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author | Reynold Xin <rxin@apache.org> | 2015-09-17 22:11:21 +0000 |
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committer | Reynold Xin <rxin@apache.org> | 2015-09-17 22:11:21 +0000 |
commit | 6f57b0c45a7d1b6255067c6e9bc549baa491acac (patch) | |
tree | dbf7d7a7700e9e6bad3c8289ab831bc9c2c20d62 /site/docs/1.5.0/ml-linear-methods.html | |
parent | ee9ffe89d608e7640a2487406b618d27e58026d6 (diff) | |
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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">"data/mllib/sample_libsvm_data.txt"</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">"Weights: ${lrModel.weights} Intercept: ${lrModel.intercept}"</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">"Logistic Regression with Elastic Net Example"</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">"data/mllib/sample_libsvm_data.txt"</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">"Weights: "</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">" Intercept: "</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">"data/mllib/sample_libsvm_data.txt"</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">"Weights: "</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">"Intercept: "</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">=></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">"F-Measure"</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">"F-Measure"</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">"threshold"</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">"FPR"</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">"F-Measure"</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">"F-Measure"</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">"threshold"</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">"data/mllib/sample_libsvm_data.txt"</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">"Weights: ${lrModel.weights} Intercept: ${lrModel.intercept}"</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">"numIterations: ${trainingSummary.totalIterations}"</span><span class="o">)</span> +<span class="n">println</span><span class="o">(</span><span class="n">s</span><span class="s">"objectiveHistory: ${trainingSummary.objectiveHistory.toList}"</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">"RMSE: ${trainingSummary.rootMeanSquaredError}"</span><span class="o">)</span> +<span class="n">println</span><span class="o">(</span><span class="n">s</span><span class="s">"r2: ${trainingSummary.r2}"</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">"Linear Regression with Elastic Net Example"</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">"data/mllib/sample_libsvm_data.txt"</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">"Weights: "</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">" Intercept: "</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">"numIterations: "</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">"objectiveHistory: "</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">"RMSE: "</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">"r2: "</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">"data/mllib/sample_libsvm_data.txt"</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">"Weights: "</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">"Intercept: "</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> + <script src="js/vendor/bootstrap.min.js"></script> + <script src="js/vendor/anchor.min.js"></script> + <script src="js/main.js"></script> + + <!-- MathJax Section --> + <script type="text/x-mathjax-config"> + MathJax.Hub.Config({ + TeX: { equationNumbers: { autoNumber: "AMS" } } + }); + </script> + <script> + // Note that we load MathJax this way to work with local file (file://), HTTP and HTTPS. + // We could use "//cdn.mathjax...", but that won't support "file://". + (function(d, script) { + script = d.createElement('script'); + script.type = 'text/javascript'; + script.async = true; + script.onload = function(){ + MathJax.Hub.Config({ + tex2jax: { + inlineMath: [ ["$", "$"], ["\\\\(","\\\\)"] ], + displayMath: [ ["$$","$$"], ["\\[", "\\]"] ], + processEscapes: true, + skipTags: ['script', 'noscript', 'style', 'textarea', 'pre'] + } + }); + }; + script.src = ('https:' == document.location.protocol ? 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