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Linear Methods - ML |
<a href="ml-guide.html">ML</a> - Linear Methods |
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In MLlib, we implement popular linear methods such as logistic
regression and linear least squares with spark.ml, we also include Pipelines API for Elastic
net, a hybrid
of \[ \alpha \left( \lambda \|\wv\|_1 \right) + (1-\alpha) \left( \frac{\lambda}{2}\|\wv\|_2^2 \right) , \alpha \in [0, 1], \lambda \geq 0 \]
By setting
The following example shows how to train a logistic regression model
with elastic net regularization. elasticNetParam corresponds to
regParam corresponds to
// Load training data val training = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt").toDF()
val lr = new LogisticRegression() .setMaxIter(10) .setRegParam(0.3) .setElasticNetParam(0.8)
// Fit the model val lrModel = lr.fit(training)
// Print the weights and intercept for logistic regression println(s"Weights: ${lrModel.weights} Intercept: ${lrModel.intercept}") {% endhighlight %}
public class LogisticRegressionWithElasticNetExample { public static void main(String[] args) { SparkConf conf = new SparkConf() .setAppName("Logistic Regression with Elastic Net Example");
SparkContext sc = new SparkContext(conf);
SQLContext sql = new SQLContext(sc);
String path = "data/mllib/sample_libsvm_data.txt";
// Load training data
DataFrame training = sql.createDataFrame(MLUtils.loadLibSVMFile(sc, path).toJavaRDD(), LabeledPoint.class);
LogisticRegression lr = new LogisticRegression()
.setMaxIter(10)
.setRegParam(0.3)
.setElasticNetParam(0.8);
// Fit the model
LogisticRegressionModel lrModel = lr.fit(training);
// Print the weights and intercept for logistic regression
System.out.println("Weights: " + lrModel.weights() + " Intercept: " + lrModel.intercept());
} } {% endhighlight %}
training = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt").toDF()
lr = LogisticRegression(maxIter=10, regParam=0.3, elasticNetParam=0.8)
lrModel = lr.fit(training)
print("Weights: " + str(lrModel.weights)) print("Intercept: " + str(lrModel.intercept)) {% endhighlight %}
The spark.ml 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 Dataframe in
BinaryLogisticRegressionSummary are annotated @transient and hence
only available on the driver.
LogisticRegressionTrainingSummary
provides a summary for a
LogisticRegressionModel.
Currently, only binary classification is supported and the
summary must be explicitly cast to
BinaryLogisticRegressionTrainingSummary.
This will likely change when multiclass classification is supported.
Continuing the earlier example:
{% highlight scala %} import org.apache.spark.ml.classification.BinaryLogisticRegressionSummary
// Extract the summary from the returned LogisticRegressionModel instance trained in the earlier example val trainingSummary = lrModel.summary
// Obtain the objective per iteration. val objectiveHistory = trainingSummary.objectiveHistory objectiveHistory.foreach(loss => println(loss))
// Obtain the metrics useful to judge performance on test data. // We cast the summary to a BinaryLogisticRegressionSummary since the problem is a // binary classification problem. val binarySummary = trainingSummary.asInstanceOf[BinaryLogisticRegressionSummary]
// Obtain the receiver-operating characteristic as a dataframe and areaUnderROC. val roc = binarySummary.roc roc.show() println(binarySummary.areaUnderROC)
// Set the model threshold to maximize F-Measure val fMeasure = binarySummary.fMeasureByThreshold val maxFMeasure = fMeasure.select(max("F-Measure")).head().getDouble(0) val bestThreshold = fMeasure.where($"F-Measure" === maxFMeasure). select("threshold").head().getDouble(0) lrModel.setThreshold(bestThreshold) {% endhighlight %}
Continuing the earlier example:
{% highlight java %} import org.apache.spark.ml.classification.LogisticRegressionTrainingSummary; import org.apache.spark.ml.classification.BinaryLogisticRegressionSummary; import org.apache.spark.sql.functions;
// Extract the summary from the returned LogisticRegressionModel instance trained in the earlier example LogisticRegressionTrainingSummary trainingSummary = lrModel.summary();
// Obtain the loss per iteration. double[] objectiveHistory = trainingSummary.objectiveHistory(); for (double lossPerIteration : objectiveHistory) { System.out.println(lossPerIteration); }
// Obtain the metrics useful to judge performance on test data. // We cast the summary to a BinaryLogisticRegressionSummary since the problem is a // binary classification problem. BinaryLogisticRegressionSummary binarySummary = (BinaryLogisticRegressionSummary) trainingSummary;
// Obtain the receiver-operating characteristic as a dataframe and areaUnderROC. DataFrame roc = binarySummary.roc(); roc.show(); roc.select("FPR").show(); System.out.println(binarySummary.areaUnderROC());
// Get the threshold corresponding to the maximum F-Measure and rerun LogisticRegression with // this selected threshold. DataFrame fMeasure = binarySummary.fMeasureByThreshold(); double maxFMeasure = fMeasure.select(functions.max("F-Measure")).head().getDouble(0); double bestThreshold = fMeasure.where(fMeasure.col("F-Measure").equalTo(maxFMeasure)). select("threshold").head().getDouble(0); lrModel.setThreshold(bestThreshold); {% endhighlight %}
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.
// Load training data val training = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt").toDF()
val lr = new LinearRegression() .setMaxIter(10) .setRegParam(0.3) .setElasticNetParam(0.8)
// Fit the model val lrModel = lr.fit(training)
// Print the weights and intercept for linear regression println(s"Weights: ${lrModel.weights} Intercept: ${lrModel.intercept}")
// Summarize the model over the training set and print out some metrics
val trainingSummary = lrModel.summary
println(s"numIterations:
public class LinearRegressionWithElasticNetExample { public static void main(String[] args) { SparkConf conf = new SparkConf() .setAppName("Linear Regression with Elastic Net Example");
SparkContext sc = new SparkContext(conf);
SQLContext sql = new SQLContext(sc);
String path = "data/mllib/sample_libsvm_data.txt";
// Load training data
DataFrame training = sql.createDataFrame(MLUtils.loadLibSVMFile(sc, path).toJavaRDD(), LabeledPoint.class);
LinearRegression lr = new LinearRegression()
.setMaxIter(10)
.setRegParam(0.3)
.setElasticNetParam(0.8);
// Fit the model
LinearRegressionModel lrModel = lr.fit(training);
// Print the weights and intercept for linear regression
System.out.println("Weights: " + lrModel.weights() + " Intercept: " + lrModel.intercept());
// Summarize the model over the training set and print out some metrics
LinearRegressionTrainingSummary trainingSummary = lrModel.summary();
System.out.println("numIterations: " + trainingSummary.totalIterations());
System.out.println("objectiveHistory: " + Vectors.dense(trainingSummary.objectiveHistory()));
trainingSummary.residuals().show();
System.out.println("RMSE: " + trainingSummary.rootMeanSquaredError());
System.out.println("r2: " + trainingSummary.r2());
} } {% endhighlight %}
training = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt").toDF()
lr = LinearRegression(maxIter=10, regParam=0.3, elasticNetParam=0.8)
lrModel = lr.fit(training)
print("Weights: " + str(lrModel.weights)) print("Intercept: " + str(lrModel.intercept))
{% endhighlight %}
The optimization algorithm underlying the implementation is called Orthant-Wise Limited-memory QuasiNewton (OWL-QN). It is an extension of L-BFGS that can effectively handle L1 regularization and elastic net.