回歸正則化方法（Lasso，Ridge和ElasticNet）在高維和資料集變量之間多重共線性情況下運作良好。
數學上，ElasticNet被定義為L1和L2正則化項的凸組合：
通過适當設定α，ElasticNet包含L1和L2正則化作為特殊情況。例如，如果用參數α設定為1來訓練線性回歸模型，則其等價于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回歸模型。
RegParam:lambda>=0
ElasticNetParam:alpha in [0, 1]
導入包
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
導入樣本資料
// Population人口,
// Income收入水準,
// 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
,
,
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"
)
建立線性回歸模型
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
// 設定線性回歸參數
val
lr
1
=
new
LinearRegression()
val
lr
2
=
lr
1
.setFeaturesCol(
"features"
).setLabelCol(
"Murder"
).setFitIntercept(
true
)
// RegParam：正則化
val
lr
3
=
lr
2
.setMaxIter(
10
).setRegParam(
0.3
).setElasticNetParam(
0.8
)
val
lr
=
lr
3
// Fit the model
val
lrModel
=
lr.fit(vecDF)
// 輸出模型全部參數
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}"
)
代碼執行結果
// 輸出模型全部參數
lrModel.extractParamMap()
res
15
:
org.apache.spark.ml.param.ParamMap
=
{
linReg
_
2
ba
28140
e
39
a-elasticNetParam
:
0.8
,
linReg
_
2
ba
28140
e
39
a-featuresCol
:
features,
linReg
_
2
ba
28140
e
39
a-fitIntercept
:
true
,
linReg
_
2
ba
28140
e
39
a-labelCol
:
Murder,
linReg
_
2
ba
28140
e
39
a-maxIter
:
10
,
linReg
_
2
ba
28140
e
39
a-predictionCol
:
prediction,
linReg
_
2
ba
28140
e
39
a-regParam
:
0.3
,
linReg
_
2
ba
28140
e
39
a-solver
:
auto,
linReg
_
2
ba
28140
e
39
a-standardization
:
true
,
linReg
_
2
ba
28140
e
39
a-tol
:
1.0
E-
6
}
// Print the coefficients and intercept for linear regression
println(s
"Coefficients: ${lrModel.coefficients} Intercept: ${lrModel.intercept}"
)
Coefficients
:
[
1.36662199778084
E-
4
,
0.0
,
1.1834384307116244
,-
1.4580829641757522
,
0.0
,-
0.010686434270049252
,
4.051355050528196
E-
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
@
68
a
83
d
76
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}"
)
r
2
:
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，設定線性回歸參數
val
lr
=
new
LinearRegression().setFeaturesCol(
"features"
).setLabelCol(
"Murder"
).fit(trainingDF)
// 設定管道
val
pipeline
=
new
Pipeline().setStages(Array(lr))
// 建立參數網格
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，評估的路徑成本是大的好，還是小的好，系統會自動識别
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
)
// 資料分割比例
// Run train validation split, and choose the best set of parameters.
val
tvModel
=
trainValidationSplit.fit(trainingDF)
// 檢視模型全部參數
tvModel.extractParamMap()
tvModel.getEstimatorParamMaps.length
tvModel.getEstimatorParamMaps.foreach { println }
// 參數組合的集合
tvModel.getEvaluator.extractParamMap()
// 評估的參數
tvModel.getEvaluator.isLargerBetter
// 評估的路徑成本是大的好，還是小的好
tvModel.getTrainRatio
// 用最好的參數組合，做出預測
tvModel.transform(testDF).select(
"features"
,
"Murder"
,
"prediction"
).show()
調優代碼執行結果
// 檢視模型全部參數
tvModel.extractParamMap()
res
45
:
org.apache.spark.ml.param.ParamMap
=
{
tvs
_
5
de
7
d
3
dd
1977
-estimator
:
pipeline
_
062
a
1
dffe
557
,
tvs
_
5
de
7
d
3
dd
1977
-estimatorParamMaps
:
[Lorg.apache.spark.ml.param.ParamMap;
@
60298
de
1
,
tvs
_
5
de
7
d
3
dd
1977
-evaluator
:
regEval
_
05204824
acb
9
,
tvs
_
5
de
7
d
3
dd
1977
-seed
:
-
1772833110
,
tvs
_
5
de
7
d
3
dd
1977
-trainRatio
:
0.8
}
tvModel.getEstimatorParamMaps.length
res
46
:
Int
=
12
tvModel.getEstimatorParamMaps.foreach { println }
// 參數組合的集合
{
linReg
_
75628
a
5554
b
4
-elasticNetParam
:
0.0
,
linReg
_
75628
a
5554
b
4
-fitIntercept
:
true
,
linReg
_
75628
a
5554
b
4
-maxIter
:
10
}
{
linReg
_
75628
a
5554
b
4
-elasticNetParam
:
0.0
,
linReg
_
75628
a
5554
b
4
-fitIntercept
:
true
,
linReg
_
75628
a
5554
b
4
-maxIter
:
100
}
{
linReg
_
75628
a
5554
b
4
-elasticNetParam
:
0.0
,
linReg
_
75628
a
5554
b
4
-fitIntercept
:
false
,
linReg
_
75628
a
5554
b
4
-maxIter
:
10
}
{
linReg
_
75628
a
5554
b
4
-elasticNetParam
:
0.0
,
linReg
_
75628
a
5554
b
4
-fitIntercept
:
false
,
linReg
_
75628
a
5554
b
4
-maxIter
:
100
}
{
linReg
_
75628
a
5554
b
4
-elasticNetParam
:
0.5
,
linReg
_
75628
a
5554
b
4
-fitIntercept
:
true
,
linReg
_
75628
a
5554
b
4
-maxIter
:
10
}
{
linReg
_
75628
a
5554
b
4
-elasticNetParam
:
0.5
,
linReg
_
75628
a
5554
b
4
-fitIntercept
:
true
,
linReg
_
75628
a
5554
b
4
-maxIter
:
100
}
{
linReg
_
75628
a
5554
b
4
-elasticNetParam
:
0.5
,
linReg
_
75628
a
5554
b
4
-fitIntercept
:
false
,
linReg
_
75628
a
5554
b
4
-maxIter
:
10
}
{
linReg
_
75628
a
5554
b
4
-elasticNetParam
:
0.5
,
linReg
_
75628
a
5554
b
4
-fitIntercept
:
false
,
linReg
_
75628
a
5554
b
4
-maxIter
:
100
}
{
linReg
_
75628
a
5554
b
4
-elasticNetParam
:
1.0
,
linReg
_
75628
a
5554
b
4
-fitIntercept
:
true
,
linReg
_
75628
a
5554
b
4
-maxIter
:
10
}
{
linReg
_
75628
a
5554
b
4
-elasticNetParam
:
1.0
,
linReg
_
75628
a
5554
b
4
-fitIntercept
:
true
,
linReg
_
75628
a
5554
b
4
-maxIter
:
100
}
{
linReg
_
75628
a
5554
b
4
-elasticNetParam
:
1.0
,
linReg
_
75628
a
5554
b
4
-fitIntercept
:
false
,
linReg
_
75628
a
5554
b
4
-maxIter
:
10
}
{
linReg
_
75628
a
5554
b
4
-elasticNetParam
:
1.0
,
linReg
_
75628
a
5554
b
4
-fitIntercept
:
false
,
linReg
_
75628
a
5554
b
4
-maxIter
:
100
}
tvModel.getEvaluator.extractParamMap()
// 評估的參數
res
48
:
org.apache.spark.ml.param.ParamMap
=
{
regEval
_
05204824
acb
9
-labelCol
:
Murder,
regEval
_
05204824
acb
9
-metricName
:
rmse,
regEval
_
05204824
acb
9
-predictionCol
:
prediction
}
tvModel.getEvaluator.isLargerBetter
// 評估的路徑成本是大的好，還是小的好
res
49
:
Boolean
=
false
tvModel.getTrainRatio
res
50
:
Double
=
0.8
tvModel.transform(testDF).select(
"features"
,
"Murder"
,
"prediction"
).show()
+--------------------+------+------------------+
| features|Murder| prediction|
+--------------------+------+------------------+
|[
1058.0
,
3694.0
,
....|
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
,
....|
3.0
|
3.483554528704758
|
+--------------------+------+------------------+
![一天搞懂機器學習PPT筆記-2[圖]](data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACwAAAAAAQABAAACAkQBADs=)