决策树回归算法原理及Spark MLlib调用实例（Scala/Java/python）

决策树回归

算法介绍：

        决策树以及其集成算法是机器学习分类和回归问题中非常流行的算法。因其易解释性、可处理类别特征、易扩展到多分类问题、不需特征缩放等性质被广泛使用。树集成算法如随机森林以及boosting算法几乎是解决分类和回归问题中表现最优的算法。

       决策树是一个贪心算法递归地将特征空间划分为两个部分，在同一个叶子节点的数据最后会拥有同样的标签。每次划分通过贪心的以获得最大信息增益为目的，从可选择的分裂方式中选择最佳的分裂节点。节点不纯度有节点所含类别的同质性来衡量。工具提供为分类提供两种不纯度衡量（基尼不纯度和熵），为回归提供一种不纯度衡量（方差）。

       spark.ml支持二分类、多分类以及回归的决策树算法，适用于连续特征以及类别特征。另外，对于分类问题，工具可以返回属于每种类别的概率（类别条件概率），对于回归问题工具可以返回预测在偏置样本上的方差。

参数：

checkpointInterval:

类型：整数型。

含义：设置检查点间隔（>=1），或不设置检查点（-1）。

featuresCol:

类型：字符串型。

含义：特征列名。

impurity:

类型：字符串型。

含义：计算信息增益的准则（不区分大小写）。

labelCol:

类型：字符串型。

含义：标签列名。

maxBins:

类型：整数型。

含义：连续特征离散化的最大数量，以及选择每个节点分裂特征的方式。

maxDepth:

类型：整数型。

含义：树的最大深度（>=0）。

minInfoGain:

类型：双精度型。

含义：分裂节点时所需最小信息增益。

minInstancesPerNode:

类型：整数型。

含义：分裂后自节点最少包含的实例数量。

predictionCol:

类型：字符串型。

含义：预测结果列名。

seed:

类型：长整型。

含义：随机种子。

varianceCol:

类型：字符串型。

含义：预测的有偏样本偏差的列名。

调用示例：

     下面的例子导入LibSVM格式数据，并将之划分为训练数据和测试数据。使用第一部分数据进行训练，剩下数据来测试。训练之前我们使用了两种数据预处理方法来对特征进行转换，并且添加了元数据到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 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[] splits = data.randomSplit(new double[]{0.7, 0.3});
Dataset trainingData = splits[0];
Dataset 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 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)