na">show</span><span class="o">(</span><span class="mi">5</span><span class="o">);</span>
+
+<span class="c1">// Select (prediction, true label) and compute test error</span>
+<span class="n">MulticlassClassificationEvaluator</span> <span class="n">evaluator</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">MulticlassClassificationEvaluator</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setLabelCol</span><span class="o">(</span><span class="s">&quot;indexedLabel&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setPredictionCol</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setMetricName</span><span class="o">(</span><span class="s">&quot;precision&quot;</span><span class="o">);</span>
+<span class="kt">double</span> <span class="n">accuracy</span> <span class="o">=</span> <span class="n">evaluator</span><span class="o">.</span><span class="na">evaluate</span><span class="o">(</span><span class="n">predictions</span><span class="o">);</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;Test Error = &quot;</span> <span class="o">+</span> <span class="o">(</span><span class="mf">1.0</span> <span class="o">-</span> <span class="n">accuracy</span><span class="o">));</span>
+
+<span class="n">GBTClassificationModel</span> <span class="n">gbtModel</span> <span class="o">=</span> <span class="o">(</span><span class="n">GBTClassificationModel</span><span class="o">)(</span><span class="n">model</span><span class="o">.</span><span class="na">stages</span><span class="o">()[</span><span class="mi">2</span><span class="o">]);</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;Learned classification GBT model:\n&quot;</span> <span class="o">+</span> <span class="n">gbtModel</span><span class="o">.</span><span class="na">toDebugString</span><span class="o">());</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaGradientBoostedTreeClassifierExample.java" in the Spark repo.</small></div>
+  </div>
+
+<div data-lang="python">
+
+    <p>Refer to the <a href="api/python/pyspark.ml.html#pyspark.ml.classification.GBTClassifier">Python API docs</a> for more details.</p>
+
+    <div class="highlight"><pre><span class="kn">from</span> <span class="nn">pyspark.ml</span> <span class="kn">import</span> <span class="n">Pipeline</span>
+<span class="kn">from</span> <span class="nn">pyspark.ml.classification</span> <span class="kn">import</span> <span class="n">GBTClassifier</span>
+<span class="kn">from</span> <span class="nn">pyspark.ml.feature</span> <span class="kn">import</span> <span class="n">StringIndexer</span><span class="p">,</span> <span class="n">VectorIndexer</span>
+<span class="kn">from</span> <span class="nn">pyspark.ml.evaluation</span> <span class="kn">import</span> <span class="n">MulticlassClassificationEvaluator</span>
+
+<span class="c"># Load and parse the data file, converting it to a DataFrame.</span>
+<span class="n">data</span> <span class="o">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="s">&quot;libsvm&quot;</span><span class="p">)</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="p">)</span>
+
+<span class="c"># Index labels, adding metadata to the label column.</span>
+<span class="c"># Fit on whole dataset to include all labels in index.</span>
+<span class="n">labelIndexer</span> <span class="o">=</span> <span class="n">StringIndexer</span><span class="p">(</span><span class="n">inputCol</span><span class="o">=</span><span class="s">&quot;label&quot;</span><span class="p">,</span> <span class="n">outputCol</span><span class="o">=</span><span class="s">&quot;indexedLabel&quot;</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
+<span class="c"># Automatically identify categorical features, and index them.</span>
+<span class="c"># Set maxCategories so features with &gt; 4 distinct values are treated as continuous.</span>
+<span class="n">featureIndexer</span> <span class="o">=</span>\
+    <span class="n">VectorIndexer</span><span class="p">(</span><span class="n">inputCol</span><span class="o">=</span><span class="s">&quot;features&quot;</span><span class="p">,</span> <span class="n">outputCol</span><span class="o">=</span><span class="s">&quot;indexedFeatures&quot;</span><span class="p">,</span> <span class="n">maxCategories</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
+
+<span class="c"># Split the data into training and test sets (30% held out for testing)</span>
+<span class="p">(</span><span class="n">trainingData</span><span class="p">,</span> <span class="n">testData</span><span class="p">)</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">randomSplit</span><span class="p">([</span><span class="mf">0.7</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">])</span>
+
+<span class="c"># Train a GBT model.</span>
+<span class="n">gbt</span> <span class="o">=</span> <span class="n">GBTClassifier</span><span class="p">(</span><span class="n">labelCol</span><span class="o">=</span><span class="s">&quot;indexedLabel&quot;</span><span class="p">,</span> <span class="n">featuresCol</span><span class="o">=</span><span class="s">&quot;indexedFeatures&quot;</span><span class="p">,</span> <span class="n">maxIter</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
+
+<span class="c"># Chain indexers and GBT in a Pipeline</span>
+<span class="n">pipeline</span> <span class="o">=</span> <span class="n">Pipeline</span><span class="p">(</span><span class="n">stages</span><span class="o">=</span><span class="p">[</span><span class="n">labelIndexer</span><span class="p">,</span> <span class="n">featureIndexer</span><span class="p">,</span> <span class="n">gbt</span><span class="p">])</span>
+
+<span class="c"># Train model.  This also runs the indexers.</span>
+<span class="n">model</span> <span class="o">=</span> <span class="n">pipeline</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">trainingData</span><span class="p">)</span>
+
+<span class="c"># Make predictions.</span>
+<span class="n">predictions</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">testData</span><span class="p">)</span>
+
+<span class="c"># Select example rows to display.</span>
+<span class="n">predictions</span><span class="o">.</span><span class="n">select</span><span class="p">(</span><span class="s">&quot;prediction&quot;</span><span class="p">,</span> <span class="s">&quot;indexedLabel&quot;</span><span class="p">,</span> <span class="s">&quot;features&quot;</span><span class="p">)</span><span class="o">.</span><span class="n">show</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+
+<span class="c"># Select (prediction, true label) and compute test error</span>
+<span class="n">evaluator</span> <span class="o">=</span> <span class="n">MulticlassClassificationEvaluator</span><span class="p">(</span>
+    <span class="n">labelCol</span><span class="o">=</span><span class="s">&quot;indexedLabel&quot;</span><span class="p">,</span> <span class="n">predictionCol</span><span class="o">=</span><span class="s">&quot;prediction&quot;</span><span class="p">,</span> <span class="n">metricName</span><span class="o">=</span><span class="s">&quot;precision&quot;</span><span class="p">)</span>
+<span class="n">accuracy</span> <span class="o">=</span> <span class="n">evaluator</span><span class="o">.</span><span class="n">evaluate</span><span class="p">(</span><span class="n">predictions</span><span class="p">)</span>
+<span class="k">print</span><span class="p">(</span><span class="s">&quot;Test Error = </span><span class="si">%g</span><span class="s">&quot;</span> <span class="o">%</span> <span class="p">(</span><span class="mf">1.0</span> <span class="o">-</span> <span class="n">accuracy</span><span class="p">))</span>
+
+<span class="n">gbtModel</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">stages</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
+<span class="k">print</span><span class="p">(</span><span class="n">gbtModel</span><span class="p">)</span>  <span class="c"># summary only</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/python/ml/gradient_boosted_tree_classifier_example.py" in the Spark repo.</small></div>
+  </div>
+</div>
+
+<h2 id="multilayer-perceptron-classifier">Multilayer perceptron classifier</h2>
+
+<p>Multilayer perceptron classifier (MLPC) is a classifier based on the <a href="https://en.wikipedia.org/wiki/Feedforward_neural_network">feedforward artificial neural network</a>. 
+MLPC consists of multiple layers of nodes. 
+Each layer is fully connected to the next layer in the network. Nodes in the input layer represent the input data. All other nodes maps inputs to the outputs 
+by performing linear combination of the inputs with the node&#8217;s weights <code>$\wv$</code> and bias <code>$\bv$</code> and applying an activation function. 
+It can be written in matrix form for MLPC with <code>$K+1$</code> layers as follows:
+<code>\[
+\mathrm{y}(\x) = \mathrm{f_K}(...\mathrm{f_2}(\wv_2^T\mathrm{f_1}(\wv_1^T \x+b_1)+b_2)...+b_K)
+\]</code>
+Nodes in intermediate layers use sigmoid (logistic) function:
+<code>\[
+\mathrm{f}(z_i) = \frac{1}{1 + e^{-z_i}}
+\]</code>
+Nodes in the output layer use softmax function:
+<code>\[
+\mathrm{f}(z_i) = \frac{e^{z_i}}{\sum_{k=1}^N e^{z_k}}
+\]</code>
+The number of nodes <code>$N$</code> in the output layer corresponds to the number of classes.</p>
+
+<p>MLPC employes backpropagation for learning the model. We use logistic loss function for optimization and L-BFGS as optimization routine.</p>
+
+<p><strong>Example</strong></p>
+
+<div class="codetabs">
+
+<div data-lang="scala">
+    <div class="highlight"><pre><span class="k">import</span> <span class="nn">org.apache.spark.ml.classification.MultilayerPerceptronClassifier</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator</span>
+
+<span class="c1">// Load the data stored in LIBSVM format as a DataFrame.</span>
+<span class="k">val</span> <span class="n">data</span> <span class="k">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_multiclass_classification_data.txt&quot;</span><span class="o">)</span>
+<span class="c1">// Split the data into train and test</span>
+<span class="k">val</span> <span class="n">splits</span> <span class="k">=</span> <span class="n">data</span><span class="o">.</span><span class="n">randomSplit</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="mf">0.6</span><span class="o">,</span> <span class="mf">0.4</span><span class="o">),</span> <span class="n">seed</span> <span class="k">=</span> <span class="mi">1234L</span><span class="o">)</span>
+<span class="k">val</span> <span class="n">train</span> <span class="k">=</span> <span class="n">splits</span><span class="o">(</span><span class="mi">0</span><span class="o">)</span>
+<span class="k">val</span> <span class="n">test</span> <span class="k">=</span> <span class="n">splits</span><span class="o">(</span><span class="mi">1</span><span class="o">)</span>
+<span class="c1">// specify layers for the neural network:</span>
+<span class="c1">// input layer of size 4 (features), two intermediate of size 5 and 4</span>
+<span class="c1">// and output of size 3 (classes)</span>
+<span class="k">val</span> <span class="n">layers</span> <span class="k">=</span> <span class="nc">Array</span><span class="o">[</span><span class="kt">Int</span><span class="o">](</span><span class="mi">4</span><span class="o">,</span> <span class="mi">5</span><span class="o">,</span> <span class="mi">4</span><span class="o">,</span> <span class="mi">3</span><span class="o">)</span>
+<span class="c1">// create the trainer and set its parameters</span>
+<span class="k">val</span> <span class="n">trainer</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">MultilayerPerceptronClassifier</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setLayers</span><span class="o">(</span><span class="n">layers</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setBlockSize</span><span class="o">(</span><span class="mi">128</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setSeed</span><span class="o">(</span><span class="mi">1234L</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setMaxIter</span><span class="o">(</span><span class="mi">100</span><span class="o">)</span>
+<span class="c1">// train the model</span>
+<span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="n">trainer</span><span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">train</span><span class="o">)</span>
+<span class="c1">// compute precision on the test set</span>
+<span class="k">val</span> <span class="n">result</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">transform</span><span class="o">(</span><span class="n">test</span><span class="o">)</span>
+<span class="k">val</span> <span class="n">predictionAndLabels</span> <span class="k">=</span> <span class="n">result</span><span class="o">.</span><span class="n">select</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">,</span> <span class="s">&quot;label&quot;</span><span class="o">)</span>
+<span class="k">val</span> <span class="n">evaluator</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">MulticlassClassificationEvaluator</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setMetricName</span><span class="o">(</span><span class="s">&quot;precision&quot;</span><span class="o">)</span>
+<span class="n">println</span><span class="o">(</span><span class="s">&quot;Precision:&quot;</span> <span class="o">+</span> <span class="n">evaluator</span><span class="o">.</span><span class="n">evaluate</span><span class="o">(</span><span class="n">predictionAndLabels</span><span class="o">))</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/MultilayerPerceptronClassifierExample.scala" in the Spark repo.</small></div>
+  </div>
+
+<div data-lang="java">
+    <div class="highlight"><pre><span class="kn">import</span> <span class="nn">org.apache.spark.SparkConf</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaSparkContext</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.SQLContext</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.classification.MultilayerPerceptronClassificationModel</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.classification.MultilayerPerceptronClassifier</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.DataFrame</span><span class="o">;</span>
+
+<span class="c1">// Load training data</span>
+<span class="n">String</span> <span class="n">path</span> <span class="o">=</span> <span class="s">&quot;data/mllib/sample_multiclass_classification_data.txt&quot;</span><span class="o">;</span>
+<span class="n">DataFrame</span> <span class="n">dataFrame</span> <span class="o">=</span> <span class="n">jsql</span><span class="o">.</span><span class="na">read</span><span class="o">().</span><span class="na">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">).</span><span class="na">load</span><span class="o">(</span><span class="n">path</span><span class="o">);</span>
+<span class="c1">// Split the data into train and test</span>
+<span class="n">DataFrame</span><span class="o">[]</span> <span class="n">splits</span> <span class="o">=</span> <span class="n">dataFrame</span><span class="o">.</span><span class="na">randomSplit</span><span class="o">(</span><span class="k">new</span> <span class="kt">double</span><span class="o">[]{</span><span class="mf">0.6</span><span class="o">,</span> <span class="mf">0.4</span><span class="o">},</span> <span class="mi">1234L</span><span class="o">);</span>
+<span class="n">DataFrame</span> <span class="n">train</span> <span class="o">=</span> <span class="n">splits</span><span class="o">[</span><span class="mi">0</span><span class="o">];</span>
+<span class="n">DataFrame</span> <span class="n">test</span> <span class="o">=</span> <span class="n">splits</span><span class="o">[</span><span class="mi">1</span><span class="o">];</span>
+<span class="c1">// specify layers for the neural network:</span>
+<span class="c1">// input layer of size 4 (features), two intermediate of size 5 and 4</span>
+<span class="c1">// and output of size 3 (classes)</span>
+<span class="kt">int</span><span class="o">[]</span> <span class="n">layers</span> <span class="o">=</span> <span class="k">new</span> <span class="kt">int</span><span class="o">[]</span> <span class="o">{</span><span class="mi">4</span><span class="o">,</span> <span class="mi">5</span><span class="o">,</span> <span class="mi">4</span><span class="o">,</span> <span class="mi">3</span><span class="o">};</span>
+<span class="c1">// create the trainer and set its parameters</span>
+<span class="n">MultilayerPerceptronClassifier</span> <span class="n">trainer</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">MultilayerPerceptronClassifier</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setLayers</span><span class="o">(</span><span class="n">layers</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setBlockSize</span><span class="o">(</span><span class="mi">128</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setSeed</span><span class="o">(</span><span class="mi">1234L</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setMaxIter</span><span class="o">(</span><span class="mi">100</span><span class="o">);</span>
+<span class="c1">// train the model</span>
+<span class="n">MultilayerPerceptronClassificationModel</span> <span class="n">model</span> <span class="o">=</span> <span class="n">trainer</span><span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">train</span><span class="o">);</span>
+<span class="c1">// compute precision on the test set</span>
+<span class="n">DataFrame</span> <span class="n">result</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="na">transform</span><span class="o">(</span><span class="n">test</span><span class="o">);</span>
+<span class="n">DataFrame</span> <span class="n">predictionAndLabels</span> <span class="o">=</span> <span class="n">result</span><span class="o">.</span><span class="na">select</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">,</span> <span class="s">&quot;label&quot;</span><span class="o">);</span>
+<span class="n">MulticlassClassificationEvaluator</span> <span class="n">evaluator</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">MulticlassClassificationEvaluator</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setMetricName</span><span class="o">(</span><span class="s">&quot;precision&quot;</span><span class="o">);</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;Precision = &quot;</span> <span class="o">+</span> <span class="n">evaluator</span><span class="o">.</span><span class="na">evaluate</span><span class="o">(</span><span class="n">predictionAndLabels</span><span class="o">));</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaMultilayerPerceptronClassifierExample.java" in the Spark repo.</small></div>
+  </div>
+
+<div data-lang="python">
+    <div class="highlight"><pre><span class="kn">from</span> <span class="nn">pyspark.ml.classification</span> <span class="kn">import</span> <span class="n">MultilayerPerceptronClassifier</span>
+<span class="kn">from</span> <span class="nn">pyspark.ml.evaluation</span> <span class="kn">import</span> <span class="n">MulticlassClassificationEvaluator</span>
+
+<span class="c"># Load training data</span>
+<span class="n">data</span> <span class="o">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="s">&quot;libsvm&quot;</span><span class="p">)</span>\
+    <span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="s">&quot;data/mllib/sample_multiclass_classification_data.txt&quot;</span><span class="p">)</span>
+<span class="c"># Split the data into train and test</span>
+<span class="n">splits</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">randomSplit</span><span class="p">([</span><span class="mf">0.6</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">],</span> <span class="mi">1234</span><span class="p">)</span>
+<span class="n">train</span> <span class="o">=</span> <span class="n">splits</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+<span class="n">test</span> <span class="o">=</span> <span class="n">splits</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+<span class="c"># specify layers for the neural network:</span>
+<span class="c"># input layer of size 4 (features), two intermediate of size 5 and 4</span>
+<span class="c"># and output of size 3 (classes)</span>
+<span class="n">layers</span> <span class="o">=</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">3</span><span class="p">]</span>
+<span class="c"># create the trainer and set its parameters</span>
+<span class="n">trainer</span> <span class="o">=</span> <span class="n">MultilayerPerceptronClassifier</span><span class="p">(</span><span class="n">maxIter</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">layers</span><span class="o">=</span><span class="n">layers</span><span class="p">,</span> <span class="n">blockSize</span><span class="o">=</span><span class="mi">128</span><span class="p">,</span> <span class="n">seed</span><span class="o">=</span><span class="mi">1234</span><span class="p">)</span>
+<span class="c"># train the model</span>
+<span class="n">model</span> <span class="o">=</span> <span class="n">trainer</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">train</span><span class="p">)</span>
+<span class="c"># compute precision on the test set</span>
+<span class="n">result</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">test</span><span class="p">)</span>
+<span class="n">predictionAndLabels</span> <span class="o">=</span> <span class="n">result</span><span class="o">.</span><span class="n">select</span><span class="p">(</span><span class="s">&quot;prediction&quot;</span><span class="p">,</span> <span class="s">&quot;label&quot;</span><span class="p">)</span>
+<span class="n">evaluator</span> <span class="o">=</span> <span class="n">MulticlassClassificationEvaluator</span><span class="p">(</span><span class="n">metricName</span><span class="o">=</span><span class="s">&quot;precision&quot;</span><span class="p">)</span>
+<span class="k">print</span><span class="p">(</span><span class="s">&quot;Precision:&quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">evaluator</span><span class="o">.</span><span class="n">evaluate</span><span class="p">(</span><span class="n">predictionAndLabels</span><span class="p">)))</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/python/ml/multilayer_perceptron_classification.py" in the Spark repo.</small></div>
+  </div>
+
+</div>
+
+<h2 id="one-vs-rest-classifier-aka-one-vs-all">One-vs-Rest classifier (a.k.a. One-vs-All)</h2>
+
+<p><a href="http://en.wikipedia.org/wiki/Multiclass_classification#One-vs.-rest">OneVsRest</a> is an example of a machine learning reduction for performing multiclass classification given a base classifier that can perform binary classification efficiently.  It is also known as &#8220;One-vs-All.&#8221;</p>
+
+<p><code>OneVsRest</code> is implemented as an <code>Estimator</code>. For the base classifier it takes instances of <code>Classifier</code> and creates a binary classification problem for each of the k classes. The classifier for class i is trained to predict whether the label is i or not, distinguishing class i from all other classes.</p>
+
+<p>Predictions are done by evaluating each binary classifier and the index of the most confident classifier is output as label.</p>
+
+<p><strong>Example</strong></p>
+
+<p>The example below demonstrates how to load the
+<a href="http://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/multiclass/iris.scale">Iris dataset</a>, parse it as a DataFrame and perform multiclass classification using <code>OneVsRest</code>. The test error is calculated to measure the algorithm accuracy.</p>
+
+<div class="codetabs">
+<div data-lang="scala">
+
+    <p>Refer to the <a href="api/scala/index.html#org.apache.spark.ml.classifier.OneVsRest">Scala API docs</a> for more details.</p>
+
+    <div class="highlight"><pre><span class="k">import</span> <span class="nn">org.apache.spark.examples.mllib.AbstractParams</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.ml.classification.</span><span class="o">{</span><span class="nc">OneVsRest</span><span class="o">,</span> <span class="nc">LogisticRegression</span><span class="o">}</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.ml.util.MetadataUtils</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.mllib.evaluation.MulticlassMetrics</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vector</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.sql.DataFrame</span>
+
+<span class="k">val</span> <span class="n">inputData</span> <span class="k">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">).</span><span class="n">load</span><span class="o">(</span><span class="n">params</span><span class="o">.</span><span class="n">input</span><span class="o">)</span>
+<span class="c1">// compute the train/test split: if testInput is not provided use part of input.</span>
+<span class="k">val</span> <span class="n">data</span> <span class="k">=</span> <span class="n">params</span><span class="o">.</span><span class="n">testInput</span> <span class="k">match</span> <span class="o">{</span>
+  <span class="k">case</span> <span class="nc">Some</span><span class="o">(</span><span class="n">t</span><span class="o">)</span> <span class="k">=&gt;</span> <span class="o">{</span>
+    <span class="c1">// compute the number of features in the training set.</span>
+    <span class="k">val</span> <span class="n">numFeatures</span> <span class="k">=</span> <span class="n">inputData</span><span class="o">.</span><span class="n">first</span><span class="o">().</span><span class="n">getAs</span><span class="o">[</span><span class="kt">Vector</span><span class="o">](</span><span class="mi">1</span><span class="o">).</span><span class="n">size</span>
+    <span class="k">val</span> <span class="n">testData</span> <span class="k">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">option</span><span class="o">(</span><span class="s">&quot;numFeatures&quot;</span><span class="o">,</span> <span class="n">numFeatures</span><span class="o">.</span><span class="n">toString</span><span class="o">)</span>
+      <span class="o">.</span><span class="n">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">).</span><span class="n">load</span><span class="o">(</span><span class="n">t</span><span class="o">)</span>
+    <span class="nc">Array</span><span class="o">[</span><span class="kt">DataFrame</span><span class="o">](</span><span class="n">inputData</span><span class="o">,</span> <span class="n">testData</span><span class="o">)</span>
+  <span class="o">}</span>
+  <span class="k">case</span> <span class="nc">None</span> <span class="k">=&gt;</span> <span class="o">{</span>
+    <span class="k">val</span> <span class="n">f</span> <span class="k">=</span> <span class="n">params</span><span class="o">.</span><span class="n">fracTest</span>
+    <span class="n">inputData</span><span class="o">.</span><span class="n">randomSplit</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">f</span><span class="o">,</span> <span class="n">f</span><span class="o">),</span> <span class="n">seed</span> <span class="k">=</span> <span class="mi">12345</span><span class="o">)</span>
+  <span class="o">}</span>
+<span class="o">}</span>
+<span class="k">val</span> <span class="nc">Array</span><span class="o">(</span><span class="n">train</span><span class="o">,</span> <span class="n">test</span><span class="o">)</span> <span class="k">=</span> <span class="n">data</span><span class="o">.</span><span class="n">map</span><span class="o">(</span><span class="k">_</span><span class="o">.</span><span class="n">cache</span><span class="o">())</span>
+
+<span class="c1">// instantiate the base classifier</span>
+<span class="k">val</span> <span class="n">classifier</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">LogisticRegression</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setMaxIter</span><span class="o">(</span><span class="n">params</span><span class="o">.</span><span class="n">maxIter</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setTol</span><span class="o">(</span><span class="n">params</span><span class="o">.</span><span class="n">tol</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setFitIntercept</span><span class="o">(</span><span class="n">params</span><span class="o">.</span><span class="n">fitIntercept</span><span class="o">)</span>
+
+<span class="c1">// Set regParam, elasticNetParam if specified in params</span>
+<span class="n">params</span><span class="o">.</span><span class="n">regParam</span><span class="o">.</span><span class="n">foreach</span><span class="o">(</span><span class="n">classifier</span><span class="o">.</span><span class="n">setRegParam</span><span class="o">)</span>
+<span class="n">params</span><span class="o">.</span><span class="n">elasticNetParam</span><span class="o">.</span><span class="n">foreach</span><span class="o">(</span><span class="n">classifier</span><span class="o">.</span><span class="n">setElasticNetParam</span><span class="o">)</span>
+
+<span class="c1">// instantiate the One Vs Rest Classifier.</span>
+
+<span class="k">val</span> <span class="n">ovr</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">OneVsRest</span><span class="o">()</span>
+<span class="n">ovr</span><span class="o">.</span><span class="n">setClassifier</span><span class="o">(</span><span class="n">classifier</span><span class="o">)</span>
+
+<span class="c1">// train the multiclass model.</span>
+<span class="k">val</span> <span class="o">(</span><span class="n">trainingDuration</span><span class="o">,</span> <span class="n">ovrModel</span><span class="o">)</span> <span class="k">=</span> <span class="n">time</span><span class="o">(</span><span class="n">ovr</span><span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">train</span><span class="o">))</span>
+
+<span class="c1">// score the model on test data.</span>
+<span class="k">val</span> <span class="o">(</span><span class="n">predictionDuration</span><span class="o">,</span> <span class="n">predictions</span><span class="o">)</span> <span class="k">=</span> <span class="n">time</span><span class="o">(</span><span class="n">ovrModel</span><span class="o">.</span><span class="n">transform</span><span class="o">(</span><span class="n">test</span><span class="o">))</span>
+
+<span class="c1">// evaluate the model</span>
+<span class="k">val</span> <span class="n">predictionsAndLabels</span> <span class="k">=</span> <span class="n">predictions</span><span class="o">.</span><span class="n">select</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">,</span> <span class="s">&quot;label&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">map</span><span class="o">(</span><span class="n">row</span> <span class="k">=&gt;</span> <span class="o">(</span><span class="n">row</span><span class="o">.</span><span class="n">getDouble</span><span class="o">(</span><span class="mi">0</span><span class="o">),</span> <span class="n">row</span><span class="o">.</span><span class="n">getDouble</span><span class="o">(</span><span class="mi">1</span><span class="o">)))</span>
+
+<span class="k">val</span> <span class="n">metrics</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">MulticlassMetrics</span><span class="o">(</span><span class="n">predictionsAndLabels</span><span class="o">)</span>
+
+<span class="k">val</span> <span class="n">confusionMatrix</span> <span class="k">=</span> <span class="n">metrics</span><span class="o">.</span><span class="n">confusionMatrix</span>
+
+<span class="c1">// compute the false positive rate per label</span>
+<span class="k">val</span> <span class="n">predictionColSchema</span> <span class="k">=</span> <span class="n">predictions</span><span class="o">.</span><span class="n">schema</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">)</span>
+<span class="k">val</span> <span class="n">numClasses</span> <span class="k">=</span> <span class="nc">MetadataUtils</span><span class="o">.</span><span class="n">getNumClasses</span><span class="o">(</span><span class="n">predictionColSchema</span><span class="o">).</span><span class="n">get</span>
+<span class="k">val</span> <span class="n">fprs</span> <span class="k">=</span> <span class="nc">Range</span><span class="o">(</span><span class="mi">0</span><span class="o">,</span> <span class="n">numClasses</span><span class="o">).</span><span class="n">map</span><span class="o">(</span><span class="n">p</span> <span class="k">=&gt;</span> <span class="o">(</span><span class="n">p</span><span class="o">,</span> <span class="n">metrics</span><span class="o">.</span><span class="n">falsePositiveRate</span><span class="o">(</span><span class="n">p</span><span class="o">.</span><span class="n">toDouble</span><span class="o">)))</span>
+
+<span class="n">println</span><span class="o">(</span><span class="n">s</span><span class="s">&quot; Training Time ${trainingDuration} sec\n&quot;</span><span class="o">)</span>
+
+<span class="n">println</span><span class="o">(</span><span class="n">s</span><span class="s">&quot; Prediction Time ${predictionDuration} sec\n&quot;</span><span class="o">)</span>
+
+<span class="n">println</span><span class="o">(</span><span class="n">s</span><span class="s">&quot; Confusion Matrix\n ${confusionMatrix.toString}\n&quot;</span><span class="o">)</span>
+
+<span class="n">println</span><span class="o">(</span><span class="s">&quot;label\tfpr&quot;</span><span class="o">)</span>
+
+<span class="n">println</span><span class="o">(</span><span class="n">fprs</span><span class="o">.</span><span class="n">map</span> <span class="o">{</span><span class="k">case</span> <span class="o">(</span><span class="n">label</span><span class="o">,</span> <span class="n">fpr</span><span class="o">)</span> <span class="k">=&gt;</span> <span class="n">label</span> <span class="o">+</span> <span class="s">&quot;\t&quot;</span> <span class="o">+</span> <span class="n">fpr</span><span class="o">}.</span><span class="n">mkString</span><span class="o">(</span><span class="s">&quot;\n&quot;</span><span class="o">))</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/OneVsRestExample.scala" in the Spark repo.</small></div>
+  </div>
+
+<div data-lang="java">
+
+    <p>Refer to the <a href="api/java/org/apache/spark/ml/classification/OneVsRest.html">Java API docs</a> for more details.</p>
+
+    <div class="highlight"><pre><span class="kn">import</span> <span class="nn">org.apache.spark.ml.classification.LogisticRegression</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.classification.OneVsRest</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.classification.OneVsRestModel</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.util.MetadataUtils</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.evaluation.MulticlassMetrics</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Matrix</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vector</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.DataFrame</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.SQLContext</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.types.StructField</span><span class="o">;</span>
+
+<span class="c1">// configure the base classifier</span>
+<span class="n">LogisticRegression</span> <span class="n">classifier</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">LogisticRegression</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setMaxIter</span><span class="o">(</span><span class="n">params</span><span class="o">.</span><span class="na">maxIter</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setTol</span><span class="o">(</span><span class="n">params</span><span class="o">.</span><span class="na">tol</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setFitIntercept</span><span class="o">(</span><span class="n">params</span><span class="o">.</span><span class="na">fitIntercept</span><span class="o">);</span>
+
+<span class="k">if</span> <span class="o">(</span><span class="n">params</span><span class="o">.</span><span class="na">regParam</span> <span class="o">!=</span> <span class="kc">null</span><span class="o">)</span> <span class="o">{</span>
+  <span class="n">classifier</span><span class="o">.</span><span class="na">setRegParam</span><span class="o">(</span><span class="n">params</span><span class="o">.</span><span class="na">regParam</span><span class="o">);</span>
+<span class="o">}</span>
+<span class="k">if</span> <span class="o">(</span><span class="n">params</span><span class="o">.</span><span class="na">elasticNetParam</span> <span class="o">!=</span> <span class="kc">null</span><span class="o">)</span> <span class="o">{</span>
+  <span class="n">classifier</span><span class="o">.</span><span class="na">setElasticNetParam</span><span class="o">(</span><span class="n">params</span><span class="o">.</span><span class="na">elasticNetParam</span><span class="o">);</span>
+<span class="o">}</span>
+
+<span class="c1">// instantiate the One Vs Rest Classifier</span>
+<span class="n">OneVsRest</span> <span class="n">ovr</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">OneVsRest</span><span class="o">().</span><span class="na">setClassifier</span><span class="o">(</span><span class="n">classifier</span><span class="o">);</span>
+
+<span class="n">String</span> <span class="n">input</span> <span class="o">=</span> <span class="n">params</span><span class="o">.</span><span class="na">input</span><span class="o">;</span>
+<span class="n">DataFrame</span> <span class="n">inputData</span> <span class="o">=</span> <span class="n">jsql</span><span class="o">.</span><span class="na">read</span><span class="o">().</span><span class="na">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">).</span><span class="na">load</span><span class="o">(</span><span class="n">input</span><span class="o">);</span>
+<span class="n">DataFrame</span> <span class="n">train</span><span class="o">;</span>
+<span class="n">DataFrame</span> <span class="n">test</span><span class="o">;</span>
+
+<span class="c1">// compute the train/ test split: if testInput is not provided use part of input</span>
+<span class="n">String</span> <span class="n">testInput</span> <span class="o">=</span> <span class="n">params</span><span class="o">.</span><span class="na">testInput</span><span class="o">;</span>
+<span class="k">if</span> <span class="o">(</span><span class="n">testInput</span> <span class="o">!=</span> <span class="kc">null</span><span class="o">)</span> <span class="o">{</span>
+  <span class="n">train</span> <span class="o">=</span> <span class="n">inputData</span><span class="o">;</span>
+  <span class="c1">// compute the number of features in the training set.</span>
+  <span class="kt">int</span> <span class="n">numFeatures</span> <span class="o">=</span> <span class="n">inputData</span><span class="o">.</span><span class="na">first</span><span class="o">().&lt;</span><span class="n">Vector</span><span class="o">&gt;</span><span class="n">getAs</span><span class="o">(</span><span class="mi">1</span><span class="o">).</span><span class="na">size</span><span class="o">();</span>
+  <span class="n">test</span> <span class="o">=</span> <span class="n">jsql</span><span class="o">.</span><span class="na">read</span><span class="o">().</span><span class="na">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">).</span><span class="na">option</span><span class="o">(</span><span class="s">&quot;numFeatures&quot;</span><span class="o">,</span>
+    <span class="n">String</span><span class="o">.</span><span class="na">valueOf</span><span class="o">(</span><span class="n">numFeatures</span><span class="o">)).</span><span class="na">load</span><span class="o">(</span><span class="n">testInput</span><span class="o">);</span>
+<span class="o">}</span> <span class="k">else</span> <span class="o">{</span>
+  <span class="kt">double</span> <span class="n">f</span> <span class="o">=</span> <span class="n">params</span><span class="o">.</span><span class="na">fracTest</span><span class="o">;</span>
+  <span class="n">DataFrame</span><span class="o">[]</span> <span class="n">tmp</span> <span class="o">=</span> <span class="n">inputData</span><span class="o">.</span><span class="na">randomSplit</span><span class="o">(</span><span class="k">new</span> <span class="kt">double</span><span class="o">[]{</span><span class="mi">1</span> <span class="o">-</span> <span class="n">f</span><span class="o">,</span> <span class="n">f</span><span class="o">},</span> <span class="mi">12345</span><span class="o">);</span>
+  <span class="n">train</span> <span class="o">=</span> <span class="n">tmp</span><span class="o">[</span><span class="mi">0</span><span class="o">];</span>
+  <span class="n">test</span> <span class="o">=</span> <span class="n">tmp</span><span class="o">[</span><span class="mi">1</span><span class="o">];</span>
+<span class="o">}</span>
+
+<span class="c1">// train the multiclass model</span>
+<span class="n">OneVsRestModel</span> <span class="n">ovrModel</span> <span class="o">=</span> <span class="n">ovr</span><span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">train</span><span class="o">.</span><span class="na">cache</span><span class="o">());</span>
+
+<span class="c1">// score the model on test data</span>
+<span class="n">DataFrame</span> <span class="n">predictions</span> <span class="o">=</span> <span class="n">ovrModel</span><span class="o">.</span><span class="na">transform</span><span class="o">(</span><span class="n">test</span><span class="o">.</span><span class="na">cache</span><span class="o">())</span>
+  <span class="o">.</span><span class="na">select</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">,</span> <span class="s">&quot;label&quot;</span><span class="o">);</span>
+
+<span class="c1">// obtain metrics</span>
+<span class="n">MulticlassMetrics</span> <span class="n">metrics</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">MulticlassMetrics</span><span class="o">(</span><span class="n">predictions</span><span class="o">);</span>
+<span class="n">StructField</span> <span class="n">predictionColSchema</span> <span class="o">=</span> <span class="n">predictions</span><span class="o">.</span><span class="na">schema</span><span class="o">().</span><span class="na">apply</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">);</span>
+<span class="n">Integer</span> <span class="n">numClasses</span> <span class="o">=</span> <span class="o">(</span><span class="n">Integer</span><span class="o">)</span> <span class="n">MetadataUtils</span><span class="o">.</span><span class="na">getNumClasses</span><span class="o">(</span><span class="n">predictionColSchema</span><span class="o">).</span><span class="na">get</span><span class="o">();</span>
+
+<span class="c1">// compute the false positive rate per label</span>
+<span class="n">StringBuilder</span> <span class="n">results</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">StringBuilder</span><span class="o">();</span>
+<span class="n">results</span><span class="o">.</span><span class="na">append</span><span class="o">(</span><span class="s">&quot;label\tfpr\n&quot;</span><span class="o">);</span>
+<span class="k">for</span> <span class="o">(</span><span class="kt">int</span> <span class="n">label</span> <span class="o">=</span> <span class="mi">0</span><span class="o">;</span> <span class="n">label</span> <span class="o">&lt;</span> <span class="n">numClasses</span><span class="o">;</span> <span class="n">label</span><span class="o">++)</span> <span class="o">{</span>
+  <span class="n">results</span><span class="o">.</span><span class="na">append</span><span class="o">(</span><span class="n">label</span><span class="o">);</span>
+  <span class="n">results</span><span class="o">.</span><span class="na">append</span><span class="o">(</span><span class="s">&quot;\t&quot;</span><span class="o">);</span>
+  <span class="n">results</span><span class="o">.</span><span class="na">append</span><span class="o">(</span><span class="n">metrics</span><span class="o">.</span><span class="na">falsePositiveRate</span><span class="o">((</span><span class="kt">double</span><span class="o">)</span> <span class="n">label</span><span class="o">));</span>
+  <span class="n">results</span><span class="o">.</span><span class="na">append</span><span class="o">(</span><span class="s">&quot;\n&quot;</span><span class="o">);</span>
+<span class="o">}</span>
+
+<span class="n">Matrix</span> <span class="n">confusionMatrix</span> <span class="o">=</span> <span class="n">metrics</span><span class="o">.</span><span class="na">confusionMatrix</span><span class="o">();</span>
+<span class="c1">// output the Confusion Matrix</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;Confusion Matrix&quot;</span><span class="o">);</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="n">confusionMatrix</span><span class="o">);</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">();</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="n">results</span><span class="o">);</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaOneVsRestExample.java" in the Spark repo.</small></div>
+  </div>
+</div>
+
+<h1 id="regression">Regression</h1>
+
+<h2 id="linear-regression">Linear regression</h2>
+
+<p>The interface for working with linear regression models and model
+summaries is similar to the logistic regression case.</p>
+
+<p><strong>Example</strong></p>
+
+<p>The following
+example demonstrates training an elastic net regularized linear
+regression model and extracting model summary statistics.</p>
+
+<div class="codetabs">
+
+<div data-lang="scala">
+    <div class="highlight"><pre><span class="k">import</span> <span class="nn">org.apache.spark.ml.regression.LinearRegression</span>
+
+<span class="c1">// Load training data</span>
+<span class="k">val</span> <span class="n">training</span> <span class="k">=</span> <span class="n">sqlCtx</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_linear_regression_data.txt&quot;</span><span class="o">)</span>
+
+<span class="k">val</span> <span class="n">lr</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">LinearRegression</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setMaxIter</span><span class="o">(</span><span class="mi">10</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setRegParam</span><span class="o">(</span><span class="mf">0.3</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setElasticNetParam</span><span class="o">(</span><span class="mf">0.8</span><span class="o">)</span>
+
+<span class="c1">// Fit the model</span>
+<span class="k">val</span> <span class="n">lrModel</span> <span class="k">=</span> <span class="n">lr</span><span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">training</span><span class="o">)</span>
+
+<span class="c1">// Print the coefficients and intercept for linear regression</span>
+<span class="n">println</span><span class="o">(</span><span class="n">s</span><span class="s">&quot;Coefficients: ${lrModel.coefficients} Intercept: ${lrModel.intercept}&quot;</span><span class="o">)</span>
+
+<span class="c1">// Summarize the model over the training set and print out some metrics</span>
+<span class="k">val</span> <span class="n">trainingSummary</span> <span class="k">=</span> <span class="n">lrModel</span><span class="o">.</span><span class="n">summary</span>
+<span class="n">println</span><span class="o">(</span><span class="n">s</span><span class="s">&quot;numIterations: ${trainingSummary.totalIterations}&quot;</span><span class="o">)</span>
+<span class="n">println</span><span class="o">(</span><span class="n">s</span><span class="s">&quot;objectiveHistory: ${trainingSummary.objectiveHistory.toList}&quot;</span><span class="o">)</span>
+<span class="n">trainingSummary</span><span class="o">.</span><span class="n">residuals</span><span class="o">.</span><span class="n">show</span><span class="o">()</span>
+<span class="n">println</span><span class="o">(</span><span class="n">s</span><span class="s">&quot;RMSE: ${trainingSummary.rootMeanSquaredError}&quot;</span><span class="o">)</span>
+<span class="n">println</span><span class="o">(</span><span class="n">s</span><span class="s">&quot;r2: ${trainingSummary.r2}&quot;</span><span class="o">)</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/LinearRegressionWithElasticNetExample.scala" in the Spark repo.</small></div>
+  </div>
+
+<div data-lang="java">
+    <div class="highlight"><pre><span class="kn">import</span> <span class="nn">org.apache.spark.ml.regression.LinearRegression</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.regression.LinearRegressionModel</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.regression.LinearRegressionTrainingSummary</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vectors</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.DataFrame</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.SQLContext</span><span class="o">;</span>
+
+<span class="c1">// Load training data</span>
+<span class="n">DataFrame</span> <span class="n">training</span> <span class="o">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="na">read</span><span class="o">().</span><span class="na">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_linear_regression_data.txt&quot;</span><span class="o">);</span>
+
+<span class="n">LinearRegression</span> <span class="n">lr</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">LinearRegression</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setMaxIter</span><span class="o">(</span><span class="mi">10</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setRegParam</span><span class="o">(</span><span class="mf">0.3</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setElasticNetParam</span><span class="o">(</span><span class="mf">0.8</span><span class="o">);</span>
+
+<span class="c1">// Fit the model</span>
+<span class="n">LinearRegressionModel</span> <span class="n">lrModel</span> <span class="o">=</span> <span class="n">lr</span><span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">training</span><span class="o">);</span>
+
+<span class="c1">// Print the coefficients and intercept for linear regression</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;Coefficients: &quot;</span>
+  <span class="o">+</span> <span class="n">lrModel</span><span class="o">.</span><span class="na">coefficients</span><span class="o">()</span> <span class="o">+</span> <span class="s">&quot; Intercept: &quot;</span> <span class="o">+</span> <span class="n">lrModel</span><span class="o">.</span><span class="na">intercept</span><span class="o">());</span>
+
+<span class="c1">// Summarize the model over the training set and print out some metrics</span>
+<span class="n">LinearRegressionTrainingSummary</span> <span class="n">trainingSummary</span> <span class="o">=</span> <span class="n">lrModel</span><span class="o">.</span><span class="na">summary</span><span class="o">();</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;numIterations: &quot;</span> <span class="o">+</span> <span class="n">trainingSummary</span><span class="o">.</span><span class="na">totalIterations</span><span class="o">());</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;objectiveHistory: &quot;</span> <span class="o">+</span> <span class="n">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="n">trainingSummary</span><span class="o">.</span><span class="na">objectiveHistory</span><span class="o">()));</span>
+<span class="n">trainingSummary</span><span class="o">.</span><span class="na">residuals</span><span class="o">().</span><span class="na">show</span><span class="o">();</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;RMSE: &quot;</span> <span class="o">+</span> <span class="n">trainingSummary</span><span class="o">.</span><span class="na">rootMeanSquaredError</span><span class="o">());</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;r2: &quot;</span> <span class="o">+</span> <span class="n">trainingSummary</span><span class="o">.</span><span class="na">r2</span><span class="o">());</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaLinearRegressionWithElasticNetExample.java" in the Spark repo.</small></div>
+  </div>
+
+<div data-lang="python">
+    <!--- TODO: Add python model summaries once implemented -->
+    <div class="highlight"><pre><span class="kn">from</span> <span class="nn">pyspark.ml.regression</span> <span class="kn">import</span> <span class="n">LinearRegression</span>
+
+<span class="c"># Load training data</span>
+<span class="n">training</span> <span class="o">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="s">&quot;libsvm&quot;</span><span class="p">)</span>\
+    <span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="s">&quot;data/mllib/sample_linear_regression_data.txt&quot;</span><span class="p">)</span>
+
+<span class="n">lr</span> <span class="o">=</span> <span class="n">LinearRegression</span><span class="p">(</span><span class="n">maxIter</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">regParam</span><span class="o">=</span><span class="mf">0.3</span><span class="p">,</span> <span class="n">elasticNetParam</span><span class="o">=</span><span class="mf">0.8</span><span class="p">)</span>
+
+<span class="c"># Fit the model</span>
+<span class="n">lrModel</span> <span class="o">=</span> <span class="n">lr</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">training</span><span class="p">)</span>
+
+<span class="c"># Print the coefficients and intercept for linear regression</span>
+<span class="k">print</span><span class="p">(</span><span class="s">&quot;Coefficients: &quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">lrModel</span><span class="o">.</span><span class="n">coefficients</span><span class="p">))</span>
+<span class="k">print</span><span class="p">(</span><span class="s">&quot;Intercept: &quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">lrModel</span><span class="o">.</span><span class="n">intercept</span><span class="p">))</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/python/ml/linear_regression_with_elastic_net.py" in the Spark repo.</small></div>
+  </div>
+
+</div>
+
+<h2 id="decision-tree-regression">Decision tree regression</h2>
+
+<p>Decision trees are a popular family of classification and regression methods.
+More information about the <code>spark.ml</code> implementation can be found further in the <a href="#decision-trees">section on decision trees</a>.</p>
+
+<p><strong>Example</strong></p>
+
+<p>The following examples load a dataset in LibSVM format, split it into training and test sets, train on the first dataset, and then evaluate on the held-out test set.
+We use a feature transformer to index categorical features, adding metadata to the <code>DataFrame</code> which the Decision Tree algorithm can recognize.</p>
+
+<div class="codetabs">
+<div data-lang="scala">
+
+    <p>More details on parameters can be found in the <a href="api/scala/index.html#org.apache.spark.ml.regression.DecisionTreeRegressor">Scala API documentation</a>.</p>
+
+    <div class="highlight"><pre><span class="k">import</span> <span class="nn">org.apache.spark.ml.Pipeline</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.ml.regression.DecisionTreeRegressor</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.ml.regression.DecisionTreeRegressionModel</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.ml.feature.VectorIndexer</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.ml.evaluation.RegressionEvaluator</span>
+
+<span class="c1">// Load the data stored in LIBSVM format as a DataFrame.</span>
+<span class="k">val</span> <span class="n">data</span> <span class="k">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">).</span><span class="n">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="o">)</span>
+
+<span class="c1">// Automatically identify categorical features, and index them.</span>
+<span class="c1">// Here, we treat features with &gt; 4 distinct values as continuous.</span>
+<span class="k">val</span> <span class="n">featureIndexer</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">VectorIndexer</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setInputCol</span><span class="o">(</span><span class="s">&quot;features&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setOutputCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setMaxCategories</span><span class="o">(</span><span class="mi">4</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">data</span><span class="o">)</span>
+
+<span class="c1">// Split the data into training and test sets (30% held out for testing)</span>
+<span class="k">val</span> <span class="nc">Array</span><span class="o">(</span><span class="n">trainingData</span><span class="o">,</span> <span class="n">testData</span><span class="o">)</span> <span class="k">=</span> <span class="n">data</span><span class="o">.</span><span class="n">randomSplit</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="mf">0.7</span><span class="o">,</span> <span class="mf">0.3</span><span class="o">))</span>
+
+<span class="c1">// Train a DecisionTree model.</span>
+<span class="k">val</span> <span class="n">dt</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">DecisionTreeRegressor</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setLabelCol</span><span class="o">(</span><span class="s">&quot;label&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setFeaturesCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">)</span>
+
+<span class="c1">// Chain indexer and tree in a Pipeline</span>
+<span class="k">val</span> <span class="n">pipeline</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">Pipeline</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setStages</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="n">featureIndexer</span><span class="o">,</span> <span class="n">dt</span><span class="o">))</span>
+
+<span class="c1">// Train model.  This also runs the indexer.</span>
+<span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="n">pipeline</span><span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">trainingData</span><span class="o">)</span>
+
+<span class="c1">// Make predictions.</span>
+<span class="k">val</span> <span class="n">predictions</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">transform</span><span class="o">(</span><span class="n">testData</span><span class="o">)</span>
+
+<span class="c1">// Select example rows to display.</span>
+<span class="n">predictions</span><span class="o">.</span><span class="n">select</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">,</span> <span class="s">&quot;label&quot;</span><span class="o">,</span> <span class="s">&quot;features&quot;</span><span class="o">).</span><span class="n">show</span><span class="o">(</span><span class="mi">5</span><span class="o">)</span>
+
+<span class="c1">// Select (prediction, true label) and compute test error</span>
+<span class="k">val</span> <span class="n">evaluator</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">RegressionEvaluator</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setLabelCol</span><span class="o">(</span><span class="s">&quot;label&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setPredictionCol</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setMetricName</span><span class="o">(</span><span class="s">&quot;rmse&quot;</span><span class="o">)</span>
+<span class="k">val</span> <span class="n">rmse</span> <span class="k">=</span> <span class="n">evaluator</span><span class="o">.</span><span class="n">evaluate</span><span class="o">(</span><span class="n">predictions</span><span class="o">)</span>
+<span class="n">println</span><span class="o">(</span><span class="s">&quot;Root Mean Squared Error (RMSE) on test data = &quot;</span> <span class="o">+</span> <span class="n">rmse</span><span class="o">)</span>
+
+<span class="k">val</span> <span class="n">treeModel</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">stages</span><span class="o">(</span><span class="mi">1</span><span class="o">).</span><span class="n">asInstanceOf</span><span class="o">[</span><span class="kt">DecisionTreeRegressionModel</span><span class="o">]</span>
+<span class="n">println</span><span class="o">(</span><span class="s">&quot;Learned regression tree model:\n&quot;</span> <span class="o">+</span> <span class="n">treeModel</span><span class="o">.</span><span class="n">toDebugString</span><span class="o">)</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/DecisionTreeRegressionExample.scala" in the Spark repo.</small></div>
+  </div>
+
+<div data-lang="java">
+
+    <p>More details on parameters can be found in the <a href="api/java/org/apache/spark/ml/regression/DecisionTreeRegressor.html">Java API documentation</a>.</p>
+
+    <div class="highlight"><pre><span class="kn">import</span> <span class="nn">org.apache.spark.SparkConf</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaSparkContext</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.Pipeline</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.PipelineModel</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.PipelineStage</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.evaluation.RegressionEvaluator</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.feature.VectorIndexer</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.feature.VectorIndexerModel</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.regression.DecisionTreeRegressionModel</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.regression.DecisionTreeRegressor</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.DataFrame</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.SQLContext</span><span class="o">;</span>
+
+<span class="c1">// Load the data stored in LIBSVM format as a DataFrame.</span>
+<span class="n">DataFrame</span> <span class="n">data</span> <span class="o">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="na">read</span><span class="o">().</span><span class="na">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="o">);</span>
+
+<span class="c1">// Automatically identify categorical features, and index them.</span>
+<span class="c1">// Set maxCategories so features with &gt; 4 distinct values are treated as continuous.</span>
+<span class="n">VectorIndexerModel</span> <span class="n">featureIndexer</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">VectorIndexer</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setInputCol</span><span class="o">(</span><span class="s">&quot;features&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setOutputCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setMaxCategories</span><span class="o">(</span><span class="mi">4</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">data</span><span class="o">);</span>
+
+<span class="c1">// Split the data into training and test sets (30% held out for testing)</span>
+<span class="n">DataFrame</span><span class="o">[]</span> <span class="n">splits</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="na">randomSplit</span><span class="o">(</span><span class="k">new</span> <span class="kt">double</span><span class="o">[]{</span><span class="mf">0.7</span><span class="o">,</span> <span class="mf">0.3</span><span class="o">});</span>
+<span class="n">DataFrame</span> <span class="n">trainingData</span> <span class="o">=</span> <span class="n">splits</span><span class="o">[</span><span class="mi">0</span><span class="o">];</span>
+<span class="n">DataFrame</span> <span class="n">testData</span> <span class="o">=</span> <span class="n">splits</span><span class="o">[</span><span class="mi">1</span><span class="o">];</span>
+
+<span class="c1">// Train a DecisionTree model.</span>
+<span class="n">DecisionTreeRegressor</span> <span class="n">dt</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">DecisionTreeRegressor</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setFeaturesCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">);</span>
+
+<span class="c1">// Chain indexer and tree in a Pipeline</span>
+<span class="n">Pipeline</span> <span class="n">pipeline</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">Pipeline</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setStages</span><span class="o">(</span><span class="k">new</span> <span class="n">PipelineStage</span><span class="o">[]{</span><span class="n">featureIndexer</span><span class="o">,</span> <span class="n">dt</span><span class="o">});</span>
+
+<span class="c1">// Train model.  This also runs the indexer.</span>
+<span class="n">PipelineModel</span> <span class="n">model</span> <span class="o">=</span> <span class="n">pipeline</span><span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">trainingData</span><span class="o">);</span>
+
+<span class="c1">// Make predictions.</span>
+<span class="n">DataFrame</span> <span class="n">predictions</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="na">transform</span><span class="o">(</span><span class="n">testData</span><span class="o">);</span>
+
+<span class="c1">// Select example rows to display.</span>
+<span class="n">predictions</span><span class="o">.</span><span class="na">select</span><span class="o">(</span><span class="s">&quot;label&quot;</span><span class="o">,</span> <span class="s">&quot;features&quot;</span><span class="o">).</span><span class="na">show</span><span class="o">(</span><span class="mi">5</span><span class="o">);</span>
+
+<span class="c1">// Select (prediction, true label) and compute test error</span>
+<span class="n">RegressionEvaluator</span> <span class="n">evaluator</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">RegressionEvaluator</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setLabelCol</span><span class="o">(</span><span class="s">&quot;label&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setPredictionCol</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setMetricName</span><span class="o">(</span><span class="s">&quot;rmse&quot;</span><span class="o">);</span>
+<span class="kt">double</span> <span class="n">rmse</span> <span class="o">=</span> <span class="n">evaluator</span><span class="o">.</span><span class="na">evaluate</span><span class="o">(</span><span class="n">predictions</span><span class="o">);</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;Root Mean Squared Error (RMSE) on test data = &quot;</span> <span class="o">+</span> <span class="n">rmse</span><span class="o">);</span>
+
+<span class="n">DecisionTreeRegressionModel</span> <span class="n">treeModel</span> <span class="o">=</span>
+  <span class="o">(</span><span class="n">DecisionTreeRegressionModel</span><span class="o">)</span> <span class="o">(</span><span class="n">model</span><span class="o">.</span><span class="na">stages</span><span class="o">()[</span><span class="mi">1</span><span class="o">]);</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;Learned regression tree model:\n&quot;</span> <span class="o">+</span> <span class="n">treeModel</span><span class="o">.</span><span class="na">toDebugString</span><span class="o">());</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaDecisionTreeRegressionExample.java" in the Spark repo.</small></div>
+  </div>
+
+<div data-lang="python">
+
+    <p>More details on parameters can be found in the <a href="api/python/pyspark.ml.html#pyspark.ml.regression.DecisionTreeRegressor">Python API documentation</a>.</p>
+
+    <div class="highlight"><pre><span class="kn">from</span> <span class="nn">pyspark.ml</span> <span class="kn">import</span> <span class="n">Pipeline</span>
+<span class="kn">from</span> <span class="nn">pyspark.ml.regression</span> <span class="kn">import</span> <span class="n">DecisionTreeRegressor</span>
+<span class="kn">from</span> <span class="nn">pyspark.ml.feature</span> <span class="kn">import</span> <span class="n">VectorIndexer</span>
+<span class="kn">from</span> <span class="nn">pyspark.ml.evaluation</span> <span class="kn">import</span> <span class="n">RegressionEvaluator</span>
+
+<span class="c"># Load the data stored in LIBSVM format as a DataFrame.</span>
+<span class="n">data</span> <span class="o">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="s">&quot;libsvm&quot;</span><span class="p">)</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="p">)</span>
+
+<span class="c"># Automatically identify categorical features, and index them.</span>
+<span class="c"># We specify maxCategories so features with &gt; 4 distinct values are treated as continuous.</span>
+<span class="n">featureIndexer</span> <span class="o">=</span>\
+    <span class="n">VectorIndexer</span><span class="p">(</span><span class="n">inputCol</span><span class="o">=</span><span class="s">&quot;features&quot;</span><span class="p">,</span> <span class="n">outputCol</span><span class="o">=</span><span class="s">&quot;indexedFeatures&quot;</span><span class="p">,</span> <span class="n">maxCategories</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
+
+<span class="c"># Split the data into training and test sets (30% held out for testing)</span>
+<span class="p">(</span><span class="n">trainingData</span><span class="p">,</span> <span class="n">testData</span><span class="p">)</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">randomSplit</span><span class="p">([</span><span class="mf">0.7</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">])</span>
+
+<span class="c"># Train a DecisionTree model.</span>
+<span class="n">dt</span> <span class="o">=</span> <span class="n">DecisionTreeRegressor</span><span class="p">(</span><span class="n">featuresCol</span><span class="o">=</span><span class="s">&quot;indexedFeatures&quot;</span><span class="p">)</span>
+
+<span class="c"># Chain indexer and tree in a Pipeline</span>
+<span class="n">pipeline</span> <span class="o">=</span> <span class="n">Pipeline</span><span class="p">(</span><span class="n">stages</span><span class="o">=</span><span class="p">[</span><span class="n">featureIndexer</span><span class="p">,</span> <span class="n">dt</span><span class="p">])</span>
+
+<span class="c"># Train model.  This also runs the indexer.</span>
+<span class="n">model</span> <span class="o">=</span> <span class="n">pipeline</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">trainingData</span><span class="p">)</span>
+
+<span class="c"># Make predictions.</span>
+<span class="n">predictions</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">testData</span><span class="p">)</span>
+
+<span class="c"># Select example rows to display.</span>
+<span class="n">predictions</span><span class="o">.</span><span class="n">select</span><span class="p">(</span><span class="s">&quot;prediction&quot;</span><span class="p">,</span> <span class="s">&quot;label&quot;</span><span class="p">,</span> <span class="s">&quot;features&quot;</span><span class="p">)</span><span class="o">.</span><span class="n">show</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+
+<span class="c"># Select (prediction, true label) and compute test error</span>
+<span class="n">evaluator</span> <span class="o">=</span> <span class="n">RegressionEvaluator</span><span class="p">(</span>
+    <span class="n">labelCol</span><span class="o">=</span><span class="s">&quot;label&quot;</span><span class="p">,</span> <span class="n">predictionCol</span><span class="o">=</span><span class="s">&quot;prediction&quot;</span><span class="p">,</span> <span class="n">metricName</span><span class="o">=</span><span class="s">&quot;rmse&quot;</span><span class="p">)</span>
+<span class="n">rmse</span> <span class="o">=</span> <span class="n">evaluator</span><span class="o">.</span><span class="n">evaluate</span><span class="p">(</span><span class="n">predictions</span><span class="p">)</span>
+<span class="k">print</span><span class="p">(</span><span class="s">&quot;Root Mean Squared Error (RMSE) on test data = </span><span class="si">%g</span><span class="s">&quot;</span> <span class="o">%</span> <span class="n">rmse</span><span class="p">)</span>
+
+<span class="n">treeModel</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">stages</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+<span class="c"># summary only</span>
+<span class="k">print</span><span class="p">(</span><span class="n">treeModel</span><span class="p">)</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/python/ml/decision_tree_regression_example.py" in the Spark repo.</small></div>
+  </div>
+
+</div>
+
+<h2 id="random-forest-regression">Random forest regression</h2>
+
+<p>Random forests are a popular family of classification and regression methods.
+More information about the <code>spark.ml</code> implementation can be found further in the <a href="#random-forests">section on random forests</a>.</p>
+
+<p><strong>Example</strong></p>
+
+<p>The following examples load a dataset in LibSVM format, split it into training and test sets, train on the first dataset, and then evaluate on the held-out test set.
+We use a feature transformer to index categorical features, adding metadata to the <code>DataFrame</code> which the tree-based algorithms can recognize.</p>
+
+<div class="codetabs">
+<div data-lang="scala">
+
+    <p>Refer to the <a href="api/scala/index.html#org.apache.spark.ml.regression.RandomForestRegressor">Scala API docs</a> for more details.</p>
+
+    <div class="highlight"><pre><span class="k">import</span> <span class="nn">org.apache.spark.ml.Pipeline</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.ml.evaluation.RegressionEvaluator</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.ml.feature.VectorIndexer</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.ml.regression.</span><span class="o">{</span><span class="nc">RandomForestRegressionModel</span><span class="o">,</span> <span class="nc">RandomForestRegressor</span><span class="o">}</span>
+
+<span class="c1">// Load and parse the data file, converting it to a DataFrame.</span>
+<span class="k">val</span> <span class="n">data</span> <span class="k">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">).</span><span class="n">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="o">)</span>
+
+<span class="c1">// Automatically identify categorical features, and index them.</span>
+<span class="c1">// Set maxCategories so features with &gt; 4 distinct values are treated as continuous.</span>
+<span class="k">val</span> <span class="n">featureIndexer</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">VectorIndexer</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setInputCol</span><span class="o">(</span><span class="s">&quot;features&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setOutputCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setMaxCategories</span><span class="o">(</span><span class="mi">4</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">data</span><span class="o">)</span>
+
+<span class="c1">// Split the data into training and test sets (30% held out for testing)</span>
+<span class="k">val</span> <span class="nc">Array</span><span class="o">(</span><span class="n">trainingData</span><span class="o">,</span> <span class="n">testData</span><span class="o">)</span> <span class="k">=</span> <span class="n">data</span><span class="o">.</span><span class="n">randomSplit</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="mf">0.7</span><span class="o">,</span> <span class="mf">0.3</span><span class="o">))</span>
+
+<span class="c1">// Train a RandomForest model.</span>
+<span class="k">val</span> <span class="n">rf</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">RandomForestRegressor</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setLabelCol</span><span class="o">(</span><span class="s">&quot;label&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setFeaturesCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">)</span>
+
+<span class="c1">// Chain indexer and forest in a Pipeline</span>
+<span class="k">val</span> <span class="n">pipeline</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">Pipeline</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setStages</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="n">featureIndexer</span><span class="o">,</span> <span class="n">rf</span><span class="o">))</span>
+
+<span class="c1">// Train model.  This also runs the indexer.</span>
+<span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="n">pipeline</span><span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">trainingData</span><span class="o">)</span>
+
+<span class="c1">// Make predictions.</span>
+<span class="k">val</span> <span class="n">predictions</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">transform</span><span class="o">(</span><span class="n">testData</span><span class="o">)</span>
+
+<span class="c1">// Select example rows to display.</span>
+<span class="n">predictions</span><span class="o">.</span><span class="n">select</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">,</span> <span class="s">&quot;label&quot;</span><span class="o">,</span> <span class="s">&quot;features&quot;</span><span class="o">).</span><span class="n">show</span><span class="o">(</span><span class="mi">5</span><span class="o">)</span>
+
+<span class="c1">// Select (prediction, true label) and compute test error</span>
+<span class="k">val</span> <span class="n">evaluator</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">RegressionEvaluator</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setLabelCol</span><span class="o">(</span><span class="s">&quot;label&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setPredictionCol</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setMetricName</span><span class="o">(</span><span class="s">&quot;rmse&quot;</span><span class="o">)</span>
+<span class="k">val</span> <span class="n">rmse</span> <span class="k">=</span> <span class="n">evaluator</span><span class="o">.</span><span class="n">evaluate</span><span class="o">(</span><span class="n">predictions</span><span class="o">)</span>
+<span class="n">println</span><span class="o">(</span><span class="s">&quot;Root Mean Squared Error (RMSE) on test data = &quot;</span> <span class="o">+</span> <span class="n">rmse</span><span class="o">)</span>
+
+<span class="k">val</span> <span class="n">rfModel</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">stages</span><span class="o">(</span><span class="mi">1</span><span class="o">).</span><span class="n">asInstanceOf</span><span class="o">[</span><span class="kt">RandomForestRegressionModel</span><span class="o">]</span>
+<span class="n">println</span><span class="o">(</span><span class="s">&quot;Learned regression forest model:\n&quot;</span> <span class="o">+</span> <span class="n">rfModel</span><span class="o">.</span><span class="n">toDebugString</span><span class="o">)</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/RandomForestRegressorExample.scala" in the Spark repo.</small></div>
+  </div>
+
+<div data-lang="java">
+
+    <p>Refer to the <a href="api/java/org/apache/spark/ml/regression/RandomForestRegressor.html">Java API docs</a> for more details.</p>
+
+    <div class="highlight"><pre><span class="kn">import</span> <span class="nn">org.apache.spark.ml.Pipeline</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.PipelineModel</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.PipelineStage</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.evaluation.RegressionEvaluator</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.feature.VectorIndexer</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.feature.VectorIndexerModel</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.regression.RandomForestRegressionModel</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.regression.RandomForestRegressor</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.DataFrame</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.SQLContext</span><span class="o">;</span>
+
+<span class="c1">// Load and parse the data file, converting it to a DataFrame.</span>
+<span class="n">DataFrame</span> <span class="n">data</span> <span class="o">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="na">read</span><span class="o">().</span><span class="na">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">).</span><span class="na">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="o">);</span>
+
+<span class="c1">// Automatically identify categorical features, and index them.</span>
+<span class="c1">// Set maxCategories so features with &gt; 4 distinct values are treated as continuous.</span>
+<span class="n">VectorIndexerModel</span> <span class="n">featureIndexer</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">VectorIndexer</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setInputCol</span><span class="o">(</span><span class="s">&quot;features&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setOutputCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setMaxCategories</span><span class="o">(</span><span class="mi">4</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">data</span><span class="o">);</span>
+
+<span class="c1">// Split the data into training and test sets (30% held out for testing)</span>
+<span class="n">DataFrame</span><span class="o">[]</span> <span class="n">splits</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="na">randomSplit</span><span class="o">(</span><span class="k">new</span> <span class="kt">double</span><span class="o">[]</span> <span class="o">{</span><span class="mf">0.7</span><span class="o">,</span> <span class="mf">0.3</span><span class="o">});</span>
+<span class="n">DataFrame</span> <span class="n">trainingData</span> <span class="o">=</span> <span class="n">splits</span><span class="o">[</span><span class="mi">0</span><span class="o">];</span>
+<span class="n">DataFrame</span> <span class="n">testData</span> <span class="o">=</span> <span class="n">splits</span><span class="o">[</span><span class="mi">1</span><span class="o">];</span>
+
+<span class="c1">// Train a RandomForest model.</span>
+<span class="n">RandomForestRegressor</span> <span class="n">rf</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">RandomForestRegressor</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setLabelCol</span><span class="o">(</span><span class="s">&quot;label&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setFeaturesCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">);</span>
+
+<span class="c1">// Chain indexer and forest in a Pipeline</span>
+<span class="n">Pipeline</span> <span class="n">pipeline</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">Pipeline</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setStages</span><span class="o">(</span><span class="k">new</span> <span class="n">PipelineStage</span><span class="o">[]</span> <span class="o">{</span><span class="n">featureIndexer</span><span class="o">,</span> <span class="n">rf</span><span class="o">});</span>
+
+<span class="c1">// Train model.  This also runs the indexer.</span>
+<span class="n">PipelineModel</span> <span class="n">model</span> <span class="o">=</span> <span class="n">pipeline</span><span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">trainingData</span><span class="o">);</span>
+
+<span class="c1">// Make predictions.</span>
+<span class="n">DataFrame</span> <span class="n">predictions</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="na">transform</span><span class="o">(</span><span class="n">testData</span><span class="o">);</span>
+
+<span class="c1">// Select example rows to display.</span>
+<span class="n">predictions</span><span class="o">.</span><span class="na">select</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">,</span> <span class="s">&quot;label&quot;</span><span class="o">,</span> <span class="s">&quot;features&quot;</span><span class="o">).</span><span class="na">show</span><span class="o">(</span><span class="mi">5</span><span class="o">);</span>
+
+<span class="c1">// Select (prediction, true label) and compute test error</span>
+<span class="n">RegressionEvaluator</span> <span class="n">evaluator</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">RegressionEvaluator</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setLabelCol</span><span class="o">(</span><span class="s">&quot;label&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setPredictionCol</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setMetricName</span><span class="o">(</span><span class="s">&quot;rmse&quot;</span><span class="o">);</span>
+<span class="kt">double</span> <span class="n">rmse</span> <span class="o">=</span> <span class="n">evaluator</span><span class="o">.</span><span class="na">evaluate</span><span class="o">(</span><span class="n">predictions</span><span class="o">);</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;Root Mean Squared Error (RMSE) on test data = &quot;</span> <span class="o">+</span> <span class="n">rmse</span><span class="o">);</span>
+
+<span class="n">RandomForestRegressionModel</span> <span class="n">rfModel</span> <span class="o">=</span> <span class="o">(</span><span class="n">RandomForestRegressionModel</span><span class="o">)(</span><span class="n">model</span><span class="o">.</span><span class="na">stages</span><span class="o">()[</span><span class="mi">1</span><span class="o">]);</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;Learned regression forest model:\n&quot;</span> <span class="o">+</span> <span class="n">rfModel</span><span class="o">.</span><span class="na">toDebugString</span><span class="o">());</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaRandomForestRegressorExample.java" in the Spark repo.</small></div>
+  </div>
+
+<div data-lang="python">
+
+    <p>Refer to the <a href="api/python/pyspark.ml.html#pyspark.ml.regression.RandomForestRegressor">Python API docs</a> for more details.</p>
+
+    <div class="highlight"><pre><span class="kn">from</span> <span class="nn">pyspark.ml</span> <span class="kn">import</span> <span class="n">Pipeline</span>
+<span class="kn">from</span> <span class="nn">pyspark.ml.regression</span> <span class="kn">import</span> <span class="n">RandomForestRegressor</span>
+<span class="kn">from</span> <span class="nn">pyspark.ml.feature</span> <span class="kn">import</span> <span class="n">VectorIndexer</span>
+<span class="kn">from</span> <span class="nn">pyspark.ml.evaluation</span> <span class="kn">import</span> <span class="n">RegressionEvaluator</span>
+
+<span class="c"># Load and parse the data file, converting it to a DataFrame.</span>
+<span class="n">data</span> <span class="o">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="s">&quot;libsvm&quot;</span><span class="p">)</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="p">)</span>
+
+<span class="c"># Automatically identify categorical features, and index them.</span>
+<span class="c"># Set maxCategories so features with &gt; 4 distinct values are treated as continuous.</span>
+<span class="n">featureIndexer</span> <span class="o">=</span>\
+    <span class="n">VectorIndexer</span><span class="p">(</span><span class="n">inputCol</span><span class="o">=</span><span class="s">&quot;features&quot;</span><span class="p">,</span> <span class="n">outputCol</span><span class="o">=</span><span class="s">&quot;indexedFeatures&quot;</span><span class="p">,</span> <span class="n">maxCategories</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
+
+<span class="c"># Split the data into training and test sets (30% held out for testing)</span>
+<span class="p">(</span><span class="n">trainingData</span><span class="p">,</span> <span class="n">testData</span><span class="p">)</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">randomSplit</span><span class="p">([</span><span class="mf">0.7</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">])</span>
+
+<span class="c"># Train a RandomForest model.</span>
+<span class="n">rf</span> <span class="o">=</span> <span class="n">RandomForestRegressor</span><span class="p">(</span><span class="n">featuresCol</span><span class="o">=</span><span class="s">&quot;indexedFeatures&quot;</span><span class="p">)</span>
+
+<span class="c"># Chain indexer and forest in a Pipeline</span>
+<span class="n">pipeline</span> <span class="o">=</span> <span class="n">Pipeline</span><span class="p">(</span><span class="n">stages</span><span class="o">=</span><span class="p">[</span><span class="n">featureIndexer</span><span class="p">,</span> <span class="n">rf</span><span class="p">])</span>
+
+<span class="c"># Train model.  This also runs the indexer.</span>
+<span class="n">model</span> <span class="o">=</span> <span class="n">pipeline</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">trainingData</span><span class="p">)</span>
+
+<span class="c"># Make predictions.</span>
+<span class="n">predictions</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">testData</span><span class="p">)</span>
+
+<span class="c"># Select example rows to display.</span>
+<span class="n">predictions</span><span class="o">.</span><span class="n">select</span><span class="p">(</span><span class="s">&quot;prediction&quot;</span><span class="p">,</span> <span class="s">&quot;label&quot;</span><span class="p">,</span> <span class="s">&quot;features&quot;</span><span class="p">)</span><span class="o">.</span><span class="n">show</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+
+<span class="c"># Select (prediction, true label) and compute test error</span>
+<span class="n">evaluator</span> <span class="o">=</span> <span class="n">RegressionEvaluator</span><span class="p">(</span>
+    <span class="n">labelCol</span><span class="o">=</span><span class="s">&quot;label&quot;</span><span class="p">,</span> <span class="n">predictionCol</span><span class="o">=</span><span class="s">&quot;prediction&quot;</span><span class="p">,</span> <span class="n">metricName</span><span class="o">=</span><span class="s">&quot;rmse&quot;</span><span class="p">)</span>
+<span class="n">rmse</span> <span class="o">=</span> <span class="n">evaluator</span><span class="o">.</span><span class="n">evaluate</span><span class="p">(</span><span class="n">predictions</span><span class="p">)</span>
+<span class="k">print</span><span class="p">(</span><span class="s">&quot;Root Mean Squared Error (RMSE) on test data = </span><span class="si">%g</span><span class="s">&quot;</span> <span class="o">%</span> <span class="n">rmse</span><span class="p">)</span>
+
+<span class="n">rfModel</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">stages</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+<span class="k">print</span><span class="p">(</span><span class="n">rfModel</span><span class="p">)</span>  <span class="c"># summary only</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/python/ml/random_forest_regressor_example.py" in the Spark repo.</small></div>
+  </div>
+</div>
+
+<h2 id="gradient-boosted-tree-regression">Gradient-boosted tree regression</h2>
+
+<p>Gradient-boosted trees (GBTs) are a popular regression method using ensembles of decision trees. 
+More information about the <code>spark.ml</code> implementation can be found further in the <a href="#gradient-boosted-trees-gbts">section on GBTs</a>.</p>
+
+<p><strong>Example</strong></p>
+
+<p>Note: For this example dataset, <code>GBTRegressor</code> actually only needs 1 iteration, but that will not
+be true in general.</p>
+
+<div class="codetabs">
+<div data-lang="scala">
+
+    <p>Refer to the <a href="api/scala/index.html#org.apache.spark.ml.regression.GBTRegressor">Scala API docs</a> for more details.</p>
+
+    <div class="highlight"><pre><span class="k">import</span> <span class="nn">org.apache.spark.ml.Pipeline</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.ml.evaluation.RegressionEvaluator</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.ml.feature.VectorIndexer</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.ml.regression.</span><span class="o">{</span><span class="nc">GBTRegressionModel</span><span class="o">,</span> <span class="nc">GBTRegressor</span><span class="o">}</span>
+
+<span class="c1">// Load and parse the data file, converting it to a DataFrame.</span>
+<span class="k">val</span> <span class="n">data</span> <span class="k">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">).</span><span class="n">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="o">)</span>
+
+<span class="c1">// Automatically identify categorical features, and index them.</span>
+<span class="c1">// Set maxCategories so features with &gt; 4 distinct values are treated as continuous.</span>
+<span class="k">val</span> <span class="n">featureIndexer</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">VectorIndexer</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setInputCol</span><span class="o">(</span><span class="s">&quot;features&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setOutputCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setMaxCategories</span><span class="o">(</span><span class="mi">4</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">data</span><span class="o">)</span>
+
+<span class="c1">// Split the data into training and test sets (30% held out for testing)</span>
+<span class="k">val</span> <span class="nc">Array</span><span class="o">(</span><span class="n">trainingData</span><span class="o">,</span> <span class="n">testData</span><span class="o">)</span> <span class="k">=</span> <span class="n">data</span><span class="o">.</span><span class="n">randomSplit</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="mf">0.7</span><span class="o">,</span> <span class="mf">0.3</span><span class="o">))</span>
+
+<span class="c1">// Train a GBT model.</span>
+<span class="k">val</span> <span class="n">gbt</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">GBTRegressor</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setLabelCol</span><span class="o">(</span><span class="s">&quot;label&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setFeaturesCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setMaxIter</span><span class="o">(</span><span class="mi">10</span><span class="o">)</span>
+
+<span class="c1">// Chain indexer and GBT in a Pipeline</span>
+<span class="k">val</span> <span class="n">pipeline</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">Pipeline</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setStages</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="n">featureIndexer</span><span class="o">,</span> <span class="n">gbt</span><span class="o">))</span>
+
+<span class="c1">// Train model.  This also runs the indexer.</span>
+<span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="n">pipeline</span><span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">trainingData</span><span class="o">)</span>
+
+<span class="c1">// Make predictions.</span>
+<span class="k">val</span> <span class="n">predictions</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">transform</span><span class="o">(</span><span class="n">testData</span><span class="o">)</span>
+
+<span class="c1">// Select example rows to display.</span>
+<span class="n">predictions</span><span class="o">.</span><span class="n">select</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">,</span> <span class="s">&quot;label&quot;</span><span class="o">,</span> <span class="s">&quot;features&quot;</span><span class="o">).</span><span class="n">show</span><span class="o">(</span><span class="mi">5</span><span class="o">)</span>
+
+<span class="c1">// Select (prediction, true label) and compute test error</span>
+<span class="k">val</span> <span class="n">evaluator</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">RegressionEvaluator</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setLabelCol</span><span class="o">(</span><span class="s">&quot;label&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setPredictionCol</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setMetricName</span><span class="o">(</span><span class="s">&quot;rmse&quot;</span><span class="o">)</span>
+<span class="k">val</span> <span class="n">rmse</span> <span class="k">=</span> <span class="n">evaluator</span><span class="o">.</span><span class="n">evaluate</span><span class="o">(</span><span class="n">predictions</span><span class="o">)</span>
+<span class="n">println</span><span class="o">(</span><span class="s">&quot;Root Mean Squared Error (RMSE) on test data = &quot;</span> <span class="o">+</span> <span class="n">rmse</span><span class="o">)</span>
+
+<span class="k">val</span> <span class="n">gbtModel</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">stages</span><span class="o">(</span><span class="mi">1</span><span class="o">).</span><span class="n">asInstanceOf</span><span class="o">[</span><span class="kt">GBTRegressionModel</span><span class="o">]</span>
+<span class="n">println</span><span class="o">(</span><span class="s">&quot;Learned regression GBT model:\n&quot;</span> <span class="o">+</span> <span class="n">gbtModel</span><span class="o">.</span><span class="n">toDebugString</span><span class="o">)</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/GradientBoostedTreeRegressorExample.scala" in the Spark repo.</small></div>
+  </div>
+
+<div data-lang="java">
+
+    <p>Refer to the <a href="api/java/org/apache/spark/ml/regression/GBTRegressor.html">Java API docs</a> for more details.</p>
+
+    <div class="highlight"><pre><span class="kn">import</span> <span class="nn">org.apache.spark.ml.Pipeline</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.PipelineModel</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.PipelineStage</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.evaluation.RegressionEvaluator</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.feature.VectorIndexer</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.feature.VectorIndexerModel</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.regression.GBTRegressionModel</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.regression.GBTRegressor</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.DataFrame</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.SQLContext</span><span class="o">;</span>
+
+<span class="c1">// Load and parse the data file, converting it to a DataFrame.</span>
+<span class="n">DataFrame</span> <span class="n">data</span> <span class="o">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="na">read</span><span class="o">().</span><span class="na">format</span><span class="o">(</span><span class="s">&quot;libsvm&quot;</span><span class="o">).</span><span class="na">load</span><span class="o">(</span><span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="o">);</span>
+
+<span class="c1">// Automatically identify categorical features, and index them.</span>
+<span class="c1">// Set maxCategories so features with &gt; 4 distinct values are treated as continuous.</span>
+<span class="n">VectorIndexerModel</span> <span class="n">featureIndexer</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">VectorIndexer</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setInputCol</span><span class="o">(</span><span class="s">&quot;features&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setOutputCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setMaxCategories</span><span class="o">(</span><span class="mi">4</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">data</span><span class="o">);</span>
+
+<span class="c1">// Split the data into training and test sets (30% held out for testing)</span>
+<span class="n">DataFrame</span><span class="o">[]</span> <span class="n">splits</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="na">randomSplit</span><span class="o">(</span><span class="k">new</span> <span class="kt">double</span><span class="o">[]</span> <span class="o">{</span><span class="mf">0.7</span><span class="o">,</span> <span class="mf">0.3</span><span class="o">});</span>
+<span class="n">DataFrame</span> <span class="n">trainingData</span> <span class="o">=</span> <span class="n">splits</span><span class="o">[</span><span class="mi">0</span><span class="o">];</span>
+<span class="n">DataFrame</span> <span class="n">testData</span> <span class="o">=</span> <span class="n">splits</span><span class="o">[</span><span class="mi">1</span><span class="o">];</span>
+
+<span class="c1">// Train a GBT model.</span>
+<span class="n">GBTRegressor</span> <span class="n">gbt</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">GBTRegressor</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setLabelCol</span><span class="o">(</span><span class="s">&quot;label&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setFeaturesCol</span><span class="o">(</span><span class="s">&quot;indexedFeatures&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setMaxIter</span><span class="o">(</span><span class="mi">10</span><span class="o">);</span>
+
+<span class="c1">// Chain indexer and GBT in a Pipeline</span>
+<span class="n">Pipeline</span> <span class="n">pipeline</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">Pipeline</span><span class="o">().</span><span class="na">setStages</span><span class="o">(</span><span class="k">new</span> <span class="n">PipelineStage</span><span class="o">[]</span> <span class="o">{</span><span class="n">featureIndexer</span><span class="o">,</span> <span class="n">gbt</span><span class="o">});</span>
+
+<span class="c1">// Train model.  This also runs the indexer.</span>
+<span class="n">PipelineModel</span> <span class="n">model</span> <span class="o">=</span> <span class="n">pipeline</span><span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">trainingData</span><span class="o">);</span>
+
+<span class="c1">// Make predictions.</span>
+<span class="n">DataFrame</span> <span class="n">predictions</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="na">transform</span><span class="o">(</span><span class="n">testData</span><span class="o">);</span>
+
+<span class="c1">// Select example rows to display.</span>
+<span class="n">predictions</span><span class="o">.</span><span class="na">select</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">,</span> <span class="s">&quot;label&quot;</span><span class="o">,</span> <span class="s">&quot;features&quot;</span><span class="o">).</span><span class="na">show</span><span class="o">(</span><span class="mi">5</span><span class="o">);</span>
+
+<span class="c1">// Select (prediction, true label) and compute test error</span>
+<span class="n">RegressionEvaluator</span> <span class="n">evaluator</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">RegressionEvaluator</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setLabelCol</span><span class="o">(</span><span class="s">&quot;label&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setPredictionCol</span><span class="o">(</span><span class="s">&quot;prediction&quot;</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setMetricName</span><span class="o">(</span><span class="s">&quot;rmse&quot;</span><span class="o">);</span>
+<span class="kt">double</span> <span class="n">rmse</span> <span class="o">=</span> <span class="n">evaluator</span><span class="o">.</span><span class="na">evaluate</span><span class="o">(</span><span class="n">predictions</span><span class="o">);</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;Root Mean Squared Error (RMSE) on test data = &quot;</span> <span class="o">+</span> <span class="n">rmse</span><span class="o">);</span>
+
+<span class="n">GBTRegressionModel</span> <span class="n">gbtModel</span> <span class="o">=</span> <span class="o">(</span><span class="n">GBTRegressionModel</span><span class="o">)(</span><span class="n">model</span><span class="o">.</span><span class="na">stages</span><span class="o">()[</span><span class="mi">1</span><span class="o">]);</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;Learned regression GBT model:\n&quot;</span> <span class="o">+</span> <span class="n">gbtModel</span><span class="o">.</span><span class="na">toDebugString</span><span class="o">());</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaGradientBoostedTreeRegressorExample.java" in the Spark repo.</small></div>
+  </div>
+
+<div data-lang="python">
+
+    <p>Refer to the <a href="api/python/pyspark.ml.html#pyspark.ml.regression.GBTRegressor">Python API docs</a> for more details.</p>
+
+    <div class="highlight"><pre><span class="kn">from</span> <span class="nn">pyspark.ml</span> <span class="kn">import</span> <span class="n">Pipeline</span>
+<span class="kn">from</span> <span class="nn">pyspark.ml.regression</span> <span class="kn">import</span> <span class="n">GBTRegressor</span>
+<span class="kn">from</span> <span class="nn">pyspark.ml.feature</span> <span class="kn">import</span> <span class="n">VectorIndexer</span>
+<span class="kn">from</span> <span class="nn">pyspark.ml.evaluation</span> <span class="kn">import</span> <span class="n">RegressionEvaluator</span>
+
+<span class="c"># Load and parse the data file, converting it to a DataFrame.</span>
+<span class="n">data</span> <span class="o">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="n">read</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="s">&quot;libsvm&quot;</span><span class="p">)</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="p">)</span>
+
+<span class="c"># Automatically identify categorical features, and index them.</span>
+<span class="c"># Set maxCategories so features with &gt; 4 distinct values are treated as continuous.</span>
+<span class="n">featureIndexer</span> <span class="o">=</span>\
+    <span class="n">VectorIndexer</span><span class="p">(</span><span class="n">inputCol</span><span class="o">=</span><span class="s">&quot;features&quot;</span><span class="p">,</span> <span class="n">outputCol</span><span class="o">=</span><span class="s">&quot;indexedFeatures&quot;</span><span class="p">,</span> <span class="n">maxCategories</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
+
+<span class="c"># Split the data into training and test sets (30% held out for testing)</span>
+<span class="p">(</span><span class="n">trainingData</span><span class="p">,</span> <span class="n">testData</span><span class="p">)</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">randomSplit</span><span class="p">([</span><span class="mf">0.7</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">])</span>
+
+<span class="c"># Train a GBT model.</span>
+<span class="n">gbt</span> <span class="o">=</span> <span class="n">GBTRegressor</span><span class="p">(</span><span class="n">featuresCol</span><span class="o">=</span><span class="s">&quot;indexedFeatures&quot;</span><span class="p">,</span> <span class="n">maxIter</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
+
+<span class="c"># Chain indexer and GBT in a Pipeline</span>
+<span class="n">pipeline</span> <span class="o">=</span> <span class="n">Pipeline</span><span class="p">(</span><span class="n">stages</span><span class="o">=</span><span class="p">[</span><span class="n">featureIndexer</span><span class="p">,</span> <span class="n">gbt</span><span class="p">])</span>
+
+<span class="c"># Train model.  This also runs the indexer.</span>
+<span class="n">model</span> <span class="o">=</span> <span class="n">pipeline</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">trainingData</span><span class="p">)</span>
+
+<span class="c"># Make predictions.</span>
+<span class="n">predictions</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">testData</span><span class="p">)</span>
+
+<span class="c"># Select example rows to display.</span>
+<span class="n">predictions</span><span class="o">.</span><span class="n">select</span><span class="p">(</span><span class="s">&quot;prediction&quot;</span><span class="p">,</span> <span class="s">&quot;label&quot;</span><span class="p">,</span> <span class="s">&quot;features&quot;</span><span class="p">)</span><span class="o">.</span><span class="n">show</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+
+<span class="c"># Select (prediction, true label) and compute test error</span>
+<span class="n">evaluator</span> <span class="o">=</span> <span class="n">RegressionEvaluator</span><span class="p">(</span>
+    <span class="n">labelCol</span><span class="o">=</span><span class="s">&quot;label&quot;</span><span class="p">,</span> <span class="n">predictionCol</span><span class="o">=</span><span class="s">&quot;prediction&quot;</span><span class="p">,</span> <span class="n">metricName</span><span class="o">=</span><span class="s">&quot;rmse&quot;</span><span class="p">)</span>
+<span class="n">rmse</span> <span class="o">=</span> <span class="n">evaluator</span><span class="o">.</span><span class="n">evaluate</span><span class="p">(</span><span class="n">predictions</span><span class="p">)</span>
+<span class="k">print</span><span class="p">(</span><span class="s">&quot;Root Mean Squared Error (RMSE) on test data = </span><span class="si">%g</span><span class="s">&quot;</span> <span class="o">%</span> <span class="n">rmse</span><span class="p">)</span>
+
+<span class="n">gbtModel</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">stages</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+<span class="k">print</span><span class="p">(</span><span class="n">gbtModel</span><span class="p">)</span>  <span class="c"># summary only</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/python/ml/gradient_boosted_tree_regressor_example.py" in the Spark repo.</small></div>
+  </div>
+</div>
+
+<h2 id="survival-regression">Survival regression</h2>
+
+<p>In <code>spark.ml</code>, we implement the <a href="https://en.wikipedia.org/wiki/Accelerated_failure_time_model">Accelerated failure time (AFT)</a> 
+model which is a parametric survival regression model for censored data. 
+It describes a model for the log of survival time, so it&#8217;s often called 
+log-linear model for survival analysis. Different from 
+<a href="https://en.wikipedia.org/wiki/Proportional_hazards_model">Proportional hazards</a> model
+designed for the same purpose, the AFT model is more easily to parallelize 
+because each instance contribute to the objective function independently.</p>
+
+<p>Given the values of the covariates $x^{&#8216;}$, for random lifetime $t_{i}$ of 
+subjects i = 1, &#8230;, n, with possible right-censoring, 
+the likelihood function under the AFT model is given as:
+<code>\[
+L(\beta,\sigma)=\prod_{i=1}^n[\frac{1}{\sigma}f_{0}(\frac{\log{t_{i}}-x^{'}\beta}{\sigma})]^{\delta_{i}}S_{0}(\frac{\log{t_{i}}-x^{'}\beta}{\sigma})^{1-\delta_{i}}
+\]</code>
+Where $\delta_{i}$ is the indicator of the event has occurred i.e. uncensored or not.
+Using $\epsilon_{i}=\frac{\log{t_{i}}-x^{&#8216;}\beta}{\sigma}$, the log-likelihood function
+assumes the form:
+<code>\[
+\iota(\beta,\sigma)=\sum_{i=1}^{n}[-\delta_{i}\log\sigma+\delta_{i}\log{f_{0}}(\epsilon_{i})+(1-\delta_{i})\log{S_{0}(\epsilon_{i})}]
+\]</code>
+Where $S_{0}(\epsilon_{i})$ is the baseline survivor function,
+and $f_{0}(\epsilon_{i})$ is corresponding density function.</p>
+
+<p>The most commonly used AFT model is based on the Weibull distribution of the survival time. 
+The Weibull distribution for lifetime corresponding to extreme value distribution for 
+log of the lifetime, and the $S_{0}(\epsilon)$ function is:
+<code>\[   
+S_{0}(\epsilon_{i})=\exp(-e^{\epsilon_{i}})
+\]</code>
+the $f_{0}(\epsilon_{i})$ function is:
+<code>\[
+f_{0}(\epsilon_{i})=e^{\epsilon_{i}}\exp(-e^{\epsilon_{i}})
+\]</code>
+The log-likelihood function for AFT model with Weibull distribution of lifetime is:
+<code>\[
+\iota(\beta,\sigma)= -\sum_{i=1}^n[\delta_{i}\log\sigma-\delta_{i}\epsilon_{i}+e^{\epsilon_{i}}]
+\]</code>
+Due to minimizing the negative log-likelihood equivalent to maximum a posteriori probability,
+the loss function we use to optimize is $-\iota(\beta,\sigma)$.
+The gradient functions for $\beta$ and $\log\sigma$ respectively are:
+<code>\[   
+\frac{\partial (-\iota)}{\partial \beta}=\sum_{1=1}^{n}[\delta_{i}-e^{\epsilon_{i}}]\frac{x_{i}}{\sigma}
+\]</code>
+<code>\[ 
+\frac{\partial (-\iota)}{\partial (\log\sigma)}=\sum_{i=1}^{n}[\delta_{i}+(\delta_{i}-e^{\epsilon_{i}})\epsilon_{i}]
+\]</code></p>
+
+<p>The AFT model can be formulated as a convex optimization problem, 
+i.e. the task of finding a minimizer of a convex function $-\iota(\beta,\sigma)$ 
+that depends coefficients vector $\beta$ and the log of scale parameter $\log\sigma$.
+The optimization algorithm underlying the implementation is L-BFGS.
+The implementation matches the result from R&#8217;s survival function 
+<a href="https://stat.ethz.ch/R-manual/R-devel/library/survival/html/survreg.html">survreg</a></p>
+
+<p><strong>Example</strong></p>
+
+<div class="codetabs">
+
+<div data-lang="scala">
+    <div class="highlight"><pre><span class="k">import</span> <span class="nn">org.apache.spark.ml.regression.AFTSurvivalRegression</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vectors</span>
+
+<span class="k">val</span> <span class="n">training</span> <span class="k">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="n">createDataFrame</span><span class="o">(</span><span class="nc">Seq</span><span class="o">(</span>
+  <span class="o">(</span><span class="mf">1.218</span><span class="o">,</span> <span class="mf">1.0</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="o">(</span><span class="mf">1.560</span><span class="o">,</span> <span class="o">-</span><span class="mf">0.605</span><span class="o">)),</span>
+  <span class="o">(</span><span class="mf">2.949</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="o">(</span><span class="mf">0.346</span><span class="o">,</span> <span class="mf">2.158</span><span class="o">)),</span>
+  <span class="o">(</span><span class="mf">3.627</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="o">(</span><span class="mf">1.380</span><span class="o">,</span> <span class="mf">0.231</span><span class="o">)),</span>
+  <span class="o">(</span><span class="mf">0.273</span><span class="o">,</span> <span class="mf">1.0</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="o">(</span><span class="mf">0.520</span><span class="o">,</span> <span class="mf">1.151</span><span class="o">)),</span>
+  <span class="o">(</span><span class="mf">4.199</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="o">(</span><span class="mf">0.795</span><span class="o">,</span> <span class="o">-</span><span class="mf">0.226</span><span class="o">))</span>
+<span class="o">)).</span><span class="n">toDF</span><span class="o">(</span><span class="s">&quot;label&quot;</span><span class="o">,</span> <span class="s">&quot;censor&quot;</span><span class="o">,</span> <span class="s">&quot;features&quot;</span><span class="o">)</span>
+<span class="k">val</span> <span class="n">quantileProbabilities</span> <span class="k">=</span> <span class="nc">Array</span><span class="o">(</span><span class="mf">0.3</span><span class="o">,</span> <span class="mf">0.6</span><span class="o">)</span>
+<span class="k">val</span> <span class="n">aft</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">AFTSurvivalRegression</span><span class="o">()</span>
+  <span class="o">.</span><span class="n">setQuantileProbabilities</span><span class="o">(</span><span class="n">quantileProbabilities</span><span class="o">)</span>
+  <span class="o">.</span><span class="n">setQuantilesCol</span><span class="o">(</span><span class="s">&quot;quantiles&quot;</span><span class="o">)</span>
+
+<span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="n">aft</span><span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">training</span><span class="o">)</span>
+
+<span class="c1">// Print the coefficients, intercept and scale parameter for AFT survival regression</span>
+<span class="n">println</span><span class="o">(</span><span class="n">s</span><span class="s">&quot;Coefficients: ${model.coefficients} Intercept: &quot;</span> <span class="o">+</span>
+  <span class="n">s</span><span class="s">&quot;${model.intercept} Scale: ${model.scale}&quot;</span><span class="o">)</span>
+<span class="n">model</span><span class="o">.</span><span class="n">transform</span><span class="o">(</span><span class="n">training</span><span class="o">).</span><span class="n">show</span><span class="o">(</span><span class="kc">false</span><span class="o">)</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/AFTSurvivalRegressionExample.scala" in the Spark repo.</small></div>
+  </div>
+
+<div data-lang="java">
+    <div class="highlight"><pre><span class="kn">import</span> <span class="nn">java.util.Arrays</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">java.util.List</span><span class="o">;</span>
+
+<span class="kn">import</span> <span class="nn">org.apache.spark.SparkConf</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaSparkContext</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.regression.AFTSurvivalRegression</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.ml.regression.AFTSurvivalRegressionModel</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.*</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.DataFrame</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.Row</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.RowFactory</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.SQLContext</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.sql.types.*</span><span class="o">;</span>
+
+<span class="n">List</span><span class="o">&lt;</span><span class="n">Row</span><span class="o">&gt;</span> <span class="n">data</span> <span class="o">=</span> <span class="n">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span>
+  <span class="n">RowFactory</span><span class="o">.</span><span class="na">create</span><span class="o">(</span><span class="mf">1.218</span><span class="o">,</span> <span class="mf">1.0</span><span class="o">,</span> <span class="n">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">1.560</span><span class="o">,</span> <span class="o">-</span><span class="mf">0.605</span><span class="o">)),</span>
+  <span class="n">RowFactory</span><span class="o">.</span><span class="na">create</span><span class="o">(</span><span class="mf">2.949</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">,</span> <span class="n">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">0.346</span><span class="o">,</span> <span class="mf">2.158</span><span class="o">)),</span>
+  <span class="n">RowFactory</span><span class="o">.</span><span class="na">create</span><span class="o">(</span><span class="mf">3.627</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">,</span> <span class="n">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">1.380</span><span class="o">,</span> <span class="mf">0.231</span><span class="o">)),</span>
+  <span class="n">RowFactory</span><span class="o">.</span><span class="na">create</span><span class="o">(</span><span class="mf">0.273</span><span class="o">,</span> <span class="mf">1.0</span><span class="o">,</span> <span class="n">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">0.520</span><span class="o">,</span> <span class="mf">1.151</span><span class="o">)),</span>
+  <span class="n">RowFactory</span><span class="o">.</span><span class="na">create</span><span class="o">(</span><span class="mf">4.199</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">,</span> <span class="n">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">0.795</span><span class="o">,</span> <span class="o">-</span><span class="mf">0.226</span><span class="o">))</span>
+<span class="o">);</span>
+<span class="n">StructType</span> <span class="n">schema</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">StructType</span><span class="o">(</span><span class="k">new</span> <span class="n">StructField</span><span class="o">[]{</span>
+  <span class="k">new</span> <span class="nf">StructField</span><span class="o">(</span><span class="s">&quot;label&quot;</span><span class="o">,</span> <span class="n">DataTypes</span><span class="o">.</span><span class="na">DoubleType</span><span class="o">,</span> <span class="kc">false</span><span class="o">,</span> <span class="n">Metadata</span><span class="o">.</span><span class="na">empty</span><span class="o">()),</span>
+  <span class="k">new</span> <span class="nf">StructField</span><span class="o">(</span><span class="s">&quot;censor&quot;</span><span class="o">,</span> <span class="n">DataTypes</span><span class="o">.</span><span class="na">DoubleType</span><span class="o">,</span> <span class="kc">false</span><span class="o">,</span> <span class="n">Metadata</span><span class="o">.</span><span class="na">empty</span><span class="o">()),</span>
+  <span class="k">new</span> <span class="nf">StructField</span><span class="o">(</span><span class="s">&quot;features&quot;</span><span class="o">,</span> <span class="k">new</span> <span class="nf">VectorUDT</span><span class="o">(),</span> <span class="kc">false</span><span class="o">,</span> <span class="n">Metadata</span><span class="o">.</span><span class="na">empty</span><span class="o">())</span>
+<span class="o">});</span>
+<span class="n">DataFrame</span> <span class="n">training</span> <span class="o">=</span> <span class="n">jsql</span><span class="o">.</span><span class="na">createDataFrame</span><span class="o">(</span><span class="n">data</span><span class="o">,</span> <span class="n">schema</span><span class="o">);</span>
+<span class="kt">double</span><span class="o">[]</span> <span class="n">quantileProbabilities</span> <span class="o">=</span> <span class="k">new</span> <span class="kt">double</span><span class="o">[]{</span><span class="mf">0.3</span><span class="o">,</span> <span class="mf">0.6</span><span class="o">};</span>
+<span class="n">AFTSurvivalRegression</span> <span class="n">aft</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">AFTSurvivalRegression</span><span class="o">()</span>
+  <span class="o">.</span><span class="na">setQuantileProbabilities</span><span class="o">(</span><span class="n">quantileProbabilities</span><span class="o">)</span>
+  <span class="o">.</span><span class="na">setQuantilesCol</span><span class="o">(</span><span class="s">&quot;quantiles&quot;</span><span class="o">);</span>
+
+<span class="n">AFTSurvivalRegressionModel</span> <span class="n">model</span> <span class="o">=</span> <span class="n">aft</span><span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">training</span><span class="o">);</span>
+
+<span class="c1">// Print the coefficients, intercept and scale parameter for AFT survival regression</span>
+<span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">&quot;Coefficients: &quot;</span> <span class="o">+</span> <span class="n">model</span><span class="o">.</span><span class="na">coefficients</span><span class="o">()</span> <span class="o">+</span> <span class="s">&quot; Intercept: &quot;</span>
+  <span class="o">+</span> <span class="n">model</span><span class="o">.</span><span class="na">intercept</span><span class="o">()</span> <span class="o">+</span> <span class="s">&quot; Scale: &quot;</span> <span class="o">+</span> <span class="n">model</span><span class="o">.</span><span class="na">scale</span><span class="o">());</span>
+<span class="n">model</span><span class="o">.</span><span class="na">transform</span><span class="o">(</span><span class="n">training</span><span class="o">).</span><span class="na">show</span><span class="o">(</span><span class="kc">false</span><span class="o">);</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaAFTSurvivalRegressionExample.java" in the Spark repo.</small></div>
+  </div>
+
+<div data-lang="python">
+    <div class="highlight"><pre><span class="kn">from</span> <span class="nn">pyspark.ml.regression</span> <span class="kn">import</span> <span class="n">AFTSurvivalRegression</span>
+<span class="kn">from</span> <span class="nn">pyspark.mllib.linalg</span> <span class="kn">import</span> <span class="n">Vectors</span>
+
+<span class="n">training</span> <span class="o">=</span> <span class="n">sqlContext</span><span class="o">.</span><span class="n">createDataFrame</span><span class="p">([</span>
+    <span class="p">(</span><span class="mf">1.218</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="n">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="p">(</span><span class="mf">1.560</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.605</span><span class="p">)),</span>
+    <span class="p">(</span><span class="mf">2.949</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="n">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="p">(</span><span class="mf">0.346</span><span class="p">,</span> <span class="mf">2.158</span><span class="p">)),</span>
+    <span class="p">(</span><span class="mf">3.627</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="n">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="p">(</span><span class="mf">1.380</span><span class="p">,</span> <span class="mf">0.231</span><span class="p">)),</span>
+    <span class="p">(</span><span class="mf">0.273</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="n">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="p">(</span><span class="mf">0.520</span><span class="p">,</span> <span class="mf">1.151</span><span class="p">)),</span>
+    <span class="p">(</span><span class="mf">4.199</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="n">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="p">(</span><span class="mf">0.795</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.226</span><span class="p">))],</span> <span class="p">[</span><span class="s">&quot;label&quot;</span><span class="p">,</span> <span class="s">&quot;censor&quot;</span><span class="p">,</span> <span class="s">&quot;features&quot;</span><span class="p">])</span>
+<span class="n">quantileProbabilities</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.3</span><span class="p">,</span> <span class="mf">0.6</span><span class="p">]</span>
+<span class="n">aft</span> <span class="o">=</span> <span class="n">AFTSurvivalRegression</span><span class="p">(</span><span class="n">quantileProbabilities</span><span class="o">=</span><span class="n">quantileProbabilities</span><span class="p">,</span>
+                            <span class="n">quantilesCol</span><span class="o">=</span><span class="s">&quot;quantiles&quot;</span><span class="p">)</span>
+
+<span class="n">model</span> <span class="o">=</span> <span class="n">aft</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">training</span><span class="p">)</span>
+
+<span class="c"># Print the coefficients, intercept and scale parameter for AFT survival regression</span>
+<span class="k">print</span><span class="p">(</span><span class="s">&quot;Coefficients: &quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">coefficients</span><span class="p">))</span>
+<span class="k">print</span><span class="p">(</span><span class="s">&quot;Intercept: &quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">intercept</span><span class="p">))</span>
+<span class="k">print</span><span class="p">(</span><span class="s">&quot;Scale: &quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">scale</span><span class="p">))</span>
+<span class="n">model</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">training</span><span class="p">)</span><span class="o">.</span><span class="n">show</span><span class="p">(</span><span class="n">truncate</span><span class="o">=</span><span class="bp">False</span><span class="p">)</span>
+</pre></div>
+    <div><small>Find full example code at "examples/src/main/python/ml/aft_survival_regression.py" in the Spark repo.</small></div>
+  </div>
+
+</div>
+
+<h1 id="decision-trees">Decision trees</h1>
+
+<p><a href="http://en.wikipedia.org/wiki/Decision_tree_learning">Decision trees</a>
+and their ensembles are popular methods for the machine learning tasks of
+classification and regression. Decision trees are widely used since they are easy to interpret,
+handle categorical features, extend to the multiclass classification setting, do not require
+feature scaling, and are able to capture non-linearities and feature interactions. Tree ensemble
+algorithms such as random forests and boosting are among the top performers for classification and
+regression tasks.</p>
+
+<p>The <code>spark.ml</code> implementation supports decision trees for binary and multiclass classification and for regression,
+using both continuous and categorical features. The implementation partitions data by rows,
+allowing distributed training with millions or even billions of instances.</p>
+
+<p>Users can find more information about the decision tree algorithm in the <a href="mllib-decision-tree.html">MLlib Decision Tree guide</a>.
+The main differences between this API and the <a href="mllib-decision-tree.html">original MLlib Decision Tree API</a> are:</p>
+
+<ul>
+  <li>support for ML Pipelines</li>
+  <li>separation of Decision Trees for classification vs. regression</li>
+  <li>use of DataFrame metadata to distinguish continuous and categorical features</li>
+</ul>
+
+<p>The Pipelines API for Decision Trees offers a bit more functionality than the original API.  In particular, for classification, users can get the predicted probability of each class (a.k.a. class conditional probabilities).</p>
+
+<p>Ensembles of trees (Random Forests and Gradient-Boosted Trees) are described below in the <a href="#tree-ensembles">Tree ensembles section</a>.</p>
+
+<h2 id="inputs-and-outputs">Inputs and Outputs</h2>
+
+<p>We list the input and output (prediction) column types here.
+All output columns are optional; to exclude an output column, set its corresponding Param to an empty string.</p>
+
+<h3 id="input-columns">Input Columns</h3>
+
+<table class="table">
+  <thead>
+    <tr>
+      <th align="left">Param name</th>
+      <th align="left">Type(s)</th>
+      <th align="left">Default</th>
+      <th align="left">Description</th>
+    </tr>
+  </thead>
+  <tbody>
+    <tr>
+      <td>labelCol</td>
+      <td>Double</td>
+      <td>"label"</td>
+      <td>Label to predict</td>
+    </tr>
+    <tr>
+      <td>featuresCol</td>
+      <td>Vector</td>
+      <td>"features"</td>
+      <td>Feature vector</td>
+    </tr>
+  </tbody>
+</table>
+
+<h3 id="output-columns">Output Columns</h3>
+
+<table class="table">
+  <thead>
+    <tr>
+      <th align="left">Param name</th>
+      <th align="left">Type(s)</th>
+      <th align="left">Default</th>
+      <th align="left">Description</th>
+      <th align="left">Notes</th>
+    </tr>
+  </thead>
+  <tbody>
+    <tr>
+      <td>predictionCol</td>
+      <td>Double</td>
+      <td>"prediction"</td>
+      <td>Predicted label</td>
+      <td></td>
+    </tr>
+    <tr>
+      <td>rawPredictionCol</td>
+      <td>Vector</td>
+      <td>"rawPrediction"</td>
+      <td>Vector of length # classes, with the counts of training instance labels at the tree node which makes the prediction</td>
+      <td>Classification only</td>
+    </tr>
+    <tr>
+      <td>probabilityCol</td>
+      <td>Vector</td>
+      <td>"probability"</td>
+      <td>Vector of length # classes equal to rawPrediction normalized to a multinomial distribution</td>
+      <td>Classification only</td>
+    </tr>
+  </tbody>
+</table>
+
+<h1 id="tree-ensembles">Tree Ensembles</h1>
+
+<p>The DataFrame API supports two major tree ensemble algorithms: <a href="http://en.wikipedia.org/wiki/Random_forest">Random Forests</a> and <a href="http://en.wikipedia.org/wiki/Gradient_boosting">Gradient-Boosted Trees (GBTs)</a>.
+Both use <a href="ml-classification-regression.html#decision-trees"><code>spark.ml</code> decision trees</a> as their base models.</p>
+
+<p>Users can find more information about ensemble algorithms in the <a href="mllib-ensembles.html">MLlib Ensemble guide</a>.<br />
+In this section, we demonstrate the DataFrame API for ensembles.</p>
+
+<p>The main differences between this API and the <a href="mllib-ensembles.html">original MLlib ensembles API</a> are:</p>
+
+<ul>
+  <li>support for DataFrames and ML Pipelines</li>
+  <li>separation of classification vs. regression</li>
+  <li>use of DataFrame metadata to distinguish continuous and categorical features</li>
+  <li>more functionality for random forests: estimates of feature importance, as well as the predicted probability of each class (a.k.a. class conditional probabilities) for classification.</li>
+</ul>
+
+<h2 id="random-forests">Random Forests</h2>
+
+<p><a href="http://en.wikipedia.org/wiki/Random_forest">Random forests</a>
+are ensembles of <a href="ml-decision-tree.html">decision trees</a>.
+Random forests combine many decision trees in order to reduce the risk of overfitting.
+The <code>spark.ml</code> implementation supports random forests for binary and multiclass classification and for regression,
+using both continuous and categorical features.</p>
+
+<p>For more information on the algorithm itself, please see the <a href="mllib-ensembles.html"><code>spark.mllib</code> documentation on random forests</a>.</p>
+
+<h3 id="inputs-and-outputs-1">Inputs and Outputs</h3>
+
+<p>We list the input and output (prediction) column types here.
+All output columns are optional; to exclude an output column, set its corresponding Param to an empty string.</p>
+
+<h4 id="input-columns-1">Input Columns</h4>
+
+<table class="table">
+  <thead>
+    <tr>
+      <th align="left">Param name</th>
+      <th align="left">Type(s)</th>
+      <th align="left">Default</th>
+      <th align="left">Description</th>
+    </tr>
+  </thead>
+  <tbody>
+    <tr>
+      <td>labelCol</td>
+      <td>Double</td>
+      <td>"label"</td>
+      <td>Label to predict</td>
+    </tr>
+    <tr>
+      <td>featuresCol</td>
+      <td>Vector</td>
+      <td>"features"</td>
+      <td>Feature vector</td>
+    </tr>
+  </tbody>
+</table>
+
+<h4 id="output-columns-predictions">Output Columns (Predictions)</h4>
+
+<table class="table">
+  <thead>
+    <tr>
+      <th align="left">Param name</th>
+      <th align="left">Type(s)</th>
+      <th align="left">Default</th>
+      <th align="left">Description</th>
+      <th align="left">Notes</th>
+    </tr>
+  </thead>
+  <tbody>
+    <tr>
+      <td>predictionCol</td>
+      <td>Double</td>
+      <td>"prediction"</td>
+      <td>Predicted label</td>
+      <td></td>
+    </tr>
+    <tr>
+      <td>rawPredictionCol</td>
+      <td>Vector</td>
+      <td>"rawPrediction"</td>
+      <td>Vector of length # classes, with the counts of training instance labels at the tree node which makes the prediction</td>
+      <td>Classification only</td>
+    </tr>
+    <tr>
+      <td>probabilityCol</td>
+      <td>Vector</td>
+      <td>"probability"</td>
+      <td>Vector of length # classes equal to rawPrediction normalized to a multinomial distribution</td>
+      <td>Classification only</td>
+    </tr>
+  </tbody>
+</table>
+
+<h2 id="gradient-boosted-trees-gbts">Gradient-Boosted Trees (GBTs)</h2>
+
+<p><a href="http://en.wikipedia.org/wiki/Gradient_boosting">Gradient-Boosted Trees (GBTs)</a>
+are ensembles of <a href="ml-decision-tree.html">decision trees</a>.
+GBTs iteratively train decision trees in order to minimize a loss function.
+The <code>spark.ml</code> implementation supports GBTs for binary classification and for regression,
+using both continuous and categorical features.</p>
+
+<p>For more information on the algorithm itself, please see the <a href="mllib-ensembles.html"><code>spark.mllib</code> documentation on GBTs</a>.</p>
+
+<h3 id="inputs-and-outputs-2">Inputs and Outputs</h3>
+
+<p>We list the input and output (prediction) column types here.
+All output columns are optional; to exclude an output column, set its corresponding Param to an empty string.</p>
+
+<h4 id="input-columns-2">Input Columns</h4>
+
+<table class="table">
+  <thead>
+    <tr>
+      <th align="left">Param name</th>
+      <th align="left">Type(s)</th>
+      <th align="left">Default</th>
+      <th align="left">Description</th>
+    </tr>
+  </thead>
+  <tbody>
+    <tr>
+      <td>labelCol</td>
+      <td>Double</td>
+      <td>"label"</td>
+      <td>Label to predict</td>
+    </tr>
+    <tr>
+      <td>featuresCol</td>
+      <td>Vector</td>
+      <td>"features"</td>
+      <td>Feature vector</td>
+    </tr>
+  </tbody>
+</table>
+
+<p>Note that <code>GBTClassifier</code> currently only supports binary labels.</p>
+
+<h4 id="output-columns-predictions-1">Output Columns (Predictions)</h4>
+
+<table class="table">
+  <thead>
+    <tr>
+      <th align="left">Param name</th>
+      <th align="left">Type(s)</th>
+      <th align="left">Default</th>
+      <th align="left">Description</th>
+      <th align="left">Notes</th>
+    </tr>
+  </thead>
+  <tbody>
+    <tr>
+      <td>predictionCol</td>
+      <td>Double</td>
+      <td>"prediction"</td>
+      <td>Predicted label</td>
+      <td></td>
+    </tr>
+  </tbody>
+</table>
+
+<p>In the future, <code>GBTClassifier</code> will also output columns for <code>rawPrediction</code> and <code>probability</code>, just as <code>RandomForestClassifier</code> does.</p>
+
+
+
+                </div>
+            
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author	Michael Armbrust <marmbrus@apache.org>	2016-01-04 17:53:21 +0000
committer	Michael Armbrust <marmbrus@apache.org>	2016-01-04 17:53:21 +0000
commit	0d824b0442707b6842ef19a589cb8a2af997273b (patch)
tree	4ac1758b478ee6cb74382733fd3eb3157b6c3161 /site/docs/1.6.0/ml-classification-regression.html
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