迴歸正則化方法（Lasso，Ridge和ElasticNet）在高維和資料集變數之間多重共線性情況下執行良好。
數學上，ElasticNet被定義為L1和L2正則化項的凸組合：
通過適當設定α，ElasticNet包含L1和L2正則化作為特殊情況。例如，如果用引數α設定為1來訓練線性迴歸模型，則其等價於Lasso模型。另一方面，如果α被設定為0，則訓練的模型簡化為ridge迴歸模型。
RegParam:lambda>=0
ElasticNetParam:alpha in [0, 1]
匯入包
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
匯入樣本資料
// Population人口,
// Income收入水平,
// Illiteracy文盲率,
// LifeExp,
// Murder謀殺率,
// HSGrad,
// Frost結霜天數(溫度在冰點以下的平均天數) ,
// Area州面積
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")
建立線性迴歸模型
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，預測謀殺率Murder
// 設定線性迴歸引數
val lr1 = new LinearRegression()
val lr2 = lr1.setFeaturesCol("features").setLabelCol("Murder").setFitIntercept(true)
// RegParam：正則化
val lr3 = lr2.setMaxIter(10).setRegParam(0.3).setElasticNetParam(0.8)
val lr = lr3
// Fit the model
val lrModel = lr.fit(vecDF)
// 輸出模型全部引數
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}")
程式碼執行結果
// 輸出模型全部引數
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
模型調優，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，預測謀殺率Murder，設定線性迴歸引數
val lr = new LinearRegression().setFeaturesCol("features").setLabelCol("Murder").fit(trainingDF)
// 設定管道
val pipeline = new Pipeline().setStages(Array(lr))
// 建立引數網格
val paramGrid = new ParamGridBuilder().addGrid(lr.fitIntercept).addGrid(lr.elasticNetParam, Array(0.0, 0.5, 1.0)).addGrid(lr.maxIter, Array(10, 100)).build()
// 選擇(prediction, true label)，計算測試誤差。
// 注意RegEvaluator.isLargerBetter，評估的度量值是大的好，還是小的好，系統會自動識別
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) // 資料分割比例
// Run train validation split, and choose the best set of parameters.
val tvModel = trainValidationSplit.fit(trainingDF)
// 檢視模型全部引數
tvModel.extractParamMap()
tvModel.getEstimatorParamMaps.length
tvModel.getEstimatorParamMaps.foreach { println } // 引數組合的集合
tvModel.getEvaluator.extractParamMap() // 評估的引數
tvModel.getEvaluator.isLargerBetter // 評估的度量值是大的好，還是小的好
tvModel.getTrainRatio
// 用最好的引數組合，做出預測
tvModel.transform(testDF).select("features", "Murder", "prediction").show()
調優程式碼執行結果
// 檢視模型全部引數
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 } // 引數組合的集合
{
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() // 評估的引數
res48: org.apache.spark.ml.param.ParamMap =
{
regEval_05204824acb9-labelCol: Murder,
regEval_05204824acb9-metricName: rmse,
regEval_05204824acb9-predictionCol: prediction
}
tvModel.getEvaluator.isLargerBetter // 評估的度量值是大的好，還是小的好
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|
+--------------------+------+------------------+