回归正则化方法（Lasso，Ridge和ElasticNet）在高维和数据集变量之间多重共线性情况下运行良好。

数学上，ElasticNet被定义为L1和L2正则化项的凸组合：

通过适当设置α，ElasticNet包含L1和L2正则化作为特殊情况。例如，如果用参数α设置为1来训练线性回归模型，则其等价于Lasso模型。另一方面，如果α被设置为0，则训练的模型简化为ridge回归模型。

RegParam:lambda>=0
ElasticNetParam:alpha in [0, 1]

导入包

import org.apache.spark.sql.SparkSession

import org.apache.spark.sql.Dataset

import org.apache.spark.sql.Row

import org.apache.spark.sql.DataFrame

import org.apache.spark.sql.Column

import org.apache.spark.sql.DataFrameReader

import org.apache.spark.rdd.RDD

import org.apache.spark.sql.catalyst.encoders.ExpressionEncoder

import org.apache.spark.sql.Encoder

import org.apache.spark.sql.DataFrameStatFunctions

import org.apache.spark.sql.functions._

import org.apache.spark.ml.linalg.Vectors

import org.apache.spark.ml.feature.VectorAssembler

import org.apache.spark.ml.evaluation.RegressionEvaluator

import org.apache.spark.ml.regression.LinearRegression

导入样本数据

// Population人口,

// Income收入水平,

// Illiteracy文盲率,

// LifeExp,

// Murder谋杀率,

// HSGrad,

// Frost结霜天数(温度在冰点以下的平均天数) ,

// Area州面积

    val spark = SparkSession.builder().appName("Spark Linear Regression").config("spark.some.config.option", "some-value").getOrCreate()

    // For implicit conversions like converting RDDs to DataFrames

    import spark.implicits._

    val dataList: List[(Double, Double, Double, Double, Double, Double, Double, Double)] = List(

      (3615, 3624, 2.1, 69.05, 15.1, 41.3, 20, 50708),

      (365, 6315, 1.5, 69.31, 11.3, 66.7, 152, 566432),

      (2212, 4530, 1.8, 70.55, 7.8, 58.1, 15, 113417),

      (2110, 3378, 1.9, 70.66, 10.1, 39.9, 65, 51945),

      (21198, 5114, 1.1, 71.71, 10.3, 62.6, 20, 156361),

      (2541, 4884, 0.7, 72.06, 6.8, 63.9, 166, 103766),

      (3100, 5348, 1.1, 72.48, 3.1, 56, 139, 4862),

      (579, 4809, 0.9, 70.06, 6.2, 54.6, 103, 1982),

      (8277, 4815, 1.3, 70.66, 10.7, 52.6, 11, 54090),

      (4931, 4091, 2, 68.54, 13.9, 40.6, 60, 58073),

      (868, 4963, 1.9, 73.6, 6.2, 61.9, 0, 6425),

      (813, 4119, 0.6, 71.87, 5.3, 59.5, 126, 82677),

      (11197, 5107, 0.9, 70.14, 10.3, 52.6, 127, 55748),

      (5313, 4458, 0.7, 70.88, 7.1, 52.9, 122, 36097),

      (2861, 4628, 0.5, 72.56, 2.3, 59, 140, 55941),

      (2280, 4669, 0.6, 72.58, 4.5, 59.9, 114, 81787),

      (3387, 3712, 1.6, 70.1, 10.6, 38.5, 95, 39650),

      (3806, 3545, 2.8, 68.76, 13.2, 42.2, 12, 44930),

      (1058, 3694, 0.7, 70.39, 2.7, 54.7, 161, 30920),

      (4122, 5299, 0.9, 70.22, 8.5, 52.3, 101, 9891),

      (5814, 4755, 1.1, 71.83, 3.3, 58.5, 103, 7826),

      (9111, 4751, 0.9, 70.63, 11.1, 52.8, 125, 56817),

      (3921, 4675, 0.6, 72.96, 2.3, 57.6, 160, 79289),

      (2341, 3098, 2.4, 68.09, 12.5, 41, 50, 47296),

      (4767, 4254, 0.8, 70.69, 9.3, 48.8, 108, 68995),

      (746, 4347, 0.6, 70.56, 5, 59.2, 155, 145587),

      (1544, 4508, 0.6, 72.6, 2.9, 59.3, 139, 76483),

      (590, 5149, 0.5, 69.03, 11.5, 65.2, 188, 109889),

      (812, 4281, 0.7, 71.23, 3.3, 57.6, 174, 9027),

      (7333, 5237, 1.1, 70.93, 5.2, 52.5, 115, 7521),

      (1144, 3601, 2.2, 70.32, 9.7, 55.2, 120, 121412),

      (18076, 4903, 1.4, 70.55, 10.9, 52.7, 82, 47831),

      (5441, 3875, 1.8, 69.21, 11.1, 38.5, 80, 48798),

      (637, 5087, 0.8, 72.78, 1.4, 50.3, 186, 69273),

      (10735, 4561, 0.8, 70.82, 7.4, 53.2, 124, 40975),

      (2715, 3983, 1.1, 71.42, 6.4, 51.6, 82, 68782),

      (2284, 4660, 0.6, 72.13, 4.2, 60, 44, 96184),

      (11860, 4449, 1, 70.43, 6.1, 50.2, 126, 44966),

      (931, 4558, 1.3, 71.9, 2.4, 46.4, 127, 1049),

      (2816, 3635, 2.3, 67.96, 11.6, 37.8, 65, 30225),

      (681, 4167, 0.5, 72.08, 1.7, 53.3, 172, 75955),

      (4173, 3821, 1.7, 70.11, 11, 41.8, 70, 41328),

      (12237, 4188, 2.2, 70.9, 12.2, 47.4, 35, 262134),

      (1203, 4022, 0.6, 72.9, 4.5, 67.3, 137, 82096),

      (472, 3907, 0.6, 71.64, 5.5, 57.1, 168, 9267),

      (4981, 4701, 1.4, 70.08, 9.5, 47.8, 85, 39780),

      (3559, 4864, 0.6, 71.72, 4.3, 63.5, 32, 66570),

      (1799, 3617, 1.4, 69.48, 6.7, 41.6, 100, 24070),

      (4589, 4468, 0.7, 72.48, 3, 54.5, 149, 54464),

      (376, 4566, 0.6, 70.29, 6.9, 62.9, 173, 97203))

    val data = dataList.toDF("Population", "Income", "Illiteracy", "LifeExp", "Murder", "HSGrad", "Frost", "Area")

建立线性回归模型

    val colArray = Array("Population", "Income", "Illiteracy", "LifeExp", "HSGrad", "Frost", "Area")

    val assembler = new VectorAssembler().setInputCols(colArray).setOutputCol("features")

    val vecDF: DataFrame = assembler.transform(data)

    // 建立模型，预测谋杀率Murder

    // 设置线性回归参数

    val lr1 = new LinearRegression()

    val lr2 = lr1.setFeaturesCol("features").setLabelCol("Murder").setFitIntercept(true)

    // RegParam：正则化

    val lr3 = lr2.setMaxIter(10).setRegParam(0.3).setElasticNetParam(0.8)

    val lr = lr3

    // Fit the model

    val lrModel = lr.fit(vecDF)

    // 输出模型全部参数

    lrModel.extractParamMap()

    // Print the coefficients and intercept for linear regression

    println(s"Coefficients: ${lrModel.coefficients} Intercept: ${lrModel.intercept}")

    val predictions = lrModel.transform(vecDF)

    predictions.selectExpr("Murder", "round(prediction,1) as prediction").show

    // Summarize the model over the training set and print out some metrics

    val trainingSummary = lrModel.summary

    println(s"numIterations: ${trainingSummary.totalIterations}")

    println(s"objectiveHistory: ${trainingSummary.objectiveHistory.toList}")

    trainingSummary.residuals.show()

    println(s"RMSE: ${trainingSummary.rootMeanSquaredError}")

    println(s"r2: ${trainingSummary.r2}")

代码执行结果

// 输出模型全部参数

lrModel.extractParamMap()

res15: org.apache.spark.ml.param.ParamMap =

{

	linReg_2ba28140e39a-elasticNetParam: 0.8,

	linReg_2ba28140e39a-featuresCol: features,

	linReg_2ba28140e39a-fitIntercept: true,

	linReg_2ba28140e39a-labelCol: Murder,

	linReg_2ba28140e39a-maxIter: 10,

	linReg_2ba28140e39a-predictionCol: prediction,

	linReg_2ba28140e39a-regParam: 0.3,

	linReg_2ba28140e39a-solver: auto,

	linReg_2ba28140e39a-standardization: true,

	linReg_2ba28140e39a-tol: 1.0E-6

}

// Print the coefficients and intercept for linear regression

println(s"Coefficients: ${lrModel.coefficients} Intercept: ${lrModel.intercept}")

Coefficients: [1.36662199778084E-4,0.0,1.1834384307116244,-1.4580829641757522,0.0,-0.010686434270049252,4.051355050528196E-6] Intercept: 109.589659881471

val predictions = lrModel.transform(vecDF)

predictions: org.apache.spark.sql.DataFrame = [Population: double, Income: double ... 8 more fields]

predictions.selectExpr("Murder", "round(prediction,1) as prediction").show

+------+----------+

|Murder|prediction|

+------+----------+

|  15.1|      11.9|

|  11.3|      11.0|

|   7.8|       9.5|

|  10.1|       8.6|

|  10.3|       9.6|

|   6.8|       4.3|

|   3.1|       4.2|

|   6.2|       7.5|

|  10.7|       9.3|

|  13.9|      12.3|

|   6.2|       4.7|

|   5.3|       4.6|

|  10.3|       8.8|

|   7.1|       6.6|

|   2.3|       3.5|

|   4.5|       3.9|

|  10.6|       8.9|

|  13.2|      13.2|

|   2.7|       6.3|

|   8.5|       7.8|

+------+----------+

only showing top 20 rows

// Summarize the model over the training set and print out some metrics

val trainingSummary = lrModel.summary

trainingSummary: org.apache.spark.ml.regression.LinearRegressionTrainingSummary = org.apache.spark.ml.regression.LinearRegressionTrainingSummary@68a83d76

println(s"numIterations: ${trainingSummary.totalIterations}")

numIterations: 11

println(s"objectiveHistory: ${trainingSummary.objectiveHistory.toList}")

objectiveHistory: List(0.49000000000000016, 0.3919242806809093, 0.19908078426904946, 0.1901453492751914, 0.17981874256031405, 0.17878173084286247, 0.1787617816935607, 0.17875431854661641, 0.1

7874702637141196, 0.17874512271568685, 0.1787449876896829)

trainingSummary.residuals.show()

+--------------------+

|           residuals|

+--------------------+

|  3.2200068116713023|

|  0.2745518816306607|

| -1.6535887417767414|

|   1.485762696757325|

|  0.6509766532389172|

|   2.457688146554534|

| -1.0675250558261182|

| -1.2879164685248439|

|  1.3672723619868314|

|  1.6125000289597242|

|   1.532060517905248|

|  0.6931301635074645|

|  1.5163001982000175|

| 0.46227066807431605|

| -1.2044058248740273|

|  0.6032541157521649|

|     1.7201545753635|

|-0.01942937427384...|

|  -3.632947522687547|

|  0.7077675962948007|

+--------------------+

only showing top 20 rows

println(s"RMSE: ${trainingSummary.rootMeanSquaredError}")

RMSE: 1.6663615527314546

println(s"r2: ${trainingSummary.r2}")

r2: 0.7920794990832152

模型调优，用Train-Validation Split

val colArray = Array("Population", "Income", "Illiteracy", "LifeExp", "HSGrad", "Frost", "Area")

val vecDF: DataFrame = new VectorAssembler().setInputCols(colArray).setOutputCol("features").transform(data)

val Array(trainingDF, testDF) = vecDF.randomSplit(Array(0.9, 0.1), seed = 12345)

// 建立模型，预测谋杀率Murder，设置线性回归参数

val lr = new LinearRegression().setFeaturesCol("features").setLabelCol("Murder").fit(trainingDF)

// 设置管道

val pipeline = new Pipeline().setStages(Array(lr))

// 建立参数网格

val paramGrid = new ParamGridBuilder().addGrid(lr.fitIntercept).addGrid(lr.elasticNetParam, Array(0.0, 0.5, 1.0)).addGrid(lr.maxIter, Array(10, 100)).build()

// 选择(prediction, true label)，计算测试误差。

// 注意RegEvaluator.isLargerBetter，评估的度量值是大的好，还是小的好，系统会自动识别

val RegEvaluator = new RegressionEvaluator().setLabelCol(lr.getLabelCol).setPredictionCol(lr.getPredictionCol).setMetricName("rmse")

val trainValidationSplit = new TrainValidationSplit().setEstimator(pipeline).setEvaluator(RegEvaluator).setEstimatorParamMaps(paramGrid).setTrainRatio(0.8) // 数据分割比例

// Run train validation split, and choose the best set of parameters.

val tvModel = trainValidationSplit.fit(trainingDF)

// 查看模型全部参数

tvModel.extractParamMap()

tvModel.getEstimatorParamMaps.length

tvModel.getEstimatorParamMaps.foreach { println } // 参数组合的集合 

tvModel.getEvaluator.extractParamMap() // 评估的参数 

tvModel.getEvaluator.isLargerBetter // 评估的度量值是大的好，还是小的好 

tvModel.getTrainRatio

// 用最好的参数组合，做出预测

tvModel.transform(testDF).select("features", "Murder", "prediction").show()

调优代码执行结果

// 查看模型全部参数

tvModel.extractParamMap()

res45: org.apache.spark.ml.param.ParamMap =

{

	tvs_5de7d3dd1977-estimator: pipeline_062a1dffe557,

	tvs_5de7d3dd1977-estimatorParamMaps: [Lorg.apache.spark.ml.param.ParamMap;@60298de1,

	tvs_5de7d3dd1977-evaluator: regEval_05204824acb9,

	tvs_5de7d3dd1977-seed: -1772833110,

	tvs_5de7d3dd1977-trainRatio: 0.8

}

tvModel.getEstimatorParamMaps.length

res46: Int = 12

tvModel.getEstimatorParamMaps.foreach { println } // 参数组合的集合

{

	linReg_75628a5554b4-elasticNetParam: 0.0,

	linReg_75628a5554b4-fitIntercept: true,

	linReg_75628a5554b4-maxIter: 10

}

{

	linReg_75628a5554b4-elasticNetParam: 0.0,

	linReg_75628a5554b4-fitIntercept: true,

	linReg_75628a5554b4-maxIter: 100

}

{

	linReg_75628a5554b4-elasticNetParam: 0.0,

	linReg_75628a5554b4-fitIntercept: false,

	linReg_75628a5554b4-maxIter: 10

}

{

	linReg_75628a5554b4-elasticNetParam: 0.0,

	linReg_75628a5554b4-fitIntercept: false,

	linReg_75628a5554b4-maxIter: 100

}

{

	linReg_75628a5554b4-elasticNetParam: 0.5,

	linReg_75628a5554b4-fitIntercept: true,

	linReg_75628a5554b4-maxIter: 10

}

{

	linReg_75628a5554b4-elasticNetParam: 0.5,

	linReg_75628a5554b4-fitIntercept: true,

	linReg_75628a5554b4-maxIter: 100

}

{

	linReg_75628a5554b4-elasticNetParam: 0.5,

	linReg_75628a5554b4-fitIntercept: false,

	linReg_75628a5554b4-maxIter: 10

}

{

	linReg_75628a5554b4-elasticNetParam: 0.5,

	linReg_75628a5554b4-fitIntercept: false,

	linReg_75628a5554b4-maxIter: 100

}

{

	linReg_75628a5554b4-elasticNetParam: 1.0,

	linReg_75628a5554b4-fitIntercept: true,

	linReg_75628a5554b4-maxIter: 10

}

{

	linReg_75628a5554b4-elasticNetParam: 1.0,

	linReg_75628a5554b4-fitIntercept: true,

	linReg_75628a5554b4-maxIter: 100

}

{

	linReg_75628a5554b4-elasticNetParam: 1.0,

	linReg_75628a5554b4-fitIntercept: false,

	linReg_75628a5554b4-maxIter: 10

}

{

	linReg_75628a5554b4-elasticNetParam: 1.0,

	linReg_75628a5554b4-fitIntercept: false,

	linReg_75628a5554b4-maxIter: 100

}

tvModel.getEvaluator.extractParamMap() // 评估的参数

res48: org.apache.spark.ml.param.ParamMap =

{

	regEval_05204824acb9-labelCol: Murder,

	regEval_05204824acb9-metricName: rmse,

	regEval_05204824acb9-predictionCol: prediction

}

tvModel.getEvaluator.isLargerBetter // 评估的度量值是大的好，还是小的好

res49: Boolean = false

tvModel.getTrainRatio

res50: Double = 0.8

tvModel.transform(testDF).select("features", "Murder", "prediction").show()

+--------------------+------+------------------+

|            features|Murder|        prediction|

+--------------------+------+------------------+

|[1058.0,3694.0,0....|   2.7| 6.917232043935343|

|[2341.0,3098.0,2....|  12.5|14.760329005533478|

|[472.0,3907.0,0.6...|   5.5| 4.182074651181182|

|[812.0,4281.0,0.7...|   3.3| 4.915905572667441|

|[2816.0,3635.0,2....|  11.6|14.219231061596304|

|[4589.0,4468.0,0....|   3.0| 3.483554528704758|

+--------------------+------+------------------+

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