Github user pwendell commented on a diff in the pull request:
https://github.com/apache/spark/pull/79#discussion_r10865481
--- Diff:
mllib/src/main/scala/org/apache/spark/mllib/tree/DecisionTree.scala ---
@@ -0,0 +1,1183 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.spark.mllib.tree
+
+import scala.util.control.Breaks._
+
+import org.apache.spark.SparkContext._
+import org.apache.spark.rdd.RDD
+import org.apache.spark.mllib.tree.model._
+import org.apache.spark.{SparkContext, Logging}
+import org.apache.spark.mllib.regression.LabeledPoint
+import org.apache.spark.mllib.tree.model.Split
+import org.apache.spark.mllib.tree.configuration.Strategy
+import org.apache.spark.mllib.tree.configuration.QuantileStrategy._
+import org.apache.spark.mllib.tree.configuration.FeatureType._
+import org.apache.spark.mllib.tree.configuration.Algo._
+import org.apache.spark.mllib.tree.impurity.{Variance, Entropy, Gini,
Impurity}
+import java.util.Random
+import org.apache.spark.util.random.XORShiftRandom
+
+/**
+ * A class that implements a decision tree algorithm for classification
and regression. It
+ * supports both continuous and categorical features.
+ * @param strategy The configuration parameters for the tree algorithm
which specify the type
+ * of algorithm (classification, regression, etc.),
feature type (continuous,
+ * categorical),
+ * depth of the tree, quantile calculation strategy, etc.
+ */
+class DecisionTree private(val strategy: Strategy) extends Serializable
with Logging {
+
+ /**
+ * Method to train a decision tree model over an RDD
+ * @param input RDD of
[[org.apache.spark.mllib.regression.LabeledPoint]] used as training data
+ * for DecisionTree
+ * @return a DecisionTreeModel that can be used for prediction
+ */
+ def train(input: RDD[LabeledPoint]): DecisionTreeModel = {
+
+ // Cache input RDD for speedup during multiple passes
+ input.cache()
+ logDebug("algo = " + strategy.algo)
+
+ // Finding the splits and the corresponding bins (interval between the
splits) using a sample
+ // of the input data.
+ val (splits, bins) = DecisionTree.findSplitsBins(input, strategy)
+ logDebug("numSplits = " + bins(0).length)
+
+ // Noting numBins for the input data
+ strategy.numBins = bins(0).length
+
+ // The depth of the decision tree
+ val maxDepth = strategy.maxDepth
+ // The max number of nodes possible given the depth of the tree
+ val maxNumNodes = scala.math.pow(2, maxDepth).toInt - 1
+ // Initalizing an array to hold filters applied to points for each node
+ val filters = new Array[List[Filter]](maxNumNodes)
+ // The filter at the top node is an empty list
+ filters(0) = List()
+ // Initializing an array to hold parent impurity calculations for each
node
+ val parentImpurities = new Array[Double](maxNumNodes)
+ // Dummy value for top node (updated during first split calculation)
+ val nodes = new Array[Node](maxNumNodes)
+
+ // The main-idea here is to perform level-wise training of the
decision tree nodes thus
+ // reducing the passes over the data from l to log2(l) where l is the
total number of nodes.
+ // Each data sample is checked for validity w.r.t to each node at a
given level -- i.e.,
+ // the sample is only used for the split calculation at the node if
the sampled would have
+ // still survived the filters of the parent nodes.
+
+ // TODO: Convert for loop to while loop
+ breakable {
+ for (level <- 0 until maxDepth) {
+
+ logDebug("#####################################")
+ logDebug("level = " + level)
+ logDebug("#####################################")
+
+ // Find best split for all nodes at a level
+ val splitsStatsForLevel = DecisionTree.findBestSplits(input,
parentImpurities, strategy,
+ level, filters, splits, bins)
+
+ for ((nodeSplitStats, index) <-
splitsStatsForLevel.view.zipWithIndex) {
+ // Extract info for nodes at the current level
+ extractNodeInfo(nodeSplitStats, level, index, nodes)
+ // Extract info for nodes at the next lower level
+ extractInfoForLowerLevels(level, index, maxDepth,
nodeSplitStats, parentImpurities,
+ filters)
+ logDebug("final best split = " + nodeSplitStats._1)
+
+ }
+ require(scala.math.pow(2, level) == splitsStatsForLevel.length)
+ // Check whether all the nodes at the current level at leaves
+ val allLeaf = splitsStatsForLevel.forall(_._2.gain <= 0)
+ logDebug("all leaf = " + allLeaf)
+ if (allLeaf) break //no more tree construction
+
+ }
+ }
+
+ // Initialize the top or root node of the tree
+ val topNode = nodes(0)
+ // Build the full tree using the node info calculated in the
level-wise best split calculations
+ topNode.build(nodes)
+
+ // Return a decision tree model
+ return new DecisionTreeModel(topNode, strategy.algo)
+ }
+
+ /**
+ * Extract the decision tree node information for the given tree level
and node index
+ */
+ private def extractNodeInfo(
+ nodeSplitStats: (Split, InformationGainStats),
+ level: Int,
+ index: Int,
+ nodes: Array[Node])
+ : Unit = {
+
+ val split = nodeSplitStats._1
+ val stats = nodeSplitStats._2
+ val nodeIndex = scala.math.pow(2, level).toInt - 1 + index
+ val isLeaf = (stats.gain <= 0) || (level == strategy.maxDepth - 1)
+ val node = new Node(nodeIndex, stats.predict, isLeaf, Some(split),
None, None, Some(stats))
+ logDebug("Node = " + node)
+ nodes(nodeIndex) = node
+ }
+
+ /**
+ * Extract the decision tree node information for the children of the
node
+ */
+ private def extractInfoForLowerLevels(
+ level: Int,
+ index: Int,
+ maxDepth: Int,
+ nodeSplitStats: (Split, InformationGainStats),
+ parentImpurities: Array[Double],
+ filters: Array[List[Filter]])
+ : Unit = {
+
+ // 0 corresponds to the left child node and 1 corresponds to the right
child node.
+ // TODO: Convert to while loop
+ for (i <- 0 to 1) {
+ // Calculating the index of the node from the node level and the
index at the current level
+ val nodeIndex = scala.math.pow(2, level + 1).toInt - 1 + 2 * index +
i
+ if (level < maxDepth - 1) {
+ val impurity = if (i == 0) {
+ nodeSplitStats._2.leftImpurity
+ } else {
+ nodeSplitStats._2.rightImpurity
+ }
+ logDebug("nodeIndex = " + nodeIndex + ", impurity = " + impurity)
+ // noting the parent impurities
+ parentImpurities(nodeIndex) = impurity
+ // noting the parents filters for the child nodes
+ val childFilter = new Filter(nodeSplitStats._1, if (i == 0) -1
else 1)
+ filters(nodeIndex) = childFilter :: filters((nodeIndex - 1) / 2)
+ for (filter <- filters(nodeIndex)) {
+ logDebug("Filter = " + filter)
+ }
+ }
+ }
+ }
+}
+
+object DecisionTree extends Serializable with Logging {
+
+ /**
+ * Method to train a decision tree model over an RDD
+ * @param input RDD of
[[org.apache.spark.mllib.regression.LabeledPoint]] used as training data
+ * for DecisionTree
+ * @param strategy The configuration parameters for the tree algorithm
which specify the type
+ * of algoritm (classification, regression, etc.),
feature type (continuous,
+ * categorical), depth of the tree, quantile calculation
strategy, etc.
+ * @return a DecisionTreeModel that can be used for prediction
+ */
+ def train(input: RDD[LabeledPoint], strategy: Strategy):
DecisionTreeModel = {
+ new DecisionTree(strategy).train(input: RDD[LabeledPoint])
+ }
+
+ /**
+ * Method to train a decision tree model over an RDD
+ * @param input input RDD of
[[org.apache.spark.mllib.regression.LabeledPoint]] used as
+ * training data
+ * @param algo algo classification or regression
+ * @param impurity impurity criterion used for information gain
calculation
+ * @param maxDepth maxDepth maximum depth of the tree
+ * @return a DecisionTreeModel that can be used for prediction
+ */
+ def train(
+ input: RDD[LabeledPoint],
+ algo: Algo,
+ impurity: Impurity,
+ maxDepth: Int)
+ : DecisionTreeModel = {
+ val strategy = new Strategy(algo,impurity,maxDepth)
+ new DecisionTree(strategy).train(input: RDD[LabeledPoint])
+ }
+
+
+ /**
+ * Method to train a decision tree model over an RDD
+ * @param input input RDD of
[[org.apache.spark.mllib.regression.LabeledPoint]] used as
+ * training data for DecisionTree
+ * @param algo classification or regression
+ * @param impurity criterion used for information gain calculation
+ * @param maxDepth maximum depth of the tree
+ * @param maxBins maximum number of bins used for splitting features
+ * @param quantileCalculationStrategy algorithm for calculating
quantiles
+ * @param categoricalFeaturesInfo A map storing information about the
categorical variables and
+ * the number of discrete values they
take. For example,
+ * an entry (n -> k) implies the feature
n is categorical with k
+ * categories 0, 1, 2, ... , k-1. It's
important to note that
+ * features are zero-indexed.
+ * @return a DecisionTreeModel that can be used for prediction
+ */
+ def train(
+ input: RDD[LabeledPoint],
+ algo: Algo,
+ impurity: Impurity,
+ maxDepth: Int,
+ maxBins: Int,
+ quantileCalculationStrategy: QuantileStrategy,
+ categoricalFeaturesInfo: Map[Int,Int])
+ : DecisionTreeModel = {
+ val strategy = new Strategy(algo, impurity, maxDepth, maxBins,
quantileCalculationStrategy,
+ categoricalFeaturesInfo)
+ new DecisionTree(strategy).train(input: RDD[LabeledPoint])
+ }
+
+ val InvalidBinIndex = -1
+
+ /**
+ * Returns an array of optimal splits for all nodes at a given level
+ * @param input RDD of
[[org.apache.spark.mllib.regression.LabeledPoint]] used as training data
+ * for DecisionTree
+ * @param parentImpurities Impurities for all parent nodes for the
current level
+ * @param strategy
[[org.apache.spark.mllib.tree.configuration.Strategy]] instance containing
+ * parameters for construction the DecisionTree
+ * @param level Level of the tree
+ * @param filters Filters for all nodes at a given level
+ * @param splits possible splits for all features
+ * @param bins possible bins for all features
+ * @return array of splits with best splits for all nodes at a given
level.
+ */
+ def findBestSplits(
+ input: RDD[LabeledPoint],
+ parentImpurities: Array[Double],
+ strategy: Strategy,
+ level: Int,
+ filters: Array[List[Filter]],
+ splits: Array[Array[Split]],
+ bins: Array[Array[Bin]])
+ : Array[(Split, InformationGainStats)] = {
+
+
+ // The high-level description for the best split optimizations are
noted here.
+ //
+ // *Level-wise training*
+ // We perform bin calculations for all nodes at the given level to
avoid making multiple
+ // passes over the data. Thus, for a slightly increased computation
and storage cost we save
+ // several iterations over the data especially at higher levels of the
decision tree.
+ //
+ // *Bin-wise computation*
+ // We use a bin-wise best split computation strategy instead of a
straightforward best split
+ // computation strategy. Instead of analyzing each sample for
contribution to the left/right
+ // child node impurity of every split, we first categorize each
feature of a sample into a
+ // bin. Each bin is an interval between a low and high split. Since
each splits, and thus bin,
+ // is ordered (read ordering for categorical variables in the
findSplitsBins method),
+ // we exploit this structure to calculate aggregates for bins and then
use these aggregates
+ // to calculate information gain for each split.
+ //
+ // *Aggregation over partitions*
+ // Instead of performing a flatMap/reduceByKey operation, we exploit
the fact that we know
+ // the number of splits in advance. Thus, we store the aggregates (at
the appropriate
+ // indices) in a single array for all bins and rely upon the RDD
aggregate method to
+ // drastically reduce the communication overhead.
+
+ // Implementation below
+
+ // Common calculations for multiple nested methods
+ val numNodes = scala.math.pow(2, level).toInt
+ logDebug("numNodes = " + numNodes)
+ // Find the number of features by looking at the first sample
+ val numFeatures = input.first().features.length
+ logDebug("numFeatures = " + numFeatures)
+ val numBins = strategy.numBins
+ logDebug("numBins = " + numBins)
+
+ /** Find the filters used before reaching the current code */
+ def findParentFilters(nodeIndex: Int): List[Filter] = {
+ if (level == 0) {
+ List[Filter]()
+ } else {
+ val nodeFilterIndex = scala.math.pow(2, level).toInt - 1 +
nodeIndex
+ filters(nodeFilterIndex)
+ }
+ }
+
+ /**
+ * Find whether the sample is valid input for the current node. In
other words,
+ * does it pass through all the filters for the current node.
+ */
+ def isSampleValid(parentFilters: List[Filter], labeledPoint:
LabeledPoint): Boolean = {
+
+ // Leaf
+ if ((level > 0) & (parentFilters.length == 0) ){
+ return false
+ }
+
+ // Apply each filter and check sample validity. Return false when
invalid condition found.
+ for (filter <- parentFilters) {
+ val features = labeledPoint.features
+ val featureIndex = filter.split.feature
+ val threshold = filter.split.threshold
+ val comparison = filter.comparison
+ val categories = filter.split.categories
+ val isFeatureContinuous = filter.split.featureType == Continuous
+ val feature = features(featureIndex)
+ if (isFeatureContinuous){
+ comparison match {
+ case(-1) => if (feature > threshold) return false
+ case(1) => if (feature <= threshold) return false
+ }
+ } else {
+ val containsFeature = categories.contains(feature)
+ comparison match {
+ case(-1) => if (!containsFeature) return false
+ case(1) => if (containsFeature) return false
+ }
+
+ }
+ }
+
+ //Return true when the sample is valid for all filters
+ true
+ }
+
+ /**
+ * Find bin for one feature
+ */
+ def findBin(
+ featureIndex: Int,
+ labeledPoint: LabeledPoint,
+ isFeatureContinuous: Boolean)
+ : Int = {
+
+ val binForFeatures = bins(featureIndex)
+ val feature = labeledPoint.features(featureIndex)
+
+ /**
+ * Binary search helper method for continuous feature
+ */
+ def binarySearchForBins(): Int = {
+ var left = 0
+ var right = binForFeatures.length - 1
+ while (left <= right) {
+ val mid = left + (right - left) / 2
+ val bin = binForFeatures(mid)
+ val lowThreshold = bin.lowSplit.threshold
+ val highThreshold = bin.highSplit.threshold
+ if ((lowThreshold < feature) & (highThreshold >= feature)){
+ return mid
+ }
+ else if ((lowThreshold >= feature)){
+ right = mid - 1
+ }
+ else {
+ left = mid + 1
+ }
+ }
+ -1
+ }
+
+ /**
+ * Sequential search helper method to find bin for categorical
feature
+ */
+ def sequentialBinSearchForCategoricalFeature() : Int = {
+ val numCategoricalBins =
strategy.categoricalFeaturesInfo(featureIndex)
+ var binIndex = 0
+ while (binIndex < numCategoricalBins) {
+ val bin = bins(featureIndex)(binIndex)
+ val category = bin.category
+ val features = labeledPoint.features
+ if (category == features(featureIndex)) {
+ return binIndex
+ }
+ binIndex += 1
+ }
+ -1
+ }
+
+ if (isFeatureContinuous){
+ // Perform binary search for finding bin for continuous features.
+ val binIndex = binarySearchForBins()
+ if (binIndex == -1){
+ throw new UnknownError("no bin was found for continuous
variable.")
+ }
+ binIndex
+ } else {
+ // Perform sequential search to find bin for categorical features.
+ val binIndex = sequentialBinSearchForCategoricalFeature()
+ if (binIndex == -1){
+ throw new UnknownError("no bin was found for categorical
variable.")
+ }
+ binIndex
+ }
+ }
+
+ /**
+ * Finds bins for all nodes (and all features) at a given level.
+ * For l nodes, k features the storage is as follows:
+ * label, b_11, b_12, .. , b_1k, b_21, b_22, .. , b_2k, b_l1, b_l2, ..
, b_lk
+ * where b_ij is an integer between 0 and numBins - 1.
+ * Invalid sample is denoted by noting bin for feature 1 as -1
+ */
+ def findBinsForLevel(labeledPoint: LabeledPoint): Array[Double] = {
+
+ // calculating bin index and label per feature per node
+ val arr = new Array[Double](1 + (numFeatures * numNodes))
+ arr(0) = labeledPoint.label
+ var nodeIndex = 0
+ while (nodeIndex < numNodes) {
+ val parentFilters = findParentFilters(nodeIndex)
+ // Find out whether the sample qualifies for the particular node
+ val sampleValid = isSampleValid(parentFilters, labeledPoint)
+ val shift = 1 + numFeatures * nodeIndex
+ if (!sampleValid) {
+ // marking one bin as -1 is sufficient
+ arr(shift) = InvalidBinIndex
+ } else {
+ var featureIndex = 0
+ while (featureIndex < numFeatures){
+ val isFeatureContinuous =
strategy.categoricalFeaturesInfo.get(featureIndex).isEmpty
+ arr(shift + featureIndex) = findBin(featureIndex,
labeledPoint,isFeatureContinuous)
+ featureIndex += 1
+ }
+ }
+ nodeIndex += 1
+ }
+ arr
+ }
+
+ /**
+ * Performs a sequential aggregation over a partition for
classification. For l nodes,
+ * k features, either the left count or the right count of one of the
p bins is
+ * incremented based upon whether the feature is classified as 0 or 1.
+ *
+ * @param agg Array[Double] storing aggregate calculation of size
+ * 2*numSplits*numFeatures*numNodes for classification
+ * @param arr Array[Double] of size 1+(numFeatures*numNodes)
+ * @return Array[Double] storing aggregate calculation of size
2*numSplits*numFeatures*numNodes
+ * for classification
+ */
+ def classificationBinSeqOp(arr: Array[Double], agg: Array[Double]) {
+ // Iterating over all nodes
+ var nodeIndex = 0
+ while (nodeIndex < numNodes) {
+ // Checking whether the instance was valid for this nodeIndex
+ val validSignalIndex = 1 + numFeatures * nodeIndex
+ val isSampleValidForNode = arr(validSignalIndex) != InvalidBinIndex
+ if (isSampleValidForNode) {
+ // Actual class label
+ val label = arr(0)
+ // Iterating over all features
+ var featureIndex = 0
+ while (featureIndex < numFeatures) {
+ // Finding the bin index for this feature
+ val arrShift = 1 + numFeatures * nodeIndex
+ val arrIndex = arrShift + featureIndex
+ // Updating the left or right count for one bin
+ val aggShift = 2 * numBins * numFeatures * nodeIndex
+ val aggIndex = aggShift + 2 * featureIndex * numBins +
arr(arrIndex).toInt * 2
+ label match {
+ case (0.0) => agg(aggIndex) = agg(aggIndex) + 1
+ case (1.0) => agg(aggIndex + 1) = agg(aggIndex + 1) + 1
+ }
+ featureIndex += 1
+ }
+ }
+ nodeIndex += 1
+ }
+ }
+
+ /**
+ * Performs a sequential aggregation over a partition for regression.
For l nodes, k features,
+ * the count, sum, sum of squares of one of the p bins is incremented.
+ *
+ * @param agg Array[Double] storing aggregate calculation of size
+ * 3*numSplits*numFeatures*numNodes for classification
+ * @param arr Array[Double] of size 1+(numFeatures*numNodes)
+ * @return Array[Double] storing aggregate calculation of size
+ * 3*numSplits*numFeatures*numNodes for regression
+ */
+ def regressionBinSeqOp(arr: Array[Double], agg: Array[Double]) {
+ // Iterating over all nodes
+ var nodeIndex = 0
+ while (nodeIndex < numNodes) {
+ // Checking whether the instance was valid for this nodeIndex
+ val validSignalIndex = 1 + numFeatures * nodeIndex
+ val isSampleValidForNode = arr(validSignalIndex) != InvalidBinIndex
+ if (isSampleValidForNode) {
+ // Actual class label
+ val label = arr(0)
+ // Iterating over all features
+ var featureIndex = 0
+ while (featureIndex < numFeatures) {
+ // Finding the bin index for this feature
+ val arrShift = 1 + numFeatures * nodeIndex
+ val arrIndex = arrShift + featureIndex
+ // updating count, sum, sum^2 for one bin
+ val aggShift = 3 * numBins * numFeatures * nodeIndex
+ val aggIndex = aggShift + 3 * featureIndex * numBins +
arr(arrIndex).toInt * 3
+ agg(aggIndex) = agg(aggIndex) + 1
+ agg(aggIndex + 1) = agg(aggIndex + 1) + label
+ agg(aggIndex + 2) = agg(aggIndex + 2) + label*label
+ // increment featureIndex
+ featureIndex += 1
+ }
+ }
+ nodeIndex += 1
+ }
+ }
+
+ /**
+ * Performs a sequential aggregation over a partition.
+ */
+ def binSeqOp(agg: Array[Double], arr: Array[Double]): Array[Double] = {
+ strategy.algo match {
+ case Classification => classificationBinSeqOp(arr, agg)
+ case Regression => regressionBinSeqOp(arr, agg)
+ }
+ agg
+ }
+
+ // Calculating bin aggregate length for classification or regression
+ val binAggregateLength = strategy.algo match {
+ case Classification => 2*numBins * numFeatures * numNodes
+ case Regression => 3*numBins * numFeatures * numNodes
+ }
+ logDebug("binAggregateLength = " + binAggregateLength)
+
+ /**
+ * Combines the aggregates from partitions
+ * @param agg1 Array containing aggregates from one or more partitions
+ * @param agg2 Array containing aggregates from one or more partitions
+ * @return Combined aggregate from agg1 and agg2
+ */
+ def binCombOp(agg1: Array[Double], agg2: Array[Double]): Array[Double]
= {
+ var index = 0
+ val combinedAggregate = new Array[Double](binAggregateLength)
+ while (index < binAggregateLength){
+ combinedAggregate(index) = agg1(index) + agg2(index)
+ index += 1
+ }
+ combinedAggregate
+ }
+
+ // find feature bins for all nodes at a level
+ val binMappedRDD = input.map(x => findBinsForLevel(x))
+
+ // calculate bin aggregates
+ val binAggregates = {
+
binMappedRDD.aggregate(Array.fill[Double](binAggregateLength)(0))(binSeqOp,binCombOp)
+ }
+ logDebug("binAggregates.length = " + binAggregates.length)
+
+ /**
+ * Calculates the information gain for all splits based upon
left/right split aggregates
+ * @param leftNodeAgg left node aggregates
+ * @param featureIndex feature index
+ * @param splitIndex split index
+ * @param rightNodeAgg right node aggregate
+ * @param topImpurity impurity of the parent node
+ * @return information gain and statistics for all splits
+ */
+ def calculateGainForSplit(
+ leftNodeAgg: Array[Array[Double]],
+ featureIndex: Int,
+ splitIndex: Int,
+ rightNodeAgg: Array[Array[Double]],
+ topImpurity: Double)
+ : InformationGainStats = {
+
+ strategy.algo match {
+ case Classification => {
+
+ val left0Count = leftNodeAgg(featureIndex)(2 * splitIndex)
+ val left1Count = leftNodeAgg(featureIndex)(2 * splitIndex + 1)
+ val leftCount = left0Count + left1Count
+
+ val right0Count = rightNodeAgg(featureIndex)(2 * splitIndex)
+ val right1Count = rightNodeAgg(featureIndex)(2 * splitIndex + 1)
+ val rightCount = right0Count + right1Count
+
+ val impurity = {
+ if (level > 0) {
+ topImpurity
+ } else {
+ // Calculating impurity for root node
+ strategy.impurity.calculate(left0Count + right0Count,
left1Count + right1Count)
+ }
+ }
+
+ if (leftCount == 0) {
+ return new InformationGainStats(0, topImpurity,
Double.MinValue, topImpurity,1)
+ }
+ if (rightCount == 0) {
+ return new InformationGainStats(0, topImpurity, topImpurity,
Double.MinValue,0)
+ }
+
+ val leftImpurity = strategy.impurity.calculate(left0Count,
left1Count)
+ val rightImpurity = strategy.impurity.calculate(right0Count,
right1Count)
+
+ val leftWeight = leftCount.toDouble / (leftCount + rightCount)
+ val rightWeight = rightCount.toDouble / (leftCount + rightCount)
+
+ val gain = {
+ if (level > 0) {
+ impurity - leftWeight * leftImpurity - rightWeight *
rightImpurity
+ } else {
+ impurity - leftWeight * leftImpurity - rightWeight *
rightImpurity
+ }
+ }
+
+ val predict = (left1Count + right1Count) / (leftCount +
rightCount)
+
+ new InformationGainStats(gain, impurity, leftImpurity,
rightImpurity, predict)
+ }
+ case Regression => {
+ val leftCount = leftNodeAgg(featureIndex)(3 * splitIndex)
+ val leftSum = leftNodeAgg(featureIndex)(3 * splitIndex + 1)
+ val leftSumSquares = leftNodeAgg(featureIndex)(3 * splitIndex +
2)
+
+ val rightCount = rightNodeAgg(featureIndex)(3 * splitIndex)
+ val rightSum = rightNodeAgg(featureIndex)(3 * splitIndex + 1)
+ val rightSumSquares = rightNodeAgg(featureIndex)(3 * splitIndex
+ 2)
+
+ val impurity = {
+ if (level > 0) {
+ topImpurity
+ } else {
+ // Calculating impurity for root node
+ val count = leftCount + rightCount
+ val sum = leftSum + rightSum
+ val sumSquares = leftSumSquares + rightSumSquares
+ strategy.impurity.calculate(count, sum, sumSquares)
+ }
+ }
+
+ if (leftCount == 0) {
+ return new InformationGainStats(0, topImpurity,
Double.MinValue, topImpurity,
+ rightSum / rightCount)
+ }
+ if (rightCount == 0) {
+ return new InformationGainStats(0, topImpurity ,topImpurity,
+ Double.MinValue, leftSum / leftCount)
+ }
+
+ val leftImpurity = strategy.impurity.calculate(leftCount,
leftSum, leftSumSquares)
+ val rightImpurity = strategy.impurity.calculate(rightCount,
rightSum, rightSumSquares)
+
+ val leftWeight = leftCount.toDouble / (leftCount + rightCount)
+ val rightWeight = rightCount.toDouble / (leftCount + rightCount)
+
+ val gain = {
+ if (level > 0) {
+ impurity - leftWeight * leftImpurity - rightWeight *
rightImpurity
+ } else {
+ impurity - leftWeight * leftImpurity - rightWeight *
rightImpurity
+ }
+ }
+
+ val predict = (leftSum + rightSum) / (leftCount + rightCount)
+ new InformationGainStats(gain, impurity, leftImpurity,
rightImpurity, predict)
+
+ }
+ }
+ }
+
+ /**
+ * Extracts left and right split aggregates
+ * @param binData Array[Double] of size 2*numFeatures*numSplits
+ * @return (leftNodeAgg, rightNodeAgg) tuple of type (Array[Double],
+ * Array[Double]) where each array is of
size(numFeature,2*(numSplits-1))
+ */
+ def extractLeftRightNodeAggregates(
+ binData: Array[Double])
+ : (Array[Array[Double]], Array[Array[Double]]) = {
+
+ strategy.algo match {
+ case Classification => {
+ // Initializing left and right split aggregates
+ val leftNodeAgg = Array.ofDim[Double](numFeatures, 2 * (numBins
- 1))
+ val rightNodeAgg = Array.ofDim[Double](numFeatures, 2 * (numBins
- 1))
+ // Iterating over all features
+ var featureIndex = 0
+ while (featureIndex < numFeatures) {
+ // shift for this featureIndex
+ val shift = 2*featureIndex*numBins
+
+ // left node aggregate for the lowest split
+ leftNodeAgg(featureIndex)(0) = binData(shift + 0)
+ leftNodeAgg(featureIndex)(1) = binData(shift + 1)
+
+ // right node aggregate for the highest split
+ rightNodeAgg(featureIndex)(2 * (numBins - 2))
+ = binData(shift + (2 * (numBins - 1)))
+ rightNodeAgg(featureIndex)(2 * (numBins - 2) + 1)
+ = binData(shift + (2 * (numBins - 1)) + 1)
+
+ // Iterating over all splits
+ var splitIndex = 1
+ while (splitIndex < numBins - 1) {
+ // calculating left node aggregate for a split as a sum of
left node aggregate of a
+ // lower split and the left bin aggregate of a bin where the
split is a high split
+ leftNodeAgg(featureIndex)(2 * splitIndex) = binData(shift +
2 * splitIndex) +
+ leftNodeAgg(featureIndex)(2 * splitIndex - 2)
+ leftNodeAgg(featureIndex)(2 * splitIndex + 1) =
binData(shift + 2 * splitIndex + 1) +
+ leftNodeAgg(featureIndex)(2 * splitIndex - 2 + 1)
+
+ // calculating right node aggregate for a split as a sum of
right node aggregate of a
+ // higher split and the right bin aggregate of a bin where
the split is a low split
+ rightNodeAgg(featureIndex)(2 * (numBins - 2 - splitIndex)) =
+ binData(shift + (2 *(numBins - 2 - splitIndex))) +
+ rightNodeAgg(featureIndex)(2 * (numBins - 1 - splitIndex))
+ rightNodeAgg(featureIndex)(2 * (numBins - 2 - splitIndex) +
1) =
+ binData(shift + (2* (numBins - 2 - splitIndex) + 1)) +
+ rightNodeAgg(featureIndex)(2 * (numBins - 1 -
splitIndex) + 1)
+
+ splitIndex += 1
+ }
+ featureIndex += 1
+ }
+ (leftNodeAgg, rightNodeAgg)
+ }
+
+ case Regression => {
+ // Initializing left and right split aggregates
+ val leftNodeAgg = Array.ofDim[Double](numFeatures, 3 * (numBins
- 1))
+ val rightNodeAgg = Array.ofDim[Double](numFeatures, 3 * (numBins
- 1))
+ // Iterating over all features
+ var featureIndex = 0
+ while (featureIndex < numFeatures) {
+ // shift for this featureIndex
+ val shift = 3*featureIndex*numBins
+ // left node aggregate for the lowest split
+ leftNodeAgg(featureIndex)(0) = binData(shift + 0)
+ leftNodeAgg(featureIndex)(1) = binData(shift + 1)
+ leftNodeAgg(featureIndex)(2) = binData(shift + 2)
+
+ // right node aggregate for the highest split
+ rightNodeAgg(featureIndex)(3 * (numBins - 2)) =
+ binData(shift + (3 * (numBins - 1)))
+ rightNodeAgg(featureIndex)(3 * (numBins - 2) + 1) =
+ binData(shift + (3 * (numBins - 1)) + 1)
+ rightNodeAgg(featureIndex)(3 * (numBins - 2) + 2) =
+ binData(shift + (3 * (numBins - 1)) + 2)
+
+ // Iterating over all splits
+ var splitIndex = 1
+ while (splitIndex < numBins - 1) {
+ // calculating left node aggregate for a split as a sum of
left node aggregate of a
+ // lower split and the left bin aggregate of a bin where the
split is a high split
+ leftNodeAgg(featureIndex)(3 * splitIndex)
+ = binData(shift + 3 * splitIndex) +
+ leftNodeAgg(featureIndex)(3 * splitIndex - 3)
+ leftNodeAgg(featureIndex)(3 * splitIndex + 1)
+ = binData(shift + 3 * splitIndex + 1) +
+ leftNodeAgg(featureIndex)(3 * splitIndex - 3 + 1)
+ leftNodeAgg(featureIndex)(3 * splitIndex + 2)
+ = binData(shift + 3 * splitIndex + 2) +
+ leftNodeAgg(featureIndex)(3 * splitIndex - 3 + 2)
+
+ // calculating right node aggregate for a split as a sum of
right node aggregate of a
+ // higher split and the right bin aggregate of a bin where
the split is a low split
+ rightNodeAgg(featureIndex)(3 * (numBins - 2 - splitIndex))
+ = binData(shift + (3 * (numBins - 2 - splitIndex))) +
+ rightNodeAgg(featureIndex)(3 * (numBins - 1 - splitIndex))
+ rightNodeAgg(featureIndex)(3 * (numBins - 2 - splitIndex) +
1)
+ = binData(shift + (3 * (numBins - 2 - splitIndex) + 1)) +
+ rightNodeAgg(featureIndex)(3 * (numBins - 1 - splitIndex)
+ 1)
+ rightNodeAgg(featureIndex)(3 * (numBins - 2 - splitIndex) +
2)
+ = binData(shift + (3 * (numBins - 2 - splitIndex) + 2)) +
+ rightNodeAgg(featureIndex)(3 * (numBins - 1 - splitIndex)
+ 2)
+
+ splitIndex += 1
+ }
+ featureIndex += 1
+ }
+ (leftNodeAgg, rightNodeAgg)
+ }
+ }
+ }
+
+ /**
+ * Calculates information gain for all nodes splits
+ */
+ def calculateGainsForAllNodeSplits(
+ leftNodeAgg: Array[Array[Double]],
+ rightNodeAgg: Array[Array[Double]],
+ nodeImpurity: Double)
+ : Array[Array[InformationGainStats]] = {
+
+ val gains = Array.ofDim[InformationGainStats](numFeatures, numBins -
1)
+
+ for (featureIndex <- 0 until numFeatures) {
+ for (splitIndex <- 0 until numBins -1) {
+ gains(featureIndex)(splitIndex) =
calculateGainForSplit(leftNodeAgg, featureIndex,
+ splitIndex, rightNodeAgg, nodeImpurity)
+ }
+ }
+ gains
+ }
+
+ /**
+ * Find the best split for a node
+ * @param binData Array[Double] of size 2*numSplits*numFeatures
+ * @param nodeImpurity impurity of the top node
+ * @return tuple of split and information gain
+ */
+ def binsToBestSplit(
+ binData: Array[Double],
+ nodeImpurity: Double)
+ : (Split, InformationGainStats) = {
+
+ logDebug("node impurity = " + nodeImpurity)
+
+ //extract left right node aggregates
+ val (leftNodeAgg, rightNodeAgg) =
extractLeftRightNodeAggregates(binData)
+
+ // calculate gains for all splits
+ val gains = calculateGainsForAllNodeSplits(leftNodeAgg,
rightNodeAgg, nodeImpurity)
+
+ val (bestFeatureIndex,bestSplitIndex, gainStats) = {
+ // Initialization with infeasible values
+ var bestFeatureIndex = Int.MinValue
+ var bestSplitIndex = Int.MinValue
+ var bestGainStats = new
InformationGainStats(Double.MinValue,-1.0,-1.0,-1.0,-1)
+ // Iterating over features
+ var featureIndex = 0
+ while (featureIndex < numFeatures) {
+ // Iterating over all splits
+ var splitIndex = 0
+ while (splitIndex < numBins - 1){
+ val gainStats = gains(featureIndex)(splitIndex)
+ if(gainStats.gain > bestGainStats.gain) {
+ bestGainStats = gainStats
+ bestFeatureIndex = featureIndex
+ bestSplitIndex = splitIndex
+ }
+ splitIndex += 1
+ }
+ featureIndex += 1
+ }
+ (bestFeatureIndex,bestSplitIndex,bestGainStats)
+ }
+
+ logDebug("best split bin = " +
bins(bestFeatureIndex)(bestSplitIndex))
+ logDebug("best split bin = " +
splits(bestFeatureIndex)(bestSplitIndex))
+ (splits(bestFeatureIndex)(bestSplitIndex),gainStats)
+ }
+
+ /**
+ * get bin data for one node
+ */
+ def getBinDataForNode(node: Int): Array[Double] = {
+ strategy.algo match {
+ case Classification => {
+ val shift = 2 * node * numBins * numFeatures
+ val binsForNode = binAggregates.slice(shift, shift + 2 * numBins
* numFeatures)
+ binsForNode
+ }
+ case Regression => {
+ val shift = 3 * node * numBins * numFeatures
+ val binsForNode = binAggregates.slice(shift, shift + 3 * numBins
* numFeatures)
+ binsForNode
+ }
+ }
+ }
+
+ // Calculate best splits for all nodes at a given level
+ val bestSplits = new Array[(Split, InformationGainStats)](numNodes)
+ // Iterating over all nodes at this level
+ var node = 0
+ while (node < numNodes){
+ val nodeImpurityIndex = scala.math.pow(2, level).toInt - 1 + node
+ val binsForNode: Array[Double] = getBinDataForNode(node)
+ logDebug("nodeImpurityIndex = " + nodeImpurityIndex)
+ val parentNodeImpurity = parentImpurities(nodeImpurityIndex)
+ logDebug("node impurity = " + parentNodeImpurity)
+ bestSplits(node) = binsToBestSplit(binsForNode, parentNodeImpurity)
+ node += 1
+ }
+
+ //Return best splits
+ bestSplits
+ }
+
+
+
+ /**
+ * Returns split and bins for decision tree calculation.
+ * @param input RDD of
[[org.apache.spark.mllib.regression.LabeledPoint]] used as training data
+ * for DecisionTree
+ * @param strategy
[[org.apache.spark.mllib.tree.configuration.Strategy]] instance containing
+ * parameters for construction the DecisionTree
+ * @return a tuple of (splits,bins) where splits is an Array of
[org.apache.spark.mllib.tree
+ * .model.Split] of size (numFeatures,numSplits-1) and bins is
an Array of [org.apache
+ * .spark.mllib.tree.model.Bin] of size (numFeatures,numSplits1)
+ */
+ def findSplitsBins(
+ input: RDD[LabeledPoint],
+ strategy: Strategy)
+ : (Array[Array[Split]], Array[Array[Bin]]) = {
+
+ val count = input.count()
+
+ // Find the number of features by looking at the first sample
+ val numFeatures = input.take(1)(0).features.length
+
+ val maxBins = strategy.maxBins
+ val numBins = if (maxBins <= count) maxBins else count.toInt
+ logDebug("numBins = " + numBins)
+
+ // I will also add a require statement ensuring #bins is always
greater than the categories
+ // It's a limitation of the current implementation but a reasonable
tradeoff since features
+ // with large number of categories get favored over continuous
features.
+ if (strategy.categoricalFeaturesInfo.size > 0){
+ val maxCategoriesForFeatures =
strategy.categoricalFeaturesInfo.maxBy(_._2)._2
+ require(numBins >= maxCategoriesForFeatures)
+ }
+
+ // Calculate the number of sample for approximate quantile calculation
+ val requiredSamples = numBins*numBins
+ val fraction = if (requiredSamples < count) requiredSamples.toDouble /
count else 1.0
+ logDebug("fraction of data used for calculating quantiles = " +
fraction)
+
+ // sampled input for RDD calculation
+ val sampledInput = input.sample(false, fraction, new
XORShiftRandom().nextInt()).collect()
+ val numSamples = sampledInput.length
+
+ val stride: Double = numSamples.toDouble / numBins
+ logDebug("stride = " + stride)
+
+ strategy.quantileCalculationStrategy match {
+ case Sort => {
+ val splits = Array.ofDim[Split](numFeatures, numBins-1)
+ val bins = Array.ofDim[Bin](numFeatures, numBins)
+
+ // Find all splits
+
+ // Iterating over all features
+ var featureIndex = 0
+ while (featureIndex < numFeatures){
+ // Checking whether the feature is continuous
+ val isFeatureContinuous =
strategy.categoricalFeaturesInfo.get(featureIndex).isEmpty
+ if (isFeatureContinuous) {
+ val featureSamples = sampledInput.map(lp =>
lp.features(featureIndex)).sorted
+ val stride: Double = numSamples.toDouble/numBins
+ logDebug("stride = " + stride)
+ for (index <- 0 until numBins-1) {
+ val sampleIndex = (index + 1)*stride.toInt
+ val split = new Split(featureIndex,
featureSamples(sampleIndex), Continuous, List())
+ splits(featureIndex)(index) = split
+ }
+ } else {
+ val maxFeatureValue =
strategy.categoricalFeaturesInfo(featureIndex)
+ require(maxFeatureValue < numBins, "number of categories
should be less than number " +
+ "of bins")
+
+ // For categorical variables, each bin is a category. The bins
are sorted and they
+ // are ordered by calculating the centriod of their
corresponding labels.
+ val centriodForCategories
+ = sampledInput.map(lp => (lp.features(featureIndex),lp.label))
+ .groupBy(_._1).mapValues(x => x.map(_._2).sum /
x.map(_._1).length)
+
+ // Checking for missing categorical variables and putting them
last in the sorted list
+ val fullCentriodForCategories =
scala.collection.mutable.Map[Double,Double]()
+ for (i <- 0 until maxFeatureValue) {
+ if (centriodForCategories.contains(i)) {
+ fullCentriodForCategories(i) = centriodForCategories(i)
+ } else {
+ fullCentriodForCategories(i) = Double.MaxValue
+ }
+ }
+
+ //bins sorted by centriods
+ val categoriesSortedByCentriod
+ = fullCentriodForCategories.toList.sortBy{_._2}
+
+ logDebug("centriod for categorical variable = " +
categoriesSortedByCentriod)
+
+ var categoriesForSplit = List[Double]()
+ categoriesSortedByCentriod.iterator.zipWithIndex foreach {
+ case((key, value), index) => {
+ categoriesForSplit = key :: categoriesForSplit
+ splits(featureIndex)(index) = new Split(featureIndex,
Double.MinValue, Categorical,
+ categoriesForSplit)
+ bins(featureIndex)(index) = {
+ if(index == 0) {
+ new Bin(new DummyCategoricalSplit(featureIndex,
Categorical),
+ splits(featureIndex)(0), Categorical, key)
+ }
+ else {
+ new Bin(splits(featureIndex)(index-1),
splits(featureIndex)(index),
+ Categorical, key)
+ }
+ }
+ }
+ }
+ }
+ featureIndex += 1
+ }
+
+ // Find all bins
+ featureIndex = 0
+ while (featureIndex < numFeatures){
+ val isFeatureContinuous =
strategy.categoricalFeaturesInfo.get(featureIndex).isEmpty
+ if (isFeatureContinuous) { // bins for categorical variables
are already assigned
+ bins(featureIndex)(0)
+ = new Bin(new DummyLowSplit(featureIndex,
Continuous),splits(featureIndex)(0),
+ Continuous,Double.MinValue)
+ for (index <- 1 until numBins - 1){
+ val bin = new Bin(splits(featureIndex)(index-1),
splits(featureIndex)(index),
+ Continuous, Double.MinValue)
+ bins(featureIndex)(index) = bin
+ }
+ bins(featureIndex)(numBins-1)
+ = new Bin(splits(featureIndex)(numBins-2),new
DummyHighSplit(featureIndex,
+ Continuous), Continuous, Double.MinValue)
+ }
+ featureIndex += 1
+ }
+ (splits,bins)
+ }
+ case MinMax => {
+ throw new UnsupportedOperationException("minmax not supported
yet.")
+ }
+ case ApproxHist => {
+ throw new UnsupportedOperationException("approximate histogram not
supported yet.")
+ }
+ }
+ }
+
+
+ val usage = """
+ Usage: DecisionTreeRunner <master>[slices] --algo <Classification,
+ Regression> --trainDataDir path --testDataDir path --maxDepth num
[--impurity <Gini,Entropy,
+ Variance>] [--maxBins num]
+ """
+
+
+ def main(args: Array[String]) {
+
+ if (args.length < 2) {
+ System.err.println(usage)
+ System.exit(1)
+ }
+
+ val sc = new SparkContext(args(0), "DecisionTree")
+
+ val argList = args.toList.drop(1)
+ type OptionMap = Map[Symbol, Any]
+
+ def nextOption(map : OptionMap, list: List[String]): OptionMap = {
+ list match {
+ case Nil => map
+ case "--algo" :: string :: tail => nextOption(map ++ Map('algo ->
string), tail)
+ case "--impurity" :: string :: tail => nextOption(map ++
Map('impurity -> string), tail)
+ case "--maxDepth" :: string :: tail => nextOption(map ++
Map('maxDepth -> string), tail)
+ case "--maxBins" :: string :: tail => nextOption(map ++
Map('maxBins -> string), tail)
+ case "--trainDataDir" :: string :: tail => nextOption(map ++
Map('trainDataDir -> string)
+ , tail)
+ case "--testDataDir" :: string :: tail => nextOption(map ++
Map('testDataDir -> string),
+ tail)
+ case string :: Nil => nextOption(map ++ Map('infile -> string),
list.tail)
+ case option :: tail => logError("Unknown option " + option)
+ sys.exit(1)
+ }
+ }
+ val options = nextOption(Map(),argList)
+ logDebug(options.toString())
+
+ // Load training data
+ val trainData = loadLabeledData(sc,
options.get('trainDataDir).get.toString)
+
+ // Identify the type of algorithm
+ val algoStr = options.get('algo).get.toString
+ val algo = algoStr match {
+ case "Classification" => Classification
+ case "Regression" => Regression
+ }
+
+ // Identify the type of impurity
+ val impurityStr = options.getOrElse('impurity,
+ if (algo == Classification) "Gini" else "Variance").toString
+ val impurity = impurityStr match {
+ case "Gini" => Gini
+ case "Entropy" => Entropy
+ case "Variance" => Variance
+ }
+
+ val maxDepth = options.getOrElse('maxDepth,"1").toString.toInt
+ val maxBins = options.getOrElse('maxBins,"100").toString.toInt
+
+ val strategy = new Strategy(algo, impurity, maxDepth, maxBins)
+ val model = DecisionTree.train(trainData, strategy)
+
+ // Load test data
+ val testData = loadLabeledData(sc,
options.get('testDataDir).get.toString)
+
+ // Measure algorithm accuracy
+ if (algo == Classification){
+ val accuracy = accuracyScore(model, testData)
+ logDebug("accuracy = " + accuracy)
+ }
+
+ if (algo == Regression){
+ val mse = meanSquaredError(model, testData)
+ logDebug("mean square error = " + mse)
+ }
+
+ sc.stop()
+ }
+
+ /**
+ * Load labeled data from a file. The data format used here is
+ * <L>, <f1> <f2> ...
+ * where <f1>, <f2> are feature values in Double and <L> is the
corresponding label as Double.
+ *
+ * @param sc SparkContext
+ * @param dir Directory to the input data files.
+ * @return An RDD of LabeledPoint. Each labeled point has two elements:
the first element is
+ * the label, and the second element represents the feature
values (an array of Double).
+ */
+ def loadLabeledData(sc: SparkContext, dir: String): RDD[LabeledPoint] = {
+ sc.textFile(dir).map { line =>
+ val parts = line.trim().split(",")
+ val label = parts(0).toDouble
+ val features = parts.slice(1,parts.length).map(_.toDouble)
+ LabeledPoint(label, features)
+ }
+ }
+
+ // TODO: Port this method to a generic metrics package
+ /**
+ * Calculates the classifier accuracy.
+ */
+ def accuracyScore(model: DecisionTreeModel, data: RDD[LabeledPoint],
+ threshold: Double = 0.5): Double = {
+ def predictedValue(features: Array[Double]) = {
+ if (model.predict(features) < threshold) 0.0 else 1.0
+ }
+ val correctCount = data.filter(y => predictedValue(y.features) ==
y.label).count()
+ val count = data.count()
+ logDebug("correct prediction count = " + correctCount)
+ logDebug("data count = " + count)
+ correctCount.toDouble / count
+ }
+
+ // TODO: Port this method to a generic metrics package
+ /**
+ * Calculates the mean squared error for regression
+ */
+ def meanSquaredError(tree: DecisionTreeModel, data: RDD[LabeledPoint]):
Double = {
--- End diff --
might make sense to make this private as well
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