SPARK-1544 Add support for deep decision trees.

@etrain and I came with a PR for arbitrarily deep decision trees at the cost of multiple passes over the data at deep tree levels.

To summarize:
1) We take a parameter that indicates the amount of memory users want to reserve for computation on each worker (and 2x that at the driver).
2) Using that information, we calculate two things - the maximum depth to which we train as usual (which is, implicitly, the maximum number of nodes we want to train in parallel), and the size of the groups we should use in the case where we exceed this depth.

cc: @atalwalkar, @hirakendu, @mengxr

Author: Manish Amde <manish9ue@gmail.com>
Author: manishamde <manish9ue@gmail.com>
Author: Evan Sparks <sparks@cs.berkeley.edu>

Closes #475 from manishamde/deep_tree and squashes the following commits:

968ca9d [Manish Amde] merged master
7fc9545 [Manish Amde] added docs
ce004a1 [Manish Amde] minor formatting
b27ad2c [Manish Amde] formatting
426bb28 [Manish Amde] programming guide blurb
8053fed [Manish Amde] more formatting
5eca9e4 [Manish Amde] grammar
4731cda [Manish Amde] formatting
5e82202 [Manish Amde] added documentation, fixed off by 1 error in max level calculation
cbd9f14 [Manish Amde] modified scala.math to math
dad9652 [Manish Amde] removed unused imports
e0426ee [Manish Amde] renamed parameter
718506b [Manish Amde] added unit test
1517155 [Manish Amde] updated documentation
9dbdabe [Manish Amde] merge from master
719d009 [Manish Amde] updating user documentation
fecf89a [manishamde] Merge pull request #6 from etrain/deep_tree
0287772 [Evan Sparks] Fixing scalastyle issue.
2f1e093 [Manish Amde] minor: added doc for maxMemory parameter
2f6072c [manishamde] Merge pull request #5 from etrain/deep_tree
abc5a23 [Evan Sparks] Parameterizing max memory.
50b143a [Manish Amde] adding support for very deep trees

1 files changed, 73 insertions, 11 deletions

diff --git a/mllib/src/test/scala/org/apache/spark/mllib/tree/DecisionTreeSuite.scala b/mllib/src/test/scala/org/apache/spark/mllib/tree/DecisionTreeSuite.scala
index be383aab71..35e92d71dc 100644
--- a/mllib/src/test/scala/org/apache/spark/mllib/tree/DecisionTreeSuite.scala
+++ b/mllib/src/test/scala/org/apache/spark/mllib/tree/DecisionTreeSuite.scala
@@ -22,7 +22,8 @@ import org.scalatest.FunSuite
 import org.apache.spark.mllib.regression.LabeledPoint
 import org.apache.spark.mllib.tree.impurity.{Entropy, Gini, Variance}
 import org.apache.spark.mllib.tree.model.Filter
-import org.apache.spark.mllib.tree.configuration.Strategy
+import org.apache.spark.mllib.tree.model.Split
+import org.apache.spark.mllib.tree.configuration.{FeatureType, Strategy}
 import org.apache.spark.mllib.tree.configuration.Algo._
 import org.apache.spark.mllib.tree.configuration.FeatureType._
 import org.apache.spark.mllib.linalg.Vectors
@@ -242,7 +243,7 @@ class DecisionTreeSuite extends FunSuite with LocalSparkContext {
       categoricalFeaturesInfo = Map(0 -> 3, 1-> 3))
     val (splits, bins) = DecisionTree.findSplitsBins(rdd, strategy)
     val bestSplits = DecisionTree.findBestSplits(rdd, new Array(7), strategy, 0,
-      Array[List[Filter]](), splits, bins)
+      Array[List[Filter]](), splits, bins, 10)
 
     val split = bestSplits(0)._1
     assert(split.categories.length === 1)
@@ -269,7 +270,7 @@ class DecisionTreeSuite extends FunSuite with LocalSparkContext {
       categoricalFeaturesInfo = Map(0 -> 3, 1-> 3))
     val (splits, bins) = DecisionTree.findSplitsBins(rdd,strategy)
     val bestSplits = DecisionTree.findBestSplits(rdd, new Array(7), strategy, 0,
-      Array[List[Filter]](), splits, bins)
+      Array[List[Filter]](), splits, bins, 10)
 
     val split = bestSplits(0)._1
     assert(split.categories.length === 1)
@@ -298,7 +299,7 @@ class DecisionTreeSuite extends FunSuite with LocalSparkContext {
     assert(bins(0).length === 100)
 
     val bestSplits = DecisionTree.findBestSplits(rdd, new Array(7), strategy, 0,
-      Array[List[Filter]](), splits, bins)
+      Array[List[Filter]](), splits, bins, 10)
     assert(bestSplits.length === 1)
     assert(bestSplits(0)._1.feature === 0)
     assert(bestSplits(0)._1.threshold === 10)
@@ -321,7 +322,7 @@ class DecisionTreeSuite extends FunSuite with LocalSparkContext {
     assert(bins(0).length === 100)
 
     val bestSplits = DecisionTree.findBestSplits(rdd, Array(0.0), strategy, 0,
-      Array[List[Filter]](), splits, bins)
+      Array[List[Filter]](), splits, bins, 10)
     assert(bestSplits.length === 1)
     assert(bestSplits(0)._1.feature === 0)
     assert(bestSplits(0)._1.threshold === 10)
@@ -345,7 +346,7 @@ class DecisionTreeSuite extends FunSuite with LocalSparkContext {
     assert(bins(0).length === 100)
 
     val bestSplits = DecisionTree.findBestSplits(rdd, Array(0.0), strategy, 0,
-      Array[List[Filter]](), splits, bins)
+      Array[List[Filter]](), splits, bins, 10)
     assert(bestSplits.length === 1)
     assert(bestSplits(0)._1.feature === 0)
     assert(bestSplits(0)._1.threshold === 10)
@@ -369,7 +370,7 @@ class DecisionTreeSuite extends FunSuite with LocalSparkContext {
     assert(bins(0).length === 100)
 
     val bestSplits = DecisionTree.findBestSplits(rdd, Array(0.0), strategy, 0,
-      Array[List[Filter]](), splits, bins)
+      Array[List[Filter]](), splits, bins, 10)
     assert(bestSplits.length === 1)
     assert(bestSplits(0)._1.feature === 0)
     assert(bestSplits(0)._1.threshold === 10)
@@ -378,13 +379,60 @@ class DecisionTreeSuite extends FunSuite with LocalSparkContext {
     assert(bestSplits(0)._2.rightImpurity === 0)
     assert(bestSplits(0)._2.predict === 1)
   }
+
+  test("test second level node building with/without groups") {
+    val arr = DecisionTreeSuite.generateOrderedLabeledPoints()
+    assert(arr.length === 1000)
+    val rdd = sc.parallelize(arr)
+    val strategy = new Strategy(Classification, Entropy, 3, 100)
+    val (splits, bins) = DecisionTree.findSplitsBins(rdd, strategy)
+    assert(splits.length === 2)
+    assert(splits(0).length === 99)
+    assert(bins.length === 2)
+    assert(bins(0).length === 100)
+    assert(splits(0).length === 99)
+    assert(bins(0).length === 100)
+
+    val leftFilter = Filter(new Split(0, 400, FeatureType.Continuous, List()), -1)
+    val rightFilter = Filter(new Split(0, 400, FeatureType.Continuous, List()) ,1)
+    val filters = Array[List[Filter]](List(), List(leftFilter), List(rightFilter))
+    val parentImpurities = Array(0.5, 0.5, 0.5)
+
+    // Single group second level tree construction.
+    val bestSplits = DecisionTree.findBestSplits(rdd, parentImpurities, strategy, 1, filters,
+      splits, bins, 10)
+    assert(bestSplits.length === 2)
+    assert(bestSplits(0)._2.gain > 0)
+    assert(bestSplits(1)._2.gain > 0)
+
+    // maxLevelForSingleGroup parameter is set to 0 to force splitting into groups for second
+    // level tree construction.
+    val bestSplitsWithGroups = DecisionTree.findBestSplits(rdd, parentImpurities, strategy, 1,
+      filters, splits, bins, 0)
+    assert(bestSplitsWithGroups.length === 2)
+    assert(bestSplitsWithGroups(0)._2.gain > 0)
+    assert(bestSplitsWithGroups(1)._2.gain > 0)
+
+    // Verify whether the splits obtained using single group and multiple group level
+    // construction strategies are the same.
+    for (i <- 0 until bestSplits.length) {
+      assert(bestSplits(i)._1 === bestSplitsWithGroups(i)._1)
+      assert(bestSplits(i)._2.gain === bestSplitsWithGroups(i)._2.gain)
+      assert(bestSplits(i)._2.impurity === bestSplitsWithGroups(i)._2.impurity)
+      assert(bestSplits(i)._2.leftImpurity === bestSplitsWithGroups(i)._2.leftImpurity)
+      assert(bestSplits(i)._2.rightImpurity === bestSplitsWithGroups(i)._2.rightImpurity)
+      assert(bestSplits(i)._2.predict === bestSplitsWithGroups(i)._2.predict)
+    }
+
+  }
+
 }
 
 object DecisionTreeSuite {
 
   def generateOrderedLabeledPointsWithLabel0(): Array[LabeledPoint] = {
     val arr = new Array[LabeledPoint](1000)
-    for (i <- 0 until 1000){
+    for (i <- 0 until 1000) {
       val lp = new LabeledPoint(0.0, Vectors.dense(i.toDouble, 1000.0 - i))
       arr(i) = lp
     }
@@ -393,17 +441,31 @@ object DecisionTreeSuite {
 
   def generateOrderedLabeledPointsWithLabel1(): Array[LabeledPoint] = {
     val arr = new Array[LabeledPoint](1000)
-    for (i <- 0 until 1000){
+    for (i <- 0 until 1000) {
       val lp = new LabeledPoint(1.0, Vectors.dense(i.toDouble, 999.0 - i))
       arr(i) = lp
     }
     arr
   }
 
+  def generateOrderedLabeledPoints(): Array[LabeledPoint] = {
+    val arr = new Array[LabeledPoint](1000)
+    for (i <- 0 until 1000) {
+      if (i < 600) {
+        val lp = new LabeledPoint(0.0, Vectors.dense(i.toDouble, 1000.0 - i))
+        arr(i) = lp
+      } else {
+        val lp = new LabeledPoint(1.0, Vectors.dense(i.toDouble, 1000.0 - i))
+        arr(i) = lp
+      }
+    }
+    arr
+  }
+
   def generateCategoricalDataPoints(): Array[LabeledPoint] = {
     val arr = new Array[LabeledPoint](1000)
-    for (i <- 0 until 1000){
-      if (i < 600){
+    for (i <- 0 until 1000) {
+      if (i < 600) {
         arr(i) = new LabeledPoint(1.0, Vectors.dense(0.0, 1.0))
       } else {
         arr(i) = new LabeledPoint(0.0, Vectors.dense(1.0, 0.0))