算法小白的第一次嘗試---BoostingTree（手撕提升樹）

import org.apache.spark.ml.feature.LabeledPoint
import org.apache.spark.ml.linalg.Vectors
import scala.collection.mutable.ArrayBuffer
/**
  * @author XiaoTangBao
  * @date 2019/3/10 16:00
  * @version 1.0
  * 基於統計學習方法--李航 例8.2 提升樹（迴歸）
  */
object BoostingTree {
  def main(args: Array[String]): Unit = {
    //初始化訓練數據
    var orignaldata = ArrayBuffer[LabeledPoint]()
    val arr = Array((1,5.56),(2,5.70),(3,5.91),(4,6.40),(5,6.80),(6,7.05),(7,8.90),(8,8.70),(9,9.00),(10,9.05))
    for(ar <- arr) orignaldata.append(LabeledPoint(ar._2,Vectors.dense(ar._1)))
    //定義切割點
    val cutpoints = ArrayBuffer[Double]()
    for(i <- 0 until arr.length-1) {cutpoints.append(arr(i)._1 + 0.5)}
    //定義滿足條件的損失誤差Li，當損失誤差 <= Li時，退出訓練
    val Li = 0.2
    //存放最終訓練好的模型
    val modelArr = ArrayBuffer[Double => Double]()
    var flag = true
    while(flag){
      val bestModel = getTree(orignaldata.toArray,cutpoints.toArray)
      modelArr.append(bestModel)
      //更新訓練數據data，生成殘差表，供下次迭代使用
      for(i<-0 until orignaldata.length ){
        val newLabel = orignaldata(i).label - bestModel(orignaldata(i).features(0))
        orignaldata(i) = LabeledPoint(newLabel,Vectors.dense(orignaldata(i).features(0)))
      }
      //根據殘差表計算平方損失誤差lx
      var sle = 0.0
      for(s <- orignaldata) sle += math.pow(s.label,2)
      if(sle <= Li) flag = false
    }
    //定義最終的模型
    val finalModel =(x:Double) => {
      var result = 0.0
      for(model <- modelArr) result += model(x)
      result
    }
    //準備相關的測試數據
    val csdata = Array(1.4,2.5,2.8,3.5,4.0,4.5,5.6,6.5,6.7)
    for(cs <- csdata) println(finalModel(cs))
  }

  def getTree(data:Array[LabeledPoint],cutpoints:Array[Double])= {
    //存儲每一次迭代產生的(cutpoint,(ms,c1,c2))
    val msArr = ArrayBuffer[(Double,(Double,Double,Double))]()
    for (cutpoint <- cutpoints) msArr.append((cutpoint,calms(cutpoint, data)))
    val best = msArr.sortBy(x => x._2._1).take(1)(0)
    //生成此次迭代的最佳模型更新訓練數據data，生成殘差表
    val bestModel =(x:Double) =>{
      val cp = best._1
      val c1 = best._2._2
      val c2 = best._2._3
      if(x < cp) c1 else c2
    }
    bestModel
  }

  //假設迴歸樹的損失函數爲平方誤差損失函數 f(x) = min[min(yi-c1)**2 + min(yi-c2)**2]
  def calms(cutpoint:Double,data:Array[LabeledPoint])={
    //計算誤差
    var ms = 0.0
    //min(yi-c1)**2
    var c1 = 0.0
    //min(yi-c2)**2
    var c2 = 0.0
    //c1、c2所對應的數據和
    var s1 = 0.0
    var s2 = 0.0
    //滿足條件c1、c2的樣本點個數
    var n1 = 0
    var n2 = 0
    for(dt <- data) if(dt.features(0) <= cutpoint) {n1 += 1;s1 += dt.label} else {n2 += 1;s2 += dt.label}
    c1 = s1 / n1
    c2 = s2 / n2
    for(dt <- data) if(dt.features(0) <= cutpoint) ms += math.pow((dt.label - c1),2) else ms += math.pow((dt.label - c2),2)
    (ms,c1,c2)
  }
}
----------------------------------------------------------result---------------------------------------
5.63
5.818310185185186
5.818310185185186
6.551643518518518
6.551643518518518
6.819699074074074
6.819699074074074
8.950162037037037
8.950162037037037
該實驗結果完全等價於統計學習上的提升樹函數