Spark MLlib: Decision Tree源码分析
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Spark MLlib: Decision Tree源码分析
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http://spark.apache.org/docs/latest/mllib-decision-tree.html
以決策樹作為開始，因為簡單，而且也比較容易用到，當前的boosting或random forest也是常以其為基礎的
決策樹算法本身參考之前的blog，其實就是貪婪算法，每次切分使得數據變得最為有序
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那么如何來定義有序或無序？
無序，node impurity?
對于分類問題，我們可以用熵entropy或Gini來表示信息的無序程度?
對于回歸問題，我們用方差Variance來表示無序程度，方差越大，說明數據間差異越大
information gain
用于表示，由父節點劃分后得到子節點，所帶來的impurity的下降，即有序性的增益
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MLib決策樹的例子
下面直接看個regression的例子，分類的case，差不多，
import org.apache.spark.mllib.tree.DecisionTree import org.apache.spark.mllib.util.MLUtils// 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. val categoricalFeaturesInfo = Map[Int, Int]() val impurity = "variance" val maxDepth = 5 val maxBins = 100val model = DecisionTree.trainRegressor(data, categoricalFeaturesInfo, impurity,maxDepth, maxBins)// Evaluate model on training instances and compute training error val labelsAndPredictions = data.map { point =>val prediction = model.predict(point.features)(point.label, prediction) } val trainMSE = labelsAndPredictions.map{ case(v, p) => math.pow((v - p), 2)}.mean() println("Training Mean Squared Error = " + trainMSE) println("Learned regression tree model:\n" + model)還是比較簡單的，
由于是回歸，所以impurity的定義為variance?
maxDepth，最大樹深，設為5?
maxBins，最大的劃分數?
先理解什么是bin，決策樹的算法就是對feature的取值不斷的進行劃分?
對于離散的feature，比較簡單，如果有m個值，最多?個劃分，如果值是有序的，那么就最多m-1個劃分?
比如年齡feature，有老，中，少3個值，如果無序有個，即3種劃分，老|中，少；老，中|少；老，少|中?
但如果是有序的，即按老，中，少的序，那么只有m-1個，即2種劃分，老|中，少；老，中|少
對于連續的feature，其實就是進行范圍劃分，而劃分的點就是split，劃分出的區間就是bin?
對于連續feature，理論上劃分點是無數的，但是出于效率我們總要選取合適的劃分點?
有個比較常用的方法是取出訓練集中該feature出現過的值作為劃分點，?
但對于分布式數據，取出所有的值進行排序也比較費資源，所以可以采取sample的方式
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源碼分析
首先調用，DecisionTree.trainRegressor，類似調用靜態函數（object DecisionTree）
org.apache.spark.mllib.tree.DecisionTree.scala
/*** Method to train a decision tree model for regression.** @param input Training dataset: RDD of [[org.apache.spark.mllib.regression.LabeledPoint]].* Labels are real numbers.* @param categoricalFeaturesInfo Map storing arity of categorical features.* E.g., an entry (n -> k) indicates that feature n is categorical* with k categories indexed from 0: {0, 1, ..., k-1}.* @param impurity Criterion used for information gain calculation.* Supported values: "variance".* @param maxDepth Maximum depth of the tree.* E.g., depth 0 means 1 leaf node; depth 1 means 1 internal node + 2 leaf nodes.* (suggested value: 5)* @param maxBins maximum number of bins used for splitting features* (suggested value: 32)* @return DecisionTreeModel that can be used for prediction*/def trainRegressor(input: RDD[LabeledPoint],categoricalFeaturesInfo: Map[Int, Int],impurity: String,maxDepth: Int,maxBins: Int): DecisionTreeModel = {val impurityType = Impurities.fromString(impurity)train(input, Regression, impurityType, maxDepth, 0, maxBins, Sort, categoricalFeaturesInfo)}調用靜態函數train
def train(input: RDD[LabeledPoint],algo: Algo,impurity: Impurity,maxDepth: Int,numClassesForClassification: Int,maxBins: Int,quantileCalculationStrategy: QuantileStrategy,categoricalFeaturesInfo: Map[Int,Int]): DecisionTreeModel = {val strategy = new Strategy(algo, impurity, maxDepth, numClassesForClassification, maxBins,quantileCalculationStrategy, categoricalFeaturesInfo)new DecisionTree(strategy).train(input)}可以看到將所有參數封裝到Strategy類，然后初始化DecisionTree類對象，繼續調用成員函數train
/*** :: Experimental ::* A class which implements a decision tree learning 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.*/ @Experimental class DecisionTree (private val strategy: Strategy) extends Serializable with Logging {strategy.assertValid()/*** Method to train a decision tree model over an RDD* @param input Training data: RDD of [[org.apache.spark.mllib.regression.LabeledPoint]]* @return DecisionTreeModel that can be used for prediction*/def train(input: RDD[LabeledPoint]): DecisionTreeModel = {// Note: random seed will not be used since numTrees = 1.val rf = new RandomForest(strategy, numTrees = 1, featureSubsetStrategy = "all", seed = 0)val rfModel = rf.train(input)rfModel.trees(0)}}可以看到，這里DecisionTree的設計是基于RandomForest的特例，即單顆樹的RandomForest?
所以調用RandomForest.train()，最終因為只有一棵樹，所以取trees(0)
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org.apache.spark.mllib.tree.RandomForest.scala
重點看下，RandomForest里面的train做了什么？
/*** Method to train a decision tree model over an RDD* @param input Training data: RDD of [[org.apache.spark.mllib.regression.LabeledPoint]]* @return RandomForestModel that can be used for prediction*/def train(input: RDD[LabeledPoint]): RandomForestModel = {//1. metadataval retaggedInput = input.retag(classOf[LabeledPoint])val metadata =DecisionTreeMetadata.buildMetadata(retaggedInput, strategy, numTrees, featureSubsetStrategy)// 2. Find the splits and the corresponding bins (interval between the splits) using a sample// of the input data.val (splits, bins) = DecisionTree.findSplitsBins(retaggedInput, metadata)// 3. Bin feature values (TreePoint representation).// Cache input RDD for speedup during multiple passes.val treeInput = TreePoint.convertToTreeRDD(retaggedInput, bins, metadata)val baggedInput = if (numTrees > 1) {BaggedPoint.convertToBaggedRDD(treeInput, numTrees, seed)} else {BaggedPoint.convertToBaggedRDDWithoutSampling(treeInput)}.persist(StorageLevel.MEMORY_AND_DISK)// set maxDepth and compute memory usage // depth of the decision tree// Max memory usage for aggregates// TODO: Calculate memory usage more precisely.//......../** The main idea here is to perform group-wise training of the decision tree nodes thus* reducing the passes over the data from (# nodes) to (# nodes / maxNumberOfNodesPerGroup).* Each data sample is handled by a particular node (or it reaches a leaf and is not used* in lower levels).*/// FIFO queue of nodes to train: (treeIndex, node)val nodeQueue = new mutable.Queue[(Int, Node)]()val rng = new scala.util.Random()rng.setSeed(seed)// Allocate and queue root nodes.val topNodes: Array[Node] = Array.fill[Node](numTrees)(Node.emptyNode(nodeIndex = 1))Range(0, numTrees).foreach(treeIndex => nodeQueue.enqueue((treeIndex, topNodes(treeIndex))))while (nodeQueue.nonEmpty) {// Collect some nodes to split, and choose features for each node (if subsampling).// Each group of nodes may come from one or multiple trees, and at multiple levels.val (nodesForGroup, treeToNodeToIndexInfo) =RandomForest.selectNodesToSplit(nodeQueue, maxMemoryUsage, metadata, rng) // 對decision tree沒有意義，nodeQueue只有一個node，不需要選// 4. Choose node splits, and enqueue new nodes as needed.DecisionTree.findBestSplits(baggedInput, metadata, topNodes, nodesForGroup,treeToNodeToIndexInfo, splits, bins, nodeQueue, timer)}val trees = topNodes.map(topNode => new DecisionTreeModel(topNode, strategy.algo))RandomForestModel.build(trees)}1. DecisionTreeMetadata.buildMetadata
org.apache.spark.mllib.tree.impl.DecisionTreeMetadata.scala
這里生成一些后面需要用到的metadata?
最關鍵的是計算每個feature的bins和splits的數目，
計算bins的數目
//bins數目最大不能超過訓練集中樣本的sizeval maxPossibleBins = math.min(strategy.maxBins, numExamples).toInt//設置默認值val numBins = Array.fill[Int](numFeatures)(maxPossibleBins)if (numClasses > 2) {// Multiclass classificationval maxCategoriesForUnorderedFeature =((math.log(maxPossibleBins / 2 + 1) / math.log(2.0)) + 1).floor.toIntstrategy.categoricalFeaturesInfo.foreach { case (featureIndex, numCategories) =>// Decide if some categorical features should be treated as unordered features,// which require 2 * ((1 << numCategories - 1) - 1) bins.// We do this check with log values to prevent overflows in case numCategories is large.// The next check is equivalent to: 2 * ((1 << numCategories - 1) - 1) <= maxBinsif (numCategories <= maxCategoriesForUnorderedFeature) {unorderedFeatures.add(featureIndex)numBins(featureIndex) = numUnorderedBins(numCategories)} else {numBins(featureIndex) = numCategories}}} else {// Binary classification or regressionstrategy.categoricalFeaturesInfo.foreach { case (featureIndex, numCategories) =>numBins(featureIndex) = numCategories}}其他case，bins數目等于feature的numCategories?
對于unordered情況，比較特殊，
根據bins數目，計算splits
/*** Number of splits for the given feature.* For unordered features, there are 2 bins per split.* For ordered features, there is 1 more bin than split.*/def numSplits(featureIndex: Int): Int = if (isUnordered(featureIndex)) {numBins(featureIndex) >> 1} else {numBins(featureIndex) - 1}?
2. DecisionTree.findSplitsBins
首先找出每個feature上可能出現的splits和相應的bins，這是后續算法的基礎?
這里的注釋解釋了上面如何計算splits和bins數目的算法
a，對于連續數據，對于一個feature，splits = numBins - 1；上面也說了對于連續值，其實splits可以無限的，如何找到numBins - 1個splits，很簡單，這里用sample?
b，對于離散數據，兩個case?
??? b.1, 無序的feature，用于low-arity（參數較少）的multiclass分類，這種case下劃分的可能性比較多，，所以用subsets of categories來作為劃分?
??? b.2, 有序的feature，用于regression，二元分類，或high-arity的多元分類，這種case下劃分的可能比較少，m-1，所以用每個category作為劃分
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3. TreePoint和BaggedPoint
TreePoint是LabeledPoint的內部數據結構，這里需要做轉換，
private def labeledPointToTreePoint(labeledPoint: LabeledPoint,bins: Array[Array[Bin]],featureArity: Array[Int],isUnordered: Array[Boolean]): TreePoint = {val numFeatures = labeledPoint.features.sizeval arr = new Array[Int](numFeatures)var featureIndex = 0while (featureIndex < numFeatures) {arr(featureIndex) = findBin(featureIndex, labeledPoint, featureArity(featureIndex),isUnordered(featureIndex), bins)featureIndex += 1}new TreePoint(labeledPoint.label, arr) //只是將labeledPoint中的value替換成arr}arr是findBin的結果，?
這里主要是針對連續特征做處理，將連續的值通過二分查找轉換為相應bin的index?
對于離散數據，bin等同于featureValue.toInt
BaggedPoint，由于random forest是比較典型的bagging算法，所以需要對訓練集做bootstrap sample?
而對于decision tree是特殊的單根random forest，所以不需要做抽樣?
BaggedPoint.convertToBaggedRDDWithoutSampling(treeInput)?
其實只是做簡單的封裝
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4. DecisionTree.findBestSplits
這段代碼寫的有點復雜，尤其和randomForest混雜一起
總之，關鍵在
// find best split for each nodeval (split: Split, stats: InformationGainStats, predict: Predict) =binsToBestSplit(aggStats, splits, featuresForNode, nodes(nodeIndex))(nodeIndex, (split, stats, predict))}.collectAsMap()看看binsToBestSplit的實現，為了清晰一點，我們只看continuous feature
四個參數，
binAggregates: DTStatsAggregator， 就是ImpurityAggregator，給出如果算出impurity的邏輯?
splits: Array[Array[Split]], feature對應的splits?
featuresForNode: Option[Array[Int]], tree node對應的feature??
node: Node， 哪個tree node
返回值，
(Split, InformationGainStats, Predict)，?
Split，最優的split對象（包含featureindex和splitindex）?
InformationGainStats，該split產生的Gain對象，表明產生多少增益，多大程度降低impurity?
Predict，該節點的預測值，對于連續feature就是平均值，看后面的分析
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Predict，這個需要分析一下?
predictWithImpurity.get._1，predictWithImpurity元組的第一個元素?
calculatePredictImpurity的返回值中的predict
這里predict和impurity有什么不同，可以看出?
impurity = ImpurityCalculator.calculate()?
predict = ImpurityCalculator.predict
對于連續feature，我們就看Variance的實現，
/*** Calculate the impurity from the stored sufficient statistics.*/def calculate(): Double = Variance.calculate(stats(0), stats(1), stats(2)) @DeveloperApioverride def calculate(count: Double, sum: Double, sumSquares: Double): Double = {if (count == 0) {return 0}val squaredLoss = sumSquares - (sum * sum) / countsquaredLoss / count}從calculate的實現可以看到，impurity求的就是方差, 不是標準差（均方差）
/*** Prediction which should be made based on the sufficient statistics.*/def predict: Double = if (count == 0) {0} else {stats(1) / count}而predict求的就是平均值
總結
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