使用树输出预测 Spark 中梯度提升树情况下的类概率

众所周知，Spark 中的 GBT 目前可以为您提供预测标签。

我正在考虑尝试计算一个类的预测概率（假设所有实例都落在某个叶子下）

构建 GBT 的代码

import org.apache.spark.SparkContext
import org.apache.spark.mllib.regression.LabeledPoint
import org.apache.spark.mllib.linalg.Vectors
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

//Importing the data
val data = sc.textFile("data/mllib/credit_approval_2_attr.csv") //using the credit approval data set from UCI machine learning repository

//Parsing the data
val parsedData = data.map { line =>
    val parts = line.split(',').map(_.toDouble)
    LabeledPoint(parts(0), Vectors.dense(parts.tail))
}

//Splitting the data
val splits = parsedData.randomSplit(Array(0.7, 0.3), seed = 11L)
val training = splits(0).cache() 
val test = splits(1)

// Train a GradientBoostedTrees model.
// The defaultParams for Classification use LogLoss by default.
val boostingStrategy = BoostingStrategy.defaultParams("Classification")
boostingStrategy.numIterations = 2 // We can use more iterations in practice.
boostingStrategy.treeStrategy.numClasses = 2
boostingStrategy.treeStrategy.maxDepth = 2
boostingStrategy.treeStrategy.maxBins = 32
boostingStrategy.treeStrategy.subsamplingRate = 0.5
boostingStrategy.treeStrategy.maxMemoryInMB =1024
boostingStrategy.learningRate = 0.1

// Empty categoricalFeaturesInfo indicates all features are continuous.
boostingStrategy.treeStrategy.categoricalFeaturesInfo = Map[Int, Int]()

val model = GradientBoostedTrees.train(training, boostingStrategy)  

model.toDebugString

为了简单起见，这给了我两棵深度为 2 的树，如下所示：

 Tree 0:
    If (feature 3 <= 2.0)
     If (feature 2 <= 1.25)
      Predict: -0.5752212389380531
     Else (feature 2 > 1.25)
      Predict: 0.07462686567164178
    Else (feature 3 > 2.0)
     If (feature 0 <= 30.17)
      Predict: 0.7272727272727273
     Else (feature 0 > 30.17)
      Predict: 1.0
  Tree 1:
    If (feature 5 <= 67.0)
     If (feature 4 <= 100.0)
      Predict: 0.5739387416147804
     Else (feature 4 > 100.0)
      Predict: -0.550117566730937
    Else (feature 5 > 67.0)
     If (feature 2 <= 0.0)
      Predict: 3.0383669122382835
     Else (feature 2 > 0.0)
      Predict: 0.4332824083446489

我的问题是：我可以使用上面的树来计算预测概率，例如：

对于用于预测的特征集中的每个实例

exp(树 0 的叶子分数 + 树 1 的叶子分数)/(1+exp(树 0 的叶子分数 + 树 1 的叶子分数))

这给了我一种概率。但不确定这是否是正确的方法。另外，是否有任何文档解释如何计算叶子分数（预测）。如果有人可以分享，我将非常感激。

任何建议都会很棒。

这是我使用 Spark 内部依赖项的方法。稍后您需要导入线性代数库进行矩阵运算，即将树预测与学习率相乘。

import org.apache.spark.mllib.linalg.{Vectors, Matrices}
import org.apache.spark.mllib.linalg.distributed.{RowMatrix}

假设您使用 GBT 构建模型：

val model = GradientBoostedTrees.train(trainingData, boostingStrategy)

使用模型对象计算概率：

// Get the log odds predictions from each tree
val treePredictions = testData.map { point => model.trees.map(_.predict(point.features)) }

// Transform the arrays into matrices for multiplication
val treePredictionsVector = treePredictions.map(array => Vectors.dense(array))
val treePredictionsMatrix = new RowMatrix(treePredictionsVector)
val learningRate = model.treeWeights
val learningRateMatrix = Matrices.dense(learningRate.size, 1, learningRate)
val weightedTreePredictions = treePredictionsMatrix.multiply(learningRateMatrix)

// Calculate probability by ensembling the log odds
val classProb = weightedTreePredictions.rows.flatMap(_.toArray).map(x => 1 / (1 + Math.exp(-1 * x)))
classProb.collect

// You may tweak your decision boundary for different class labels
val classLabel = classProb.map(x => if (x > 0.5) 1.0 else 0.0)
classLabel.collect

以下是您可以直接复制并粘贴到 Spark-Shell 中的代码片段：

import org.apache.spark.mllib.regression.LabeledPoint
import org.apache.spark.mllib.linalg.{Vectors, Matrices}
import org.apache.spark.mllib.linalg.distributed.{RowMatrix}
import org.apache.spark.mllib.tree.GradientBoostedTrees
import org.apache.spark.mllib.tree.configuration.BoostingStrategy
import org.apache.spark.mllib.tree.model.GradientBoostedTreesModel

// Load and parse the data file.
val csvData = sc.textFile("data/mllib/sample_tree_data.csv")
val data = csvData.map { line =>
  val parts = line.split(',').map(_.toDouble)
  LabeledPoint(parts(0), Vectors.dense(parts.tail))
}
// 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 GBT model.
val boostingStrategy = BoostingStrategy.defaultParams("Classification")
boostingStrategy.numIterations = 50
boostingStrategy.treeStrategy.numClasses = 2
boostingStrategy.treeStrategy.maxDepth = 6
boostingStrategy.treeStrategy.categoricalFeaturesInfo = Map[Int, Int]()

val model = GradientBoostedTrees.train(trainingData, boostingStrategy)

// Get class label from raw predict function
val predictedLabels = model.predict(testData.map(_.features))
predictedLabels.collect

// Get class probability
val treePredictions = testData.map { point => model.trees.map(_.predict(point.features)) }
val treePredictionsVector = treePredictions.map(array => Vectors.dense(array))
val treePredictionsMatrix = new RowMatrix(treePredictionsVector)
val learningRate = model.treeWeights
val learningRateMatrix = Matrices.dense(learningRate.size, 1, learningRate)
val weightedTreePredictions = treePredictionsMatrix.multiply(learningRateMatrix)
val classProb = weightedTreePredictions.rows.flatMap(_.toArray).map(x => 1 / (1 + Math.exp(-1 * x)))
val classLabel = classProb.map(x => if (x > 0.5) 1.0 else 0.0)
classLabel.collect