[SPARK-4580] [SPARK-4610] [mllib] [docs] Documentation for tree ensembles + DecisionTree API fix

Major changes:
* Added programming guide sections for tree ensembles
* Added examples for tree ensembles
* Updated DecisionTree programming guide with more info on parameters
* **API change**: Standardized the tree parameter for the number of classes (for classification)

Minor changes:
* Updated decision tree documentation
* Updated existing tree and tree ensemble examples
 * Use train/test split, and compute test error instead of training error.
 * Fixed decision_tree_runner.py to actually use the number of classes it computes from data. (small bug fix)

Note: I know this is a lot of lines, but most is covered by:
* Programming guide sections for gradient boosting and random forests.  (The changes are probably best viewed by generating the docs locally.)
* New examples (which were copied from the programming guide)
* The "numClasses" renaming

I have run all examples and relevant unit tests.

CC: mengxr manishamde codedeft

Author: Joseph K. Bradley <joseph@databricks.com>
Author: Joseph K. Bradley <joseph.kurata.bradley@gmail.com>

Closes #3461 from jkbradley/ensemble-docs and squashes the following commits:

70a75f3 [Joseph K. Bradley] updated forest vs boosting comparison
d1de753 [Joseph K. Bradley] Added note about toString and toDebugString for DecisionTree to migration guide
8e87f8f [Joseph K. Bradley] Combined GBT and RandomForest guides into one ensembles guide
6fab846 [Joseph K. Bradley] small fixes based on review
b9f8576 [Joseph K. Bradley] updated decision tree doc
375204c [Joseph K. Bradley] fixed python style
2b60b6e [Joseph K. Bradley] merged Java RandomForest examples into 1 file.  added header.  Fixed small bug in same example in the programming guide.
706d332 [Joseph K. Bradley] updated python DT runner to print full model if it is small
c76c823 [Joseph K. Bradley] added migration guide for mllib
abe5ed7 [Joseph K. Bradley] added examples for random forest in Java and Python to examples folder
07fc11d [Joseph K. Bradley] Renamed numClassesForClassification to numClasses everywhere in trees and ensembles. This is a breaking API change, but it was necessary to correct an API inconsistency in Spark 1.1 (where Python DecisionTree used numClasses but Scala used numClassesForClassification).
cdfdfbc [Joseph K. Bradley] added examples for GBT
6372a2b [Joseph K. Bradley] updated decision tree examples to use random split.  tested all of them.
ad3e695 [Joseph K. Bradley] added gbt and random forest to programming guide.  still need to update their examples

1 files changed, 653 insertions, 0 deletions

diff --git a/docs/mllib-ensembles.md b/docs/mllib-ensembles.md
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+---
+layout: global
+title: Ensembles - MLlib
+displayTitle: <a href="mllib-guide.html">MLlib</a> - Ensembles
+---
+
+* Table of contents
+{:toc}
+
+An [ensemble method](http://en.wikipedia.org/wiki/Ensemble_learning)
+is a learning algorithm which creates a model composed of a set of other base models.
+MLlib supports two major ensemble algorithms: [`GradientBoostedTrees`](api/scala/index.html#org.apache.spark.mllib.tree.GradientBosotedTrees) and [`RandomForest`](api/scala/index.html#org.apache.spark.mllib.tree.RandomForest).
+Both use [decision trees](mllib-decision-tree.html) as their base models.
+
+## Gradient-Boosted Trees vs. Random Forests
+
+Both [Gradient-Boosted Trees (GBTs)](mllib-ensembles.html#Gradient-Boosted-Trees-(GBTS)) and [Random Forests](mllib-ensembles.html#Random-Forests) are algorithms for learning ensembles of trees, but the training processes are different.  There are several practical trade-offs:
+
+ * GBTs train one tree at a time, so they can take longer to train than random forests.  Random Forests can train multiple trees in parallel.
+   * On the other hand, it is often reasonable to use smaller (shallower) trees with GBTs than with Random Forests, and training smaller trees takes less time.
+ * Random Forests can be less prone to overfitting.  Training more trees in a Random Forest reduces the likelihood of overfitting, but training more trees with GBTs increases the likelihood of overfitting.  (In statistical language, Random Forests reduce variance by using more trees, whereas GBTs reduce bias by using more trees.)
+ * Random Forests can be easier to tune since performance improves monotonically with the number of trees (whereas performance can start to decrease for GBTs if the number of trees grows too large).
+
+In short, both algorithms can be effective, and the choice should be based on the particular dataset.
+
+## Random Forests
+
+[Random forests](http://en.wikipedia.org/wiki/Random_forest)
+are ensembles of [decision trees](mllib-decision-tree.html).
+Random forests are one of the most successful machine learning models for classification and
+regression.  They combine many decision trees in order to reduce the risk of overfitting.
+Like decision trees, random forests handle categorical features,
+extend to the multiclass classification setting, do not require
+feature scaling, and are able to capture non-linearities and feature interactions.
+
+MLlib supports random forests for binary and multiclass classification and for regression,
+using both continuous and categorical features.
+MLlib implements random forests using the existing [decision tree](mllib-decision-tree.html)
+implementation.  Please see the decision tree guide for more information on trees.
+
+### Basic algorithm
+
+Random forests train a set of decision trees separately, so the training can be done in parallel.
+The algorithm injects randomness into the training process so that each decision tree is a bit
+different.  Combining the predictions from each tree reduces the variance of the predictions,
+improving the performance on test data.
+
+#### Training
+
+The randomness injected into the training process includes:
+
+* Subsampling the original dataset on each iteration to get a different training set (a.k.a. bootstrapping).
+* Considering different random subsets of features to split on at each tree node.
+
+Apart from these randomizations, decision tree training is done in the same way as for individual decision trees.
+
+#### Prediction
+
+To make a prediction on a new instance, a random forest must aggregate the predictions from its set of decision trees.  This aggregation is done differently for classification and regression.
+
+*Classification*: Majority vote. Each tree's prediction is counted as a vote for one class.  The label is predicted to be the class which receives the most votes.
+
+*Regression*: Averaging. Each tree predicts a real value.  The label is predicted to be the average of the tree predictions.
+
+### Usage tips
+
+We include a few guidelines for using random forests by discussing the various parameters.
+We omit some decision tree parameters since those are covered in the [decision tree guide](mllib-decision-tree.html).
+
+The first two parameters we mention are the most important, and tuning them can often improve performance:
+
+* **`numTrees`**: Number of trees in the forest.
+  * Increasing the number of trees will decrease the variance in predictions, improving the model's test-time accuracy.
+  * Training time increases roughly linearly in the number of trees.
+
+* **`maxDepth`**: Maximum depth of each tree in the forest.
+  * Increasing the depth makes the model more expressive and powerful.  However, deep trees take longer to train and are also more prone to overfitting.
+  * In general, it is acceptable to train deeper trees when using random forests than when using a single decision tree.  One tree is more likely to overfit than a random forest (because of the variance reduction from averaging multiple trees in the forest).
+
+The next two parameters generally do not require tuning.  However, they can be tuned to speed up training.
+
+* **`subsamplingRate`**: This parameter specifies the size of the dataset used for training each tree in the forest, as a fraction of the size of the original dataset.  The default (1.0) is recommended, but decreasing this fraction can speed up training.
+
+* **`featureSubsetStrategy`**: Number of features to use as candidates for splitting at each tree node.  The number is specified as a fraction or function of the total number of features.  Decreasing this number will speed up training, but can sometimes impact performance if too low.
+
+### Examples
+
+#### Classification
+
+The example below demonstrates how to load a
+[LIBSVM data file](http://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/),
+parse it as an RDD of `LabeledPoint` and then
+perform classification using a Random Forest.
+The test error is calculated to measure the algorithm accuracy.
+
+<div class="codetabs">
+
+<div data-lang="scala">
+{% highlight scala %}
+import org.apache.spark.mllib.tree.RandomForest
+import org.apache.spark.mllib.util.MLUtils
+
+// Load and parse the data file.
+val data = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt")
+// Split the data into training and test sets (30% held out for testing)
+val splits = data.randomSplit(Array(0.7, 0.3))
+val (trainingData, testData) = (splits(0), splits(1))
+
+// Train a RandomForest model.
+//  Empty categoricalFeaturesInfo indicates all features are continuous.
+val numClasses = 2
+val categoricalFeaturesInfo = Map[Int, Int]()
+val numTrees = 3 // Use more in practice.
+val featureSubsetStrategy = "auto" // Let the algorithm choose.
+val impurity = "gini"
+val maxDepth = 4
+val maxBins = 32
+
+val model = RandomForest.trainClassifier(trainingData, numClasses, categoricalFeaturesInfo,
+  numTrees, featureSubsetStrategy, impurity, maxDepth, maxBins)
+
+// Evaluate model on test instances and compute test error
+val labelAndPreds = testData.map { point =>
+  val prediction = model.predict(point.features)
+  (point.label, prediction)
+}
+val testErr = labelAndPreds.filter(r => r._1 != r._2).count.toDouble / testData.count()
+println("Test Error = " + testErr)
+println("Learned classification forest model:\n" + model.toDebugString)
+{% endhighlight %}
+</div>
+
+<div data-lang="java">
+{% highlight java %}
+import scala.Tuple2;
+import java.util.HashMap;
+import org.apache.spark.SparkConf;
+import org.apache.spark.api.java.JavaPairRDD;
+import org.apache.spark.api.java.JavaRDD;
+import org.apache.spark.api.java.JavaSparkContext;
+import org.apache.spark.api.java.function.Function;
+import org.apache.spark.api.java.function.PairFunction;
+import org.apache.spark.mllib.regression.LabeledPoint;
+import org.apache.spark.mllib.tree.RandomForest;
+import org.apache.spark.mllib.tree.model.RandomForestModel;
+import org.apache.spark.mllib.util.MLUtils;
+
+SparkConf sparkConf = new SparkConf().setAppName("JavaRandomForestClassification");
+JavaSparkContext sc = new JavaSparkContext(sparkConf);
+
+// Load and parse the data file.
+String datapath = "data/mllib/sample_libsvm_data.txt";
+JavaRDD<LabeledPoint> data = MLUtils.loadLibSVMFile(sc.sc(), datapath).toJavaRDD();
+// Split the data into training and test sets (30% held out for testing)
+JavaRDD<LabeledPoint>[] splits = data.randomSplit(new double[]{0.7, 0.3});
+JavaRDD<LabeledPoint> trainingData = splits[0];
+JavaRDD<LabeledPoint> testData = splits[1];
+
+// Train a RandomForest model.
+//  Empty categoricalFeaturesInfo indicates all features are continuous.
+Integer numClasses = 2;
+HashMap<Integer, Integer> categoricalFeaturesInfo = new HashMap<Integer, Integer>();
+Integer numTrees = 3; // Use more in practice.
+String featureSubsetStrategy = "auto"; // Let the algorithm choose.
+String impurity = "gini";
+Integer maxDepth = 5;
+Integer maxBins = 32;
+Integer seed = 12345;
+
+final RandomForestModel model = RandomForest.trainClassifier(trainingData, numClasses,
+  categoricalFeaturesInfo, numTrees, featureSubsetStrategy, impurity, maxDepth, maxBins,
+  seed);
+
+// Evaluate model on test instances and compute test error
+JavaPairRDD<Double, Double> predictionAndLabel =
+  testData.mapToPair(new PairFunction<LabeledPoint, Double, Double>() {
+    @Override
+    public Tuple2<Double, Double> call(LabeledPoint p) {
+      return new Tuple2<Double, Double>(model.predict(p.features()), p.label());
+    }
+  });
+Double testErr =
+  1.0 * predictionAndLabel.filter(new Function<Tuple2<Double, Double>, Boolean>() {
+    @Override
+    public Boolean call(Tuple2<Double, Double> pl) {
+      return !pl._1().equals(pl._2());
+    }
+  }).count() / testData.count();
+System.out.println("Test Error: " + testErr);
+System.out.println("Learned classification forest model:\n" + model.toDebugString());
+{% endhighlight %}
+</div>
+
+<div data-lang="python">
+{% highlight python %}
+from pyspark.mllib.tree import RandomForest
+from pyspark.mllib.util import MLUtils
+
+# Load and parse the data file into an RDD of LabeledPoint.
+data = MLUtils.loadLibSVMFile(sc, 'data/mllib/sample_libsvm_data.txt')
+# Split the data into training and test sets (30% held out for testing)
+(trainingData, testData) = data.randomSplit([0.7, 0.3])
+
+# Train a RandomForest model.
+#  Empty categoricalFeaturesInfo indicates all features are continuous.
+#  Note: Use larger numTrees in practice.
+#  Setting featureSubsetStrategy="auto" lets the algorithm choose.
+model = RandomForest.trainClassifier(trainingData, numClasses=2, categoricalFeaturesInfo={},
+                                     numTrees=3, featureSubsetStrategy="auto",
+                                     impurity='gini', maxDepth=4, maxBins=32)
+
+# Evaluate model on test instances and compute test error
+predictions = model.predict(testData.map(lambda x: x.features))
+labelsAndPredictions = testData.map(lambda lp: lp.label).zip(predictions)
+testErr = labelsAndPredictions.filter(lambda (v, p): v != p).count() / float(testData.count())
+print('Test Error = ' + str(testErr))
+print('Learned classification forest model:')
+print(model.toDebugString())
+{% endhighlight %}
+</div>
+
+</div>
+
+#### Regression
+
+The example below demonstrates how to load a
+[LIBSVM data file](http://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/),
+parse it as an RDD of `LabeledPoint` and then
+perform regression using a Random Forest.
+The Mean Squared Error (MSE) is computed at the end to evaluate
+[goodness of fit](http://en.wikipedia.org/wiki/Goodness_of_fit).
+
+<div class="codetabs">
+
+<div data-lang="scala">
+{% highlight scala %}
+import org.apache.spark.mllib.tree.RandomForest
+import org.apache.spark.mllib.util.MLUtils
+
+// Load and parse the data file.
+val data = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt")
+// Split the data into training and test sets (30% held out for testing)
+val splits = data.randomSplit(Array(0.7, 0.3))
+val (trainingData, testData) = (splits(0), splits(1))
+
+// Train a RandomForest model.
+//  Empty categoricalFeaturesInfo indicates all features are continuous.
+val numClasses = 2
+val categoricalFeaturesInfo = Map[Int, Int]()
+val numTrees = 3 // Use more in practice.
+val featureSubsetStrategy = "auto" // Let the algorithm choose.
+val impurity = "variance"
+val maxDepth = 4
+val maxBins = 32
+
+val model = RandomForest.trainRegressor(trainingData, categoricalFeaturesInfo,
+  numTrees, featureSubsetStrategy, impurity, maxDepth, maxBins)
+
+// Evaluate model on test instances and compute test error
+val labelsAndPredictions = testData.map { point =>
+  val prediction = model.predict(point.features)
+  (point.label, prediction)
+}
+val testMSE = labelsAndPredictions.map{ case(v, p) => math.pow((v - p), 2)}.mean()
+println("Test Mean Squared Error = " + testMSE)
+println("Learned regression forest model:\n" + model.toDebugString)
+{% endhighlight %}
+</div>
+
+<div data-lang="java">
+{% highlight java %}
+import java.util.HashMap;
+import scala.Tuple2;
+import org.apache.spark.api.java.function.Function2;
+import org.apache.spark.api.java.JavaPairRDD;
+import org.apache.spark.api.java.JavaRDD;
+import org.apache.spark.api.java.JavaSparkContext;
+import org.apache.spark.api.java.function.Function;
+import org.apache.spark.api.java.function.PairFunction;
+import org.apache.spark.mllib.regression.LabeledPoint;
+import org.apache.spark.mllib.tree.RandomForest;
+import org.apache.spark.mllib.tree.model.RandomForestModel;
+import org.apache.spark.mllib.util.MLUtils;
+import org.apache.spark.SparkConf;
+
+SparkConf sparkConf = new SparkConf().setAppName("JavaRandomForest");
+JavaSparkContext sc = new JavaSparkContext(sparkConf);
+
+// Load and parse the data file.
+String datapath = "data/mllib/sample_libsvm_data.txt";
+JavaRDD<LabeledPoint> data = MLUtils.loadLibSVMFile(sc.sc(), datapath).toJavaRDD();
+// Split the data into training and test sets (30% held out for testing)
+JavaRDD<LabeledPoint>[] splits = data.randomSplit(new double[]{0.7, 0.3});
+JavaRDD<LabeledPoint> trainingData = splits[0];
+JavaRDD<LabeledPoint> testData = splits[1];
+
+// Set parameters.
+//  Empty categoricalFeaturesInfo indicates all features are continuous.
+Map<Integer, Integer> categoricalFeaturesInfo = new HashMap<Integer, Integer>();
+String impurity = "variance";
+Integer maxDepth = 4;
+Integer maxBins = 32;
+
+// Train a RandomForest model.
+final RandomForestModel model = RandomForest.trainRegressor(trainingData,
+  categoricalFeaturesInfo, impurity, maxDepth, maxBins);
+
+// Evaluate model on test instances and compute test error
+JavaPairRDD<Double, Double> predictionAndLabel =
+  testData.mapToPair(new PairFunction<LabeledPoint, Double, Double>() {
+    @Override
+    public Tuple2<Double, Double> call(LabeledPoint p) {
+      return new Tuple2<Double, Double>(model.predict(p.features()), p.label());
+    }
+  });
+Double testMSE =
+  predictionAndLabel.map(new Function<Tuple2<Double, Double>, Double>() {
+    @Override
+    public Double call(Tuple2<Double, Double> pl) {
+      Double diff = pl._1() - pl._2();
+      return diff * diff;
+    }
+  }).reduce(new Function2<Double, Double, Double>() {
+    @Override
+    public Double call(Double a, Double b) {
+      return a + b;
+    }
+  }) / testData.count();
+System.out.println("Test Mean Squared Error: " + testMSE);
+System.out.println("Learned regression forest model:\n" + model.toDebugString());
+{% endhighlight %}
+</div>
+
+<div data-lang="python">
+{% highlight python %}
+from pyspark.mllib.tree import RandomForest
+from pyspark.mllib.util import MLUtils
+
+# Load and parse the data file into an RDD of LabeledPoint.
+data = MLUtils.loadLibSVMFile(sc, 'data/mllib/sample_libsvm_data.txt')
+# Split the data into training and test sets (30% held out for testing)
+(trainingData, testData) = data.randomSplit([0.7, 0.3])
+
+# Train a RandomForest model.
+#  Empty categoricalFeaturesInfo indicates all features are continuous.
+#  Note: Use larger numTrees in practice.
+#  Setting featureSubsetStrategy="auto" lets the algorithm choose.
+model = RandomForest.trainRegressor(trainingData, categoricalFeaturesInfo={},
+                                    numTrees=3, featureSubsetStrategy="auto",
+                                    impurity='variance', maxDepth=4, maxBins=32)
+
+# Evaluate model on test instances and compute test error
+predictions = model.predict(testData.map(lambda x: x.features))
+labelsAndPredictions = testData.map(lambda lp: lp.label).zip(predictions)
+testMSE = labelsAndPredictions.map(lambda (v, p): (v - p) * (v - p)).sum() / float(testData.count())
+print('Test Mean Squared Error = ' + str(testMSE))
+print('Learned regression forest model:')
+print(model.toDebugString())
+{% endhighlight %}
+</div>
+
+</div>
+
+## Gradient-Boosted Trees (GBTs)
+
+[Gradient-Boosted Trees (GBTs)](http://en.wikipedia.org/wiki/Gradient_boosting)
+are ensembles of [decision trees](mllib-decision-tree.html).
+GBTs iteratively train decision trees in order to minimize a loss function.
+Like decision trees, GBTs handle categorical features,
+extend to the multiclass classification setting, do not require
+feature scaling, and are able to capture non-linearities and feature interactions.
+
+MLlib supports GBTs for binary classification and for regression,
+using both continuous and categorical features.
+MLlib implements GBTs using the existing [decision tree](mllib-decision-tree.html) implementation.  Please see the decision tree guide for more information on trees.
+
+*Note*: GBTs do not yet support multiclass classification.  For multiclass problems, please use
+[decision trees](mllib-decision-tree.html) or [Random Forests](mllib-ensembles.html#Random-Forest).
+
+### Basic algorithm
+
+Gradient boosting iteratively trains a sequence of decision trees.
+On each iteration, the algorithm uses the current ensemble to predict the label of each training instance and then compares the prediction with the true label.  The dataset is re-labeled to put more emphasis on training instances with poor predictions.  Thus, in the next iteration, the decision tree will help correct for previous mistakes.
+
+The specific mechanism for re-labeling instances is defined by a loss function (discussed below).  With each iteration, GBTs further reduce this loss function on the training data.
+
+#### Losses
+
+The table below lists the losses currently supported by GBTs in MLlib.
+Note that each loss is applicable to one of classification or regression, not both.
+
+Notation: $N$ = number of instances. $y_i$ = label of instance $i$.  $x_i$ = features of instance $i$.  $F(x_i)$ = model's predicted label for instance $i$.
+
+<table class="table">
+  <thead>
+    <tr><th>Loss</th><th>Task</th><th>Formula</th><th>Description</th></tr>
+  </thead>
+  <tbody>
+    <tr>
+      <td>Log Loss</td>
+	  <td>Classification</td>
+	  <td>$2 \sum_{i=1}^{N} \log(1+\exp(-2 y_i F(x_i)))$</td><td>Twice binomial negative log likelihood.</td>
+    </tr>
+    <tr>
+      <td>Squared Error</td>
+	  <td>Regression</td>
+	  <td>$\sum_{i=1}^{N} (y_i - F(x_i))^2$</td><td>Also called L2 loss.  Default loss for regression tasks.</td>
+    </tr>
+    <tr>
+      <td>Absolute Error</td>
+	  <td>Regression</td>
+     <td>$\sum_{i=1}^{N} |y_i - F(x_i)|$</td><td>Also called L1 loss.  Can be more robust to outliers than Squared Error.</td>
+    </tr>
+  </tbody>
+</table>
+
+### Usage tips
+
+We include a few guidelines for using GBTs by discussing the various parameters.
+We omit some decision tree parameters since those are covered in the [decision tree guide](mllib-decision-tree.html).
+
+* **`loss`**: See the section above for information on losses and their applicability to tasks (classification vs. regression).  Different losses can give significantly different results, depending on the dataset.
+
+* **`numIterations`**: This sets the number of trees in the ensemble.  Each iteration produces one tree.  Increasing this number makes the model more expressive, improving training data accuracy.  However, test-time accuracy may suffer if this is too large.
+
+* **`learningRate`**: This parameter should not need to be tuned.  If the algorithm behavior seems unstable, decreasing this value may improve stability.
+
+* **`algo`**: The algorithm or task (classification vs. regression) is set using the tree [Strategy] parameter.
+
+
+### Examples
+
+GBTs currently have APIs in Scala and Java.  Examples in both languages are shown below.
+
+#### Classification
+
+The example below demonstrates how to load a
+[LIBSVM data file](http://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/),
+parse it as an RDD of `LabeledPoint` and then
+perform classification using Gradient-Boosted Trees with log loss.
+The test error is calculated to measure the algorithm accuracy.
+
+<div class="codetabs">
+
+<div data-lang="scala">
+{% highlight scala %}
+import org.apache.spark.mllib.tree.GradientBoostedTrees
+import org.apache.spark.mllib.tree.configuration.BoostingStrategy
+import org.apache.spark.mllib.util.MLUtils
+
+// Load and parse the data file.
+val data = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt")
+// Split the data into training and test sets (30% held out for testing)
+val splits = data.randomSplit(Array(0.7, 0.3))
+val (trainingData, testData) = (splits(0), splits(1))
+
+// Train a GradientBoostedTrees model.
+//  The defaultParams for Classification use LogLoss by default.
+val boostingStrategy = BoostingStrategy.defaultParams("Classification")
+boostingStrategy.numIterations = 3 // Note: Use more iterations in practice.
+boostingStrategy.treeStrategy.numClassesForClassification = 2
+boostingStrategy.treeStrategy.maxDepth = 5
+//  Empty categoricalFeaturesInfo indicates all features are continuous.
+boostingStrategy.treeStrategy.categoricalFeaturesInfo = Map[Int, Int]()
+
+val model = GradientBoostedTrees.train(trainingData, boostingStrategy)
+
+// Evaluate model on test instances and compute test error
+val labelAndPreds = testData.map { point =>
+  val prediction = model.predict(point.features)
+  (point.label, prediction)
+}
+val testErr = labelAndPreds.filter(r => r._1 != r._2).count.toDouble / testData.count()
+println("Test Error = " + testErr)
+println("Learned classification GBT model:\n" + model.toDebugString)
+{% endhighlight %}
+</div>
+
+<div data-lang="java">
+{% highlight java %}
+import scala.Tuple2;
+import java.util.HashMap;
+import java.util.Map;
+import org.apache.spark.SparkConf;
+import org.apache.spark.api.java.JavaPairRDD;
+import org.apache.spark.api.java.JavaRDD;
+import org.apache.spark.api.java.JavaSparkContext;
+import org.apache.spark.api.java.function.Function;
+import org.apache.spark.api.java.function.PairFunction;
+import org.apache.spark.mllib.regression.LabeledPoint;
+import org.apache.spark.mllib.tree.GradientBoostedTrees;
+import org.apache.spark.mllib.tree.configuration.BoostingStrategy;
+import org.apache.spark.mllib.tree.model.GradientBoostedTreesModel;
+import org.apache.spark.mllib.util.MLUtils;
+
+SparkConf sparkConf = new SparkConf().setAppName("JavaGradientBoostedTrees");
+JavaSparkContext sc = new JavaSparkContext(sparkConf);
+
+// Load and parse the data file.
+String datapath = "data/mllib/sample_libsvm_data.txt";
+JavaRDD<LabeledPoint> data = MLUtils.loadLibSVMFile(sc.sc(), datapath).toJavaRDD();
+// Split the data into training and test sets (30% held out for testing)
+JavaRDD<LabeledPoint>[] splits = data.randomSplit(new double[]{0.7, 0.3});
+JavaRDD<LabeledPoint> trainingData = splits[0];
+JavaRDD<LabeledPoint> testData = splits[1];
+
+// Train a GradientBoostedTrees model.
+//  The defaultParams for Classification use LogLoss by default.
+BoostingStrategy boostingStrategy = BoostingStrategy.defaultParams("Classification");
+boostingStrategy.setNumIterations(3); // Note: Use more iterations in practice.
+boostingStrategy.getTreeStrategy().setNumClassesForClassification(2);
+boostingStrategy.getTreeStrategy().setMaxDepth(5);
+//  Empty categoricalFeaturesInfo indicates all features are continuous.
+Map<Integer, Integer> categoricalFeaturesInfo = new HashMap<Integer, Integer>();
+boostingStrategy.treeStrategy().setCategoricalFeaturesInfo(categoricalFeaturesInfo);
+
+final GradientBoostedTreesModel model =
+  GradientBoostedTrees.train(trainingData, boostingStrategy);
+
+// Evaluate model on test instances and compute test error
+JavaPairRDD<Double, Double> predictionAndLabel =
+  testData.mapToPair(new PairFunction<LabeledPoint, Double, Double>() {
+    @Override
+    public Tuple2<Double, Double> call(LabeledPoint p) {
+      return new Tuple2<Double, Double>(model.predict(p.features()), p.label());
+    }
+  });
+Double testErr =
+  1.0 * predictionAndLabel.filter(new Function<Tuple2<Double, Double>, Boolean>() {
+    @Override
+    public Boolean call(Tuple2<Double, Double> pl) {
+      return !pl._1().equals(pl._2());
+    }
+  }).count() / testData.count();
+System.out.println("Test Error: " + testErr);
+System.out.println("Learned classification GBT model:\n" + model.toDebugString());
+{% endhighlight %}
+</div>
+
+</div>
+
+#### Regression
+
+The example below demonstrates how to load a
+[LIBSVM data file](http://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/),
+parse it as an RDD of `LabeledPoint` and then
+perform regression using Gradient-Boosted Trees with Squared Error as the loss.
+The Mean Squared Error (MSE) is computed at the end to evaluate
+[goodness of fit](http://en.wikipedia.org/wiki/Goodness_of_fit).
+
+<div class="codetabs">
+
+<div data-lang="scala">
+{% highlight scala %}
+import org.apache.spark.mllib.tree.GradientBoostedTrees
+import org.apache.spark.mllib.tree.configuration.BoostingStrategy
+import org.apache.spark.mllib.util.MLUtils
+
+// Load and parse the data file.
+val data = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt")
+// Split the data into training and test sets (30% held out for testing)
+val splits = data.randomSplit(Array(0.7, 0.3))
+val (trainingData, testData) = (splits(0), splits(1))
+
+// Train a GradientBoostedTrees model.
+//  The defaultParams for Regression use SquaredError by default.
+val boostingStrategy = BoostingStrategy.defaultParams("Regression")
+boostingStrategy.numIterations = 3 // Note: Use more iterations in practice.
+boostingStrategy.treeStrategy.maxDepth = 5
+//  Empty categoricalFeaturesInfo indicates all features are continuous.
+boostingStrategy.treeStrategy.categoricalFeaturesInfo = Map[Int, Int]()
+
+val model = GradientBoostedTrees.train(trainingData, boostingStrategy)
+
+// Evaluate model on test instances and compute test error
+val labelsAndPredictions = testData.map { point =>
+  val prediction = model.predict(point.features)
+  (point.label, prediction)
+}
+val testMSE = labelsAndPredictions.map{ case(v, p) => math.pow((v - p), 2)}.mean()
+println("Test Mean Squared Error = " + testMSE)
+println("Learned regression GBT model:\n" + model.toDebugString)
+{% endhighlight %}
+</div>
+
+<div data-lang="java">
+{% highlight java %}
+import scala.Tuple2;
+import java.util.HashMap;
+import java.util.Map;
+import org.apache.spark.SparkConf;
+import org.apache.spark.api.java.function.Function2;
+import org.apache.spark.api.java.JavaPairRDD;
+import org.apache.spark.api.java.JavaRDD;
+import org.apache.spark.api.java.JavaSparkContext;
+import org.apache.spark.api.java.function.Function;
+import org.apache.spark.api.java.function.PairFunction;
+import org.apache.spark.mllib.regression.LabeledPoint;
+import org.apache.spark.mllib.tree.GradientBoostedTrees;
+import org.apache.spark.mllib.tree.configuration.BoostingStrategy;
+import org.apache.spark.mllib.tree.model.GradientBoostedTreesModel;
+import org.apache.spark.mllib.util.MLUtils;
+
+SparkConf sparkConf = new SparkConf().setAppName("JavaGradientBoostedTrees");
+JavaSparkContext sc = new JavaSparkContext(sparkConf);
+
+// Load and parse the data file.
+String datapath = "data/mllib/sample_libsvm_data.txt";
+JavaRDD<LabeledPoint> data = MLUtils.loadLibSVMFile(sc.sc(), datapath).toJavaRDD();
+// Split the data into training and test sets (30% held out for testing)
+JavaRDD<LabeledPoint>[] splits = data.randomSplit(new double[]{0.7, 0.3});
+JavaRDD<LabeledPoint> trainingData = splits[0];
+JavaRDD<LabeledPoint> testData = splits[1];
+
+// Train a GradientBoostedTrees model.
+//  The defaultParams for Regression use SquaredError by default.
+BoostingStrategy boostingStrategy = BoostingStrategy.defaultParams("Regression");
+boostingStrategy.setNumIterations(3); // Note: Use more iterations in practice.
+boostingStrategy.getTreeStrategy().setMaxDepth(5);
+//  Empty categoricalFeaturesInfo indicates all features are continuous.
+Map<Integer, Integer> categoricalFeaturesInfo = new HashMap<Integer, Integer>();
+boostingStrategy.treeStrategy().setCategoricalFeaturesInfo(categoricalFeaturesInfo);
+
+final GradientBoostedTreesModel model =
+  GradientBoostedTrees.train(trainingData, boostingStrategy);
+
+// Evaluate model on test instances and compute test error
+JavaPairRDD<Double, Double> predictionAndLabel =
+  testData.mapToPair(new PairFunction<LabeledPoint, Double, Double>() {
+    @Override
+    public Tuple2<Double, Double> call(LabeledPoint p) {
+      return new Tuple2<Double, Double>(model.predict(p.features()), p.label());
+    }
+  });
+Double testMSE =
+  predictionAndLabel.map(new Function<Tuple2<Double, Double>, Double>() {
+    @Override
+    public Double call(Tuple2<Double, Double> pl) {
+      Double diff = pl._1() - pl._2();
+      return diff * diff;
+    }
+  }).reduce(new Function2<Double, Double, Double>() {
+    @Override
+    public Double call(Double a, Double b) {
+      return a + b;
+    }
+  }) / data.count();
+System.out.println("Test Mean Squared Error: " + testMSE);
+System.out.println("Learned regression GBT model:\n" + model.toDebugString());
+{% endhighlight %}
+</div>
+
+</div>