add 1.5.0 back

author: Reynold Xin <rxin@apache.org> 2015-09-17 22:11:21 +0000
committer: Reynold Xin <rxin@apache.org> 2015-09-17 22:11:21 +0000
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tree: dbf7d7a7700e9e6bad3c8289ab831bc9c2c20d62 /site/docs/1.5.0/ml-linear-methods.html
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+          
+            <h1 class="title"><a href="ml-guide.html">ML</a> - Linear Methods</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>In MLlib, 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.  In <code>spark.ml</code>, we also include Pipelines 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>
+
+<h2 id="example-logistic-regression">Example: Logistic Regression</h2>
+
+<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><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.ml.classification.LogisticRegression</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.mllib.util.MLUtils</span>
+
+<span class="c1">// Load training data</span>
+<span class="k">val</span> <span class="n">training</span> <span class="k">=</span> <span class="nc">MLUtils</span><span class="o">.</span><span class="n">loadLibSVMFile</span><span class="o">(</span><span class="n">sc</span><span class="o">,</span> <span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="o">).</span><span class="n">toDF</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 weights and intercept for logistic regression</span>
+<span class="n">println</span><span class="o">(</span><span class="n">s</span><span class="s">&quot;Weights: ${lrModel.weights} Intercept: ${lrModel.intercept}&quot;</span><span class="o">)</span></code></pre></div>
+
+  </div>
+
+<div data-lang="java">
+
+    <div class="highlight"><pre><code class="language-java" data-lang="java"><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.mllib.regression.LabeledPoint</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.util.MLUtils</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.SparkContext</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="kd">public</span> <span class="kd">class</span> <span class="nc">LogisticRegressionWithElasticNetExample</span> <span class="o">{</span>
+  <span class="kd">public</span> <span class="kd">static</span> <span class="kt">void</span> <span class="nf">main</span><span class="o">(</span><span class="n">String</span><span class="o">[]</span> <span class="n">args</span><span class="o">)</span> <span class="o">{</span>
+    <span class="n">SparkConf</span> <span class="n">conf</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">SparkConf</span><span class="o">()</span>
+      <span class="o">.</span><span class="na">setAppName</span><span class="o">(</span><span class="s">&quot;Logistic Regression with Elastic Net Example&quot;</span><span class="o">);</span>
+
+    <span class="n">SparkContext</span> <span class="n">sc</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">SparkContext</span><span class="o">(</span><span class="n">conf</span><span class="o">);</span>
+    <span class="n">SQLContext</span> <span class="n">sql</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">SQLContext</span><span class="o">(</span><span class="n">sc</span><span class="o">);</span>
+    <span class="n">String</span> <span class="n">path</span> <span class="o">=</span> <span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</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">sql</span><span class="o">.</span><span class="na">createDataFrame</span><span class="o">(</span><span class="n">MLUtils</span><span class="o">.</span><span class="na">loadLibSVMFile</span><span class="o">(</span><span class="n">sc</span><span class="o">,</span> <span class="n">path</span><span class="o">).</span><span class="na">toJavaRDD</span><span class="o">(),</span> <span class="n">LabeledPoint</span><span class="o">.</span><span class="na">class</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 weights 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;Weights: &quot;</span> <span class="o">+</span> <span class="n">lrModel</span><span class="o">.</span><span class="na">weights</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="o">}</span>
+<span class="o">}</span></code></pre></div>
+
+  </div>
+
+<div data-lang="python">
+
+    <div class="highlight"><pre><code class="language-python" data-lang="python"><span class="kn">from</span> <span class="nn">pyspark.ml.classification</span> <span class="kn">import</span> <span class="n">LogisticRegression</span>
+<span class="kn">from</span> <span class="nn">pyspark.mllib.regression</span> <span class="kn">import</span> <span class="n">LabeledPoint</span>
+<span class="kn">from</span> <span class="nn">pyspark.mllib.util</span> <span class="kn">import</span> <span class="n">MLUtils</span>
+
+<span class="c"># Load training data</span>
+<span class="n">training</span> <span class="o">=</span> <span class="n">MLUtils</span><span class="o">.</span><span class="n">loadLibSVMFile</span><span class="p">(</span><span class="n">sc</span><span class="p">,</span> <span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="p">)</span><span class="o">.</span><span class="n">toDF</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 weights and intercept for logistic regression</span>
+<span class="k">print</span><span class="p">(</span><span class="s">&quot;Weights: &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">weights</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></code></pre></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><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.ml.classification.BinaryLogisticRegressionSummary</span>
+
+<span class="c1">// Extract the summary from the returned LogisticRegressionModel instance trained in the earlier 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="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></code></pre></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><code class="language-java" data-lang="java"><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.ml.classification.BinaryLogisticRegressionSummary</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 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</span>
+<span class="c1">// binary 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="n">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></code></pre></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="example-linear-regression">Example: Linear Regression</h2>
+
+<p>The interface for working with linear regression models and model
+summaries is similar to the logistic regression case. 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><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.ml.regression.LinearRegression</span>
+<span class="k">import</span> <span class="nn">org.apache.spark.mllib.util.MLUtils</span>
+
+<span class="c1">// Load training data</span>
+<span class="k">val</span> <span class="n">training</span> <span class="k">=</span> <span class="nc">MLUtils</span><span class="o">.</span><span class="n">loadLibSVMFile</span><span class="o">(</span><span class="n">sc</span><span class="o">,</span> <span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="o">).</span><span class="n">toDF</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 weights and intercept for linear regression</span>
+<span class="n">println</span><span class="o">(</span><span class="n">s</span><span class="s">&quot;Weights: ${lrModel.weights} 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></code></pre></div>
+
+  </div>
+
+<div data-lang="java">
+
+    <div class="highlight"><pre><code class="language-java" data-lang="java"><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.mllib.regression.LabeledPoint</span><span class="o">;</span>
+<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.util.MLUtils</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.SparkContext</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="kd">public</span> <span class="kd">class</span> <span class="nc">LinearRegressionWithElasticNetExample</span> <span class="o">{</span>
+  <span class="kd">public</span> <span class="kd">static</span> <span class="kt">void</span> <span class="nf">main</span><span class="o">(</span><span class="n">String</span><span class="o">[]</span> <span class="n">args</span><span class="o">)</span> <span class="o">{</span>
+    <span class="n">SparkConf</span> <span class="n">conf</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">SparkConf</span><span class="o">()</span>
+      <span class="o">.</span><span class="na">setAppName</span><span class="o">(</span><span class="s">&quot;Linear Regression with Elastic Net Example&quot;</span><span class="o">);</span>
+
+    <span class="n">SparkContext</span> <span class="n">sc</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">SparkContext</span><span class="o">(</span><span class="n">conf</span><span class="o">);</span>
+    <span class="n">SQLContext</span> <span class="n">sql</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">SQLContext</span><span class="o">(</span><span class="n">sc</span><span class="o">);</span>
+    <span class="n">String</span> <span class="n">path</span> <span class="o">=</span> <span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</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">sql</span><span class="o">.</span><span class="na">createDataFrame</span><span class="o">(</span><span class="n">MLUtils</span><span class="o">.</span><span class="na">loadLibSVMFile</span><span class="o">(</span><span class="n">sc</span><span class="o">,</span> <span class="n">path</span><span class="o">).</span><span class="na">toJavaRDD</span><span class="o">(),</span> <span class="n">LabeledPoint</span><span class="o">.</span><span class="na">class</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 weights 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;Weights: &quot;</span> <span class="o">+</span> <span class="n">lrModel</span><span class="o">.</span><span class="na">weights</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>
+  <span class="o">}</span>
+<span class="o">}</span></code></pre></div>
+
+  </div>
+
+<div data-lang="python">
+    <!--- TODO: Add python model summaries once implemented -->
+
+    <div class="highlight"><pre><code class="language-python" data-lang="python"><span class="kn">from</span> <span class="nn">pyspark.ml.regression</span> <span class="kn">import</span> <span class="n">LinearRegression</span>
+<span class="kn">from</span> <span class="nn">pyspark.mllib.regression</span> <span class="kn">import</span> <span class="n">LabeledPoint</span>
+<span class="kn">from</span> <span class="nn">pyspark.mllib.util</span> <span class="kn">import</span> <span class="n">MLUtils</span>
+
+<span class="c"># Load training data</span>
+<span class="n">training</span> <span class="o">=</span> <span class="n">MLUtils</span><span class="o">.</span><span class="n">loadLibSVMFile</span><span class="p">(</span><span class="n">sc</span><span class="p">,</span> <span class="s">&quot;data/mllib/sample_libsvm_data.txt&quot;</span><span class="p">)</span><span class="o">.</span><span class="n">toDF</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 weights and intercept for linear regression</span>
+<span class="k">print</span><span class="p">(</span><span class="s">&quot;Weights: &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">weights</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>
+
+<span class="c"># Linear regression model summary is not yet supported in Python.</span></code></pre></div>
+
+  </div>
+
+</div>
+
+<h1 id="optimization">Optimization</h1>
+
+<p>The optimization algorithm underlying the implementation is called
+<a href="http://research-srv.microsoft.com/en-us/um/people/jfgao/paper/icml07scalable.pdf">Orthant-Wise Limited-memory
+QuasiNewton</a>
+(OWL-QN). It is an extension of L-BFGS that can effectively handle L1
+regularization and elastic net.</p>
+
+
+
+        </div> <!-- /container -->
+
+        <script src="js/vendor/jquery-1.8.0.min.js"></script>
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author	Reynold Xin <rxin@apache.org>	2015-09-17 22:11:21 +0000
committer	Reynold Xin <rxin@apache.org>	2015-09-17 22:11:21 +0000
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tree	dbf7d7a7700e9e6bad3c8289ab831bc9c2c20d62 /site/docs/1.5.0/ml-linear-methods.html
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