決策樹迴歸算法原理及Spark MLlib調用實例（Scala/Java/python）

決策樹迴歸

算法介紹：

        決策樹以及其集成算法是機器學習分類和迴歸問題中非常流行的算法。因其易解釋性、可處理類別特徵、易擴展到多分類問題、不需特徵縮放等性質被廣泛使用。樹集成算法如隨機森林以及boosting算法幾乎是解決分類和迴歸問題中表現最優的算法。

       決策樹是一個貪心算法遞歸地將特徵空間劃分爲兩個部分，在同一個葉子節點的數據最後會擁有同樣的標籤。每次劃分通過貪心的以獲得最大信息增益爲目的，從可選擇的分裂方式中選擇最佳的分裂節點。節點不純度有節點所含類別的同質性來衡量。工具提供爲分類提供兩種不純度衡量（基尼不純度和熵），爲迴歸提供一種不純度衡量（方差）。

       spark.ml支持二分類、多分類以及迴歸的決策樹算法，適用於連續特徵以及類別特徵。另外，對於分類問題，工具可以返回屬於每種類別的概率（類別條件概率），對於迴歸問題工具可以返回預測在偏置樣本上的方差。

參數：

checkpointInterval:

類型：整數型。

含義：設置檢查點間隔（>=1），或不設置檢查點（-1）。

featuresCol:

類型：字符串型。

含義：特徵列名。

impurity:

類型：字符串型。

含義：計算信息增益的準則（不區分大小寫）。

labelCol:

類型：字符串型。

含義：標籤列名。

maxBins:

類型：整數型。

含義：連續特徵離散化的最大數量，以及選擇每個節點分裂特徵的方式。

maxDepth:

類型：整數型。

含義：樹的最大深度（>=0）。

minInfoGain:

類型：雙精度型。

含義：分裂節點時所需最小信息增益。

minInstancesPerNode:

類型：整數型。

含義：分裂後自節點最少包含的實例數量。

predictionCol:

類型：字符串型。

含義：預測結果列名。

seed:

類型：長整型。

含義：隨機種子。

varianceCol:

類型：字符串型。

含義：預測的有偏樣本偏差的列名。

調用示例：

     下面的例子導入LibSVM格式數據，並將之劃分爲訓練數據和測試數據。使用第一部分數據進行訓練，剩下數據來測試。訓練之前我們使用了兩種數據預處理方法來對特徵進行轉換，並且添加了元數據到DataFrame。

Scala：

import org.apache.spark.ml.Pipeline
import org.apache.spark.ml.evaluation.RegressionEvaluator
import org.apache.spark.ml.feature.VectorIndexer
import org.apache.spark.ml.regression.DecisionTreeRegressionModel
import org.apache.spark.ml.regression.DecisionTreeRegressor

// Load the data stored in LIBSVM format as a DataFrame.
val data = spark.read.format("libsvm").load("data/mllib/sample_libsvm_data.txt")

// Automatically identify categorical features, and index them.
// Here, we treat features with > 4 distinct values as continuous.
val featureIndexer = new VectorIndexer()
  .setInputCol("features")
  .setOutputCol("indexedFeatures")
  .setMaxCategories(4)
  .fit(data)

// Split the data into training and test sets (30% held out for testing).
val Array(trainingData, testData) = data.randomSplit(Array(0.7, 0.3))

// Train a DecisionTree model.
val dt = new DecisionTreeRegressor()
  .setLabelCol("label")
  .setFeaturesCol("indexedFeatures")

// Chain indexer and tree in a Pipeline.
val pipeline = new Pipeline()
  .setStages(Array(featureIndexer, dt))

// Train model. This also runs the indexer.
val model = pipeline.fit(trainingData)

// Make predictions.
val predictions = model.transform(testData)

// Select example rows to display.
predictions.select("prediction", "label", "features").show(5)

// Select (prediction, true label) and compute test error.
val evaluator = new RegressionEvaluator()
  .setLabelCol("label")
  .setPredictionCol("prediction")
  .setMetricName("rmse")
val rmse = evaluator.evaluate(predictions)
println("Root Mean Squared Error (RMSE) on test data = " + rmse)

val treeModel = model.stages(1).asInstanceOf[DecisionTreeRegressionModel]
println("Learned regression tree model:\n" + treeModel.toDebugString)

Java：

import org.apache.spark.ml.Pipeline;
import org.apache.spark.ml.PipelineModel;
import org.apache.spark.ml.PipelineStage;
import org.apache.spark.ml.evaluation.RegressionEvaluator;
import org.apache.spark.ml.feature.VectorIndexer;
import org.apache.spark.ml.feature.VectorIndexerModel;
import org.apache.spark.ml.regression.DecisionTreeRegressionModel;
import org.apache.spark.ml.regression.DecisionTreeRegressor;
import org.apache.spark.sql.Dataset;
import org.apache.spark.sql.Row;
import org.apache.spark.sql.SparkSession;

// Load the data stored in LIBSVM format as a DataFrame.
Dataset<Row> data = spark.read().format("libsvm")
  .load("data/mllib/sample_libsvm_data.txt");

// Automatically identify categorical features, and index them.
// Set maxCategories so features with > 4 distinct values are treated as continuous.
VectorIndexerModel featureIndexer = new VectorIndexer()
  .setInputCol("features")
  .setOutputCol("indexedFeatures")
  .setMaxCategories(4)
  .fit(data);

// Split the data into training and test sets (30% held out for testing).
Dataset<Row>[] splits = data.randomSplit(new double[]{0.7, 0.3});
Dataset<Row> trainingData = splits[0];
Dataset<Row> testData = splits[1];

// Train a DecisionTree model.
DecisionTreeRegressor dt = new DecisionTreeRegressor()
  .setFeaturesCol("indexedFeatures");

// Chain indexer and tree in a Pipeline.
Pipeline pipeline = new Pipeline()
  .setStages(new PipelineStage[]{featureIndexer, dt});

// Train model. This also runs the indexer.
PipelineModel model = pipeline.fit(trainingData);

// Make predictions.
Dataset<Row> predictions = model.transform(testData);

// Select example rows to display.
predictions.select("label", "features").show(5);

// Select (prediction, true label) and compute test error.
RegressionEvaluator evaluator = new RegressionEvaluator()
  .setLabelCol("label")
  .setPredictionCol("prediction")
  .setMetricName("rmse");
double rmse = evaluator.evaluate(predictions);
System.out.println("Root Mean Squared Error (RMSE) on test data = " + rmse);

DecisionTreeRegressionModel treeModel =
  (DecisionTreeRegressionModel) (model.stages()[1]);
System.out.println("Learned regression tree model:\n" + treeModel.toDebugString());

Python：

from pyspark.ml import Pipeline
from pyspark.ml.regression import DecisionTreeRegressor
from pyspark.ml.feature import VectorIndexer
from pyspark.ml.evaluation import RegressionEvaluator

# Load the data stored in LIBSVM format as a DataFrame.
data = spark.read.format("libsvm").load("data/mllib/sample_libsvm_data.txt")

# Automatically identify categorical features, and index them.
# We specify maxCategories so features with > 4 distinct values are treated as continuous.
featureIndexer =\
    VectorIndexer(inputCol="features", outputCol="indexedFeatures", maxCategories=4).fit(data)

# Split the data into training and test sets (30% held out for testing)
(trainingData, testData) = data.randomSplit([0.7, 0.3])

# Train a DecisionTree model.
dt = DecisionTreeRegressor(featuresCol="indexedFeatures")

# Chain indexer and tree in a Pipeline
pipeline = Pipeline(stages=[featureIndexer, dt])

# Train model.  This also runs the indexer.
model = pipeline.fit(trainingData)

# Make predictions.
predictions = model.transform(testData)

# Select example rows to display.
predictions.select("prediction", "label", "features").show(5)

# Select (prediction, true label) and compute test error
evaluator = RegressionEvaluator(
    labelCol="label", predictionCol="prediction", metricName="rmse")
rmse = evaluator.evaluate(predictions)
print("Root Mean Squared Error (RMSE) on test data = %g" % rmse)

treeModel = model.stages[1]
# summary only
print(treeModel)