Updated decision tree doc.

docs/mllib-decision-tree.md

@@ -12,7 +12,7 @@ and their ensembles are popular methods for the machine learning tasks of
 classification and regression. Decision trees are widely used since they are easy to interpret,
 handle categorical features, extend to the multiclass classification setting, do not require
 feature scaling and are able to capture nonlinearities and feature interactions. Tree ensemble
-algorithms such as decision forests and boosting are among the top performers for classification and
+algorithms such as random forests and boosting are among the top performers for classification and
 regression tasks.
 
 MLlib supports decision trees for binary and multiclass classification and for regression,
@@ -94,13 +94,13 @@ Section 9.2.4 in
 details). For example, for a binary classification problem with one categorical feature with three
 categories A, B and C whose corresponding proportions of label 1 are 0.2, 0.6 and 0.4, the categorical
 features are ordered as A, C, B. The two split candidates are A \| C, B
-and A , C \| B where \| denotes the split. A similar heuristic is used for multiclass classification
-when `$2^{M-1}-1$` is greater than the `maxBins` parameter: the impurity for each categorical feature value
-is used for ordering. In multiclass classification, all `$2^{M-1}-1$` possible splits are used
-whenever possible.
+and A , C \| B where \| denotes the split.
 
-Note that the `maxBins` parameter must be at least `$M_{max}$`, the maximum number of categories for
-any categorical feature.
+In multiclass classification, all `$2^{M-1}-1$` possible splits are used whenever possible.
+When `$2^{M-1}-1$` is greater than the `maxBins` parameter, we use a (heuristic) method
+similar to the method used for binary classification and regression.
+The `$M$` categorical feature values are ordered by impurity,
+and the resulting `$M-1$` split candidates are considered.
 
 ### Stopping rule
 
@@ -109,6 +109,8 @@ The recursive tree construction is stopped at a node when one of the two conditi
 1. The node depth is equal to the `maxDepth` training parameter.
 2. No split candidate leads to an information gain at the node.
 
+## Implementation details
+
 ### Max memory requirements
 
 For faster processing, the decision tree algorithm performs simultaneous histogram computations for
@@ -120,11 +122,24 @@ be 128 MB to allow the decision algorithm to work in most scenarios. Once the me
 for a level-wise computation cross the `maxMemoryInMB` threshold, the node training tasks at each
 subsequent level are split into smaller tasks.
 
-### Practical limitations
+Note that, if you have a large amount of memory, increasing `maxMemoryInMB` can lead to faster
+training by requiring fewer passes over the data.
+
+### Binning feature values
+
+Increasing `maxBins` allows the algorithm to consider more split candidates and make fine-grained
+split decisions.  However, it also increases computation and communication.
+
+Note that the `maxBins` parameter must be at least the maximum number of categories `$M$` for
+any categorical feature.
+
+### Scaling
+
+Computation scales approximately linearly in the number of training instances,
+in the number of features, and in the `maxBins` parameter.
+Communication scales approximately linearly in the number of features and in `maxBins`.
 
-1. The implemented algorithm reads both sparse and dense data. However, it is not optimized for sparse input.
-2. Computation scales approximately linearly in the number of training instances,
-    in the number of features, and in the `maxBins` parameter.
+The implemented algorithm reads both sparse and dense data. However, it is not optimized for sparse input.
 
 ## Examples
 
@@ -143,8 +158,9 @@ maximum tree depth of 5. The training error is calculated to measure the algorit
 import org.apache.spark.mllib.tree.DecisionTree
 import org.apache.spark.mllib.util.MLUtils
 
-// Load and parse the data file
-val data = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt")
+// Load and parse the data file.
+// Cache the data since we will use it again to compute training error.
+val data = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt").cache()
 
 // Train a DecisionTree model.
 //  Empty categoricalFeaturesInfo indicates all features are continuous.
@@ -187,17 +203,14 @@ import org.apache.spark.SparkConf;
 SparkConf sparkConf = new SparkConf().setAppName("JavaDecisionTree");
 JavaSparkContext sc = new JavaSparkContext(sparkConf);
 
+// Load and parse the data file.
+// Cache the data since we will use it again to compute training error.
 String datapath = "data/mllib/sample_libsvm_data.txt";
 JavaRDD<LabeledPoint> data = MLUtils.loadLibSVMFile(sc.sc(), datapath).toJavaRDD().cache();
-// Compute the number of classes from the data.
-Integer numClasses = data.map(new Function<LabeledPoint, Double>() {
-  @Override public Double call(LabeledPoint p) {
-    return p.label();
-  }
-}).countByValue().size();
 
 // Set parameters.
 //  Empty categoricalFeaturesInfo indicates all features are continuous.
+Integer numClasses = 2;
 HashMap<Integer, Integer> categoricalFeaturesInfo = new HashMap<Integer, Integer>();
 String impurity = "gini";
 Integer maxDepth = 5;
@@ -231,8 +244,9 @@ from pyspark.mllib.regression import LabeledPoint
 from pyspark.mllib.tree import DecisionTree
 from pyspark.mllib.util import MLUtils
 
-# an RDD of LabeledPoint
-data = MLUtils.loadLibSVMFile(sc, 'data/mllib/sample_libsvm_data.txt')
+# Load and parse the data file into an RDD of LabeledPoint.
+# Cache the data since we will use it again to compute training error.
+data = MLUtils.loadLibSVMFile(sc, 'data/mllib/sample_libsvm_data.txt').cache()
 
 # Train a DecisionTree model.
 #  Empty categoricalFeaturesInfo indicates all features are continuous.
@@ -271,8 +285,9 @@ depth of 5. The Mean Squared Error (MSE) is computed at the end to evaluate
 import org.apache.spark.mllib.tree.DecisionTree
 import org.apache.spark.mllib.util.MLUtils
 
-// Load and parse the data file
-val data = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt")
+// Load and parse the data file.
+// Cache the data since we will use it again to compute training error.
+val data = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt").cache()
 
 // Train a DecisionTree model.
 //  Empty categoricalFeaturesInfo indicates all features are continuous.
@@ -311,6 +326,8 @@ import org.apache.spark.mllib.tree.model.DecisionTreeModel;
 import org.apache.spark.mllib.util.MLUtils;
 import org.apache.spark.SparkConf;
 
+// Load and parse the data file.
+// Cache the data since we will use it again to compute training error.
 String datapath = "data/mllib/sample_libsvm_data.txt";
 JavaRDD<LabeledPoint> data = MLUtils.loadLibSVMFile(sc.sc(), datapath).toJavaRDD().cache();
 
@@ -357,8 +374,9 @@ from pyspark.mllib.regression import LabeledPoint
 from pyspark.mllib.tree import DecisionTree
 from pyspark.mllib.util import MLUtils
 
-# an RDD of LabeledPoint
-data = MLUtils.loadLibSVMFile(sc, 'data/mllib/sample_libsvm_data.txt')
+# Load and parse the data file into an RDD of LabeledPoint.
+# Cache the data since we will use it again to compute training error.
+data = MLUtils.loadLibSVMFile(sc, 'data/mllib/sample_libsvm_data.txt').cache()
 
 # Train a DecisionTree model.
 #  Empty categoricalFeaturesInfo indicates all features are continuous.