1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
|
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.spark.ml.regression
import breeze.stats.{distributions => dist}
import org.apache.hadoop.fs.Path
import org.apache.spark.SparkException
import org.apache.spark.annotation.{Experimental, Since}
import org.apache.spark.internal.Logging
import org.apache.spark.ml.PredictorParams
import org.apache.spark.ml.feature.Instance
import org.apache.spark.ml.linalg.{BLAS, Vector}
import org.apache.spark.ml.optim._
import org.apache.spark.ml.param._
import org.apache.spark.ml.param.shared._
import org.apache.spark.ml.util._
import org.apache.spark.rdd.RDD
import org.apache.spark.sql.{Column, DataFrame, Dataset, Row}
import org.apache.spark.sql.functions._
import org.apache.spark.sql.types.{DataType, DoubleType, StructType}
/**
* Params for Generalized Linear Regression.
*/
private[regression] trait GeneralizedLinearRegressionBase extends PredictorParams
with HasFitIntercept with HasMaxIter with HasTol with HasRegParam with HasWeightCol
with HasSolver with Logging {
import GeneralizedLinearRegression._
/**
* Param for the name of family which is a description of the error distribution
* to be used in the model.
* Supported options: "gaussian", "binomial", "poisson" and "gamma".
* Default is "gaussian".
*
* @group param
*/
@Since("2.0.0")
final val family: Param[String] = new Param(this, "family",
"The name of family which is a description of the error distribution to be used in the " +
s"model. Supported options: ${supportedFamilyNames.mkString(", ")}.",
ParamValidators.inArray[String](supportedFamilyNames.toArray))
/** @group getParam */
@Since("2.0.0")
def getFamily: String = $(family)
/**
* Param for the name of link function which provides the relationship
* between the linear predictor and the mean of the distribution function.
* Supported options: "identity", "log", "inverse", "logit", "probit", "cloglog" and "sqrt".
*
* @group param
*/
@Since("2.0.0")
final val link: Param[String] = new Param(this, "link", "The name of link function " +
"which provides the relationship between the linear predictor and the mean of the " +
s"distribution function. Supported options: ${supportedLinkNames.mkString(", ")}",
ParamValidators.inArray[String](supportedLinkNames.toArray))
/** @group getParam */
@Since("2.0.0")
def getLink: String = $(link)
/**
* Param for link prediction (linear predictor) column name.
* Default is not set, which means we do not output link prediction.
*
* @group param
*/
@Since("2.0.0")
final val linkPredictionCol: Param[String] = new Param[String](this, "linkPredictionCol",
"link prediction (linear predictor) column name")
/** @group getParam */
@Since("2.0.0")
def getLinkPredictionCol: String = $(linkPredictionCol)
/** Checks whether we should output link prediction. */
private[regression] def hasLinkPredictionCol: Boolean = {
isDefined(linkPredictionCol) && $(linkPredictionCol).nonEmpty
}
import GeneralizedLinearRegression._
@Since("2.0.0")
override def validateAndTransformSchema(
schema: StructType,
fitting: Boolean,
featuresDataType: DataType): StructType = {
if (isDefined(link)) {
require(supportedFamilyAndLinkPairs.contains(
Family.fromName($(family)) -> Link.fromName($(link))), "Generalized Linear Regression " +
s"with ${$(family)} family does not support ${$(link)} link function.")
}
val newSchema = super.validateAndTransformSchema(schema, fitting, featuresDataType)
if (hasLinkPredictionCol) {
SchemaUtils.appendColumn(newSchema, $(linkPredictionCol), DoubleType)
} else {
newSchema
}
}
}
/**
* :: Experimental ::
*
* Fit a Generalized Linear Model ([[https://en.wikipedia.org/wiki/Generalized_linear_model]])
* specified by giving a symbolic description of the linear predictor (link function) and
* a description of the error distribution (family).
* It supports "gaussian", "binomial", "poisson" and "gamma" as family.
* Valid link functions for each family is listed below. The first link function of each family
* is the default one.
* - "gaussian" -> "identity", "log", "inverse"
* - "binomial" -> "logit", "probit", "cloglog"
* - "poisson" -> "log", "identity", "sqrt"
* - "gamma" -> "inverse", "identity", "log"
*/
@Experimental
@Since("2.0.0")
class GeneralizedLinearRegression @Since("2.0.0") (@Since("2.0.0") override val uid: String)
extends Regressor[Vector, GeneralizedLinearRegression, GeneralizedLinearRegressionModel]
with GeneralizedLinearRegressionBase with DefaultParamsWritable with Logging {
import GeneralizedLinearRegression._
@Since("2.0.0")
def this() = this(Identifiable.randomUID("glm"))
/**
* Sets the value of param [[family]].
* Default is "gaussian".
*
* @group setParam
*/
@Since("2.0.0")
def setFamily(value: String): this.type = set(family, value)
setDefault(family -> Gaussian.name)
/**
* Sets the value of param [[link]].
*
* @group setParam
*/
@Since("2.0.0")
def setLink(value: String): this.type = set(link, value)
/**
* Sets if we should fit the intercept.
* Default is true.
*
* @group setParam
*/
@Since("2.0.0")
def setFitIntercept(value: Boolean): this.type = set(fitIntercept, value)
/**
* Sets the maximum number of iterations (applicable for solver "irls").
* Default is 25.
*
* @group setParam
*/
@Since("2.0.0")
def setMaxIter(value: Int): this.type = set(maxIter, value)
setDefault(maxIter -> 25)
/**
* Sets the convergence tolerance of iterations.
* Smaller value will lead to higher accuracy with the cost of more iterations.
* Default is 1E-6.
*
* @group setParam
*/
@Since("2.0.0")
def setTol(value: Double): this.type = set(tol, value)
setDefault(tol -> 1E-6)
/**
* Sets the regularization parameter for L2 regularization.
* The regularization term is
* {{{
* 0.5 * regParam * L2norm(coefficients)^2
* }}}
* Default is 0.0.
*
* @group setParam
*/
@Since("2.0.0")
def setRegParam(value: Double): this.type = set(regParam, value)
setDefault(regParam -> 0.0)
/**
* Sets the value of param [[weightCol]].
* If this is not set or empty, we treat all instance weights as 1.0.
* Default is not set, so all instances have weight one.
*
* @group setParam
*/
@Since("2.0.0")
def setWeightCol(value: String): this.type = set(weightCol, value)
/**
* Sets the solver algorithm used for optimization.
* Currently only supports "irls" which is also the default solver.
*
* @group setParam
*/
@Since("2.0.0")
def setSolver(value: String): this.type = set(solver, value)
setDefault(solver -> "irls")
/**
* Sets the link prediction (linear predictor) column name.
*
* @group setParam
*/
@Since("2.0.0")
def setLinkPredictionCol(value: String): this.type = set(linkPredictionCol, value)
override protected def train(dataset: Dataset[_]): GeneralizedLinearRegressionModel = {
val familyObj = Family.fromName($(family))
val linkObj = if (isDefined(link)) {
Link.fromName($(link))
} else {
familyObj.defaultLink
}
val familyAndLink = new FamilyAndLink(familyObj, linkObj)
val numFeatures = dataset.select(col($(featuresCol))).first().getAs[Vector](0).size
if (numFeatures > WeightedLeastSquares.MAX_NUM_FEATURES) {
val msg = "Currently, GeneralizedLinearRegression only supports number of features" +
s" <= ${WeightedLeastSquares.MAX_NUM_FEATURES}. Found $numFeatures in the input dataset."
throw new SparkException(msg)
}
val w = if (!isDefined(weightCol) || $(weightCol).isEmpty) lit(1.0) else col($(weightCol))
val instances: RDD[Instance] =
dataset.select(col($(labelCol)).cast(DoubleType), w, col($(featuresCol))).rdd.map {
case Row(label: Double, weight: Double, features: Vector) =>
Instance(label, weight, features)
}
if (familyObj == Gaussian && linkObj == Identity) {
// TODO: Make standardizeFeatures and standardizeLabel configurable.
val optimizer = new WeightedLeastSquares($(fitIntercept), $(regParam),
standardizeFeatures = true, standardizeLabel = true)
val wlsModel = optimizer.fit(instances)
val model = copyValues(
new GeneralizedLinearRegressionModel(uid, wlsModel.coefficients, wlsModel.intercept)
.setParent(this))
val trainingSummary = new GeneralizedLinearRegressionTrainingSummary(dataset, model,
wlsModel.diagInvAtWA.toArray, 1, getSolver)
return model.setSummary(trainingSummary)
}
// Fit Generalized Linear Model by iteratively reweighted least squares (IRLS).
val initialModel = familyAndLink.initialize(instances, $(fitIntercept), $(regParam))
val optimizer = new IterativelyReweightedLeastSquares(initialModel, familyAndLink.reweightFunc,
$(fitIntercept), $(regParam), $(maxIter), $(tol))
val irlsModel = optimizer.fit(instances)
val model = copyValues(
new GeneralizedLinearRegressionModel(uid, irlsModel.coefficients, irlsModel.intercept)
.setParent(this))
val trainingSummary = new GeneralizedLinearRegressionTrainingSummary(dataset, model,
irlsModel.diagInvAtWA.toArray, irlsModel.numIterations, getSolver)
model.setSummary(trainingSummary)
}
@Since("2.0.0")
override def copy(extra: ParamMap): GeneralizedLinearRegression = defaultCopy(extra)
}
@Since("2.0.0")
object GeneralizedLinearRegression extends DefaultParamsReadable[GeneralizedLinearRegression] {
@Since("2.0.0")
override def load(path: String): GeneralizedLinearRegression = super.load(path)
/** Set of family and link pairs that GeneralizedLinearRegression supports. */
private[regression] lazy val supportedFamilyAndLinkPairs = Set(
Gaussian -> Identity, Gaussian -> Log, Gaussian -> Inverse,
Binomial -> Logit, Binomial -> Probit, Binomial -> CLogLog,
Poisson -> Log, Poisson -> Identity, Poisson -> Sqrt,
Gamma -> Inverse, Gamma -> Identity, Gamma -> Log
)
/** Set of family names that GeneralizedLinearRegression supports. */
private[regression] lazy val supportedFamilyNames = supportedFamilyAndLinkPairs.map(_._1.name)
/** Set of link names that GeneralizedLinearRegression supports. */
private[regression] lazy val supportedLinkNames = supportedFamilyAndLinkPairs.map(_._2.name)
private[regression] val epsilon: Double = 1E-16
/**
* Wrapper of family and link combination used in the model.
*/
private[regression] class FamilyAndLink(val family: Family, val link: Link) extends Serializable {
/** Linear predictor based on given mu. */
def predict(mu: Double): Double = link.link(family.project(mu))
/** Fitted value based on linear predictor eta. */
def fitted(eta: Double): Double = family.project(link.unlink(eta))
/**
* Get the initial guess model for [[IterativelyReweightedLeastSquares]].
*/
def initialize(
instances: RDD[Instance],
fitIntercept: Boolean,
regParam: Double): WeightedLeastSquaresModel = {
val newInstances = instances.map { instance =>
val mu = family.initialize(instance.label, instance.weight)
val eta = predict(mu)
Instance(eta, instance.weight, instance.features)
}
// TODO: Make standardizeFeatures and standardizeLabel configurable.
val initialModel = new WeightedLeastSquares(fitIntercept, regParam,
standardizeFeatures = true, standardizeLabel = true)
.fit(newInstances)
initialModel
}
/**
* The reweight function used to update offsets and weights
* at each iteration of [[IterativelyReweightedLeastSquares]].
*/
val reweightFunc: (Instance, WeightedLeastSquaresModel) => (Double, Double) = {
(instance: Instance, model: WeightedLeastSquaresModel) => {
val eta = model.predict(instance.features)
val mu = fitted(eta)
val offset = eta + (instance.label - mu) * link.deriv(mu)
val weight = instance.weight / (math.pow(this.link.deriv(mu), 2.0) * family.variance(mu))
(offset, weight)
}
}
}
/**
* A description of the error distribution to be used in the model.
*
* @param name the name of the family.
*/
private[regression] abstract class Family(val name: String) extends Serializable {
/** The default link instance of this family. */
val defaultLink: Link
/** Initialize the starting value for mu. */
def initialize(y: Double, weight: Double): Double
/** The variance of the endogenous variable's mean, given the value mu. */
def variance(mu: Double): Double
/** Deviance of (y, mu) pair. */
def deviance(y: Double, mu: Double, weight: Double): Double
/**
* Akaike Information Criterion (AIC) value of the family for a given dataset.
*
* @param predictions an RDD of (y, mu, weight) of instances in evaluation dataset
* @param deviance the deviance for the fitted model in evaluation dataset
* @param numInstances number of instances in evaluation dataset
* @param weightSum weights sum of instances in evaluation dataset
*/
def aic(
predictions: RDD[(Double, Double, Double)],
deviance: Double,
numInstances: Double,
weightSum: Double): Double
/** Trim the fitted value so that it will be in valid range. */
def project(mu: Double): Double = mu
}
private[regression] object Family {
/**
* Gets the [[Family]] object from its name.
*
* @param name family name: "gaussian", "binomial", "poisson" or "gamma".
*/
def fromName(name: String): Family = {
name match {
case Gaussian.name => Gaussian
case Binomial.name => Binomial
case Poisson.name => Poisson
case Gamma.name => Gamma
}
}
}
/**
* Gaussian exponential family distribution.
* The default link for the Gaussian family is the identity link.
*/
private[regression] object Gaussian extends Family("gaussian") {
val defaultLink: Link = Identity
override def initialize(y: Double, weight: Double): Double = y
override def variance(mu: Double): Double = 1.0
override def deviance(y: Double, mu: Double, weight: Double): Double = {
weight * (y - mu) * (y - mu)
}
override def aic(
predictions: RDD[(Double, Double, Double)],
deviance: Double,
numInstances: Double,
weightSum: Double): Double = {
val wt = predictions.map(x => math.log(x._3)).sum()
numInstances * (math.log(deviance / numInstances * 2.0 * math.Pi) + 1.0) + 2.0 - wt
}
override def project(mu: Double): Double = {
if (mu.isNegInfinity) {
Double.MinValue
} else if (mu.isPosInfinity) {
Double.MaxValue
} else {
mu
}
}
}
/**
* Binomial exponential family distribution.
* The default link for the Binomial family is the logit link.
*/
private[regression] object Binomial extends Family("binomial") {
val defaultLink: Link = Logit
override def initialize(y: Double, weight: Double): Double = {
val mu = (weight * y + 0.5) / (weight + 1.0)
require(mu > 0.0 && mu < 1.0, "The response variable of Binomial family" +
s"should be in range (0, 1), but got $mu")
mu
}
override def variance(mu: Double): Double = mu * (1.0 - mu)
override def deviance(y: Double, mu: Double, weight: Double): Double = {
val my = 1.0 - y
2.0 * weight * (y * math.log(math.max(y, 1.0) / mu) +
my * math.log(math.max(my, 1.0) / (1.0 - mu)))
}
override def aic(
predictions: RDD[(Double, Double, Double)],
deviance: Double,
numInstances: Double,
weightSum: Double): Double = {
-2.0 * predictions.map { case (y: Double, mu: Double, weight: Double) =>
weight * dist.Binomial(1, mu).logProbabilityOf(math.round(y).toInt)
}.sum()
}
override def project(mu: Double): Double = {
if (mu < epsilon) {
epsilon
} else if (mu > 1.0 - epsilon) {
1.0 - epsilon
} else {
mu
}
}
}
/**
* Poisson exponential family distribution.
* The default link for the Poisson family is the log link.
*/
private[regression] object Poisson extends Family("poisson") {
val defaultLink: Link = Log
override def initialize(y: Double, weight: Double): Double = {
require(y > 0.0, "The response variable of Poisson family " +
s"should be positive, but got $y")
y
}
override def variance(mu: Double): Double = mu
override def deviance(y: Double, mu: Double, weight: Double): Double = {
2.0 * weight * (y * math.log(y / mu) - (y - mu))
}
override def aic(
predictions: RDD[(Double, Double, Double)],
deviance: Double,
numInstances: Double,
weightSum: Double): Double = {
-2.0 * predictions.map { case (y: Double, mu: Double, weight: Double) =>
weight * dist.Poisson(mu).logProbabilityOf(y.toInt)
}.sum()
}
override def project(mu: Double): Double = {
if (mu < epsilon) {
epsilon
} else if (mu.isInfinity) {
Double.MaxValue
} else {
mu
}
}
}
/**
* Gamma exponential family distribution.
* The default link for the Gamma family is the inverse link.
*/
private[regression] object Gamma extends Family("gamma") {
val defaultLink: Link = Inverse
override def initialize(y: Double, weight: Double): Double = {
require(y > 0.0, "The response variable of Gamma family " +
s"should be positive, but got $y")
y
}
override def variance(mu: Double): Double = mu * mu
override def deviance(y: Double, mu: Double, weight: Double): Double = {
-2.0 * weight * (math.log(y / mu) - (y - mu)/mu)
}
override def aic(
predictions: RDD[(Double, Double, Double)],
deviance: Double,
numInstances: Double,
weightSum: Double): Double = {
val disp = deviance / weightSum
-2.0 * predictions.map { case (y: Double, mu: Double, weight: Double) =>
weight * dist.Gamma(1.0 / disp, mu * disp).logPdf(y)
}.sum() + 2.0
}
override def project(mu: Double): Double = {
if (mu < epsilon) {
epsilon
} else if (mu.isInfinity) {
Double.MaxValue
} else {
mu
}
}
}
/**
* A description of the link function to be used in the model.
* The link function provides the relationship between the linear predictor
* and the mean of the distribution function.
*
* @param name the name of link function.
*/
private[regression] abstract class Link(val name: String) extends Serializable {
/** The link function. */
def link(mu: Double): Double
/** Derivative of the link function. */
def deriv(mu: Double): Double
/** The inverse link function. */
def unlink(eta: Double): Double
}
private[regression] object Link {
/**
* Gets the [[Link]] object from its name.
*
* @param name link name: "identity", "logit", "log",
* "inverse", "probit", "cloglog" or "sqrt".
*/
def fromName(name: String): Link = {
name match {
case Identity.name => Identity
case Logit.name => Logit
case Log.name => Log
case Inverse.name => Inverse
case Probit.name => Probit
case CLogLog.name => CLogLog
case Sqrt.name => Sqrt
}
}
}
private[regression] object Identity extends Link("identity") {
override def link(mu: Double): Double = mu
override def deriv(mu: Double): Double = 1.0
override def unlink(eta: Double): Double = eta
}
private[regression] object Logit extends Link("logit") {
override def link(mu: Double): Double = math.log(mu / (1.0 - mu))
override def deriv(mu: Double): Double = 1.0 / (mu * (1.0 - mu))
override def unlink(eta: Double): Double = 1.0 / (1.0 + math.exp(-1.0 * eta))
}
private[regression] object Log extends Link("log") {
override def link(mu: Double): Double = math.log(mu)
override def deriv(mu: Double): Double = 1.0 / mu
override def unlink(eta: Double): Double = math.exp(eta)
}
private[regression] object Inverse extends Link("inverse") {
override def link(mu: Double): Double = 1.0 / mu
override def deriv(mu: Double): Double = -1.0 * math.pow(mu, -2.0)
override def unlink(eta: Double): Double = 1.0 / eta
}
private[regression] object Probit extends Link("probit") {
override def link(mu: Double): Double = dist.Gaussian(0.0, 1.0).icdf(mu)
override def deriv(mu: Double): Double = {
1.0 / dist.Gaussian(0.0, 1.0).pdf(dist.Gaussian(0.0, 1.0).icdf(mu))
}
override def unlink(eta: Double): Double = dist.Gaussian(0.0, 1.0).cdf(eta)
}
private[regression] object CLogLog extends Link("cloglog") {
override def link(mu: Double): Double = math.log(-1.0 * math.log(1 - mu))
override def deriv(mu: Double): Double = 1.0 / ((mu - 1.0) * math.log(1.0 - mu))
override def unlink(eta: Double): Double = 1.0 - math.exp(-1.0 * math.exp(eta))
}
private[regression] object Sqrt extends Link("sqrt") {
override def link(mu: Double): Double = math.sqrt(mu)
override def deriv(mu: Double): Double = 1.0 / (2.0 * math.sqrt(mu))
override def unlink(eta: Double): Double = eta * eta
}
}
/**
* :: Experimental ::
* Model produced by [[GeneralizedLinearRegression]].
*/
@Experimental
@Since("2.0.0")
class GeneralizedLinearRegressionModel private[ml] (
@Since("2.0.0") override val uid: String,
@Since("2.0.0") val coefficients: Vector,
@Since("2.0.0") val intercept: Double)
extends RegressionModel[Vector, GeneralizedLinearRegressionModel]
with GeneralizedLinearRegressionBase with MLWritable {
/**
* Sets the link prediction (linear predictor) column name.
*
* @group setParam
*/
@Since("2.0.0")
def setLinkPredictionCol(value: String): this.type = set(linkPredictionCol, value)
import GeneralizedLinearRegression._
private lazy val familyObj = Family.fromName($(family))
private lazy val linkObj = if (isDefined(link)) {
Link.fromName($(link))
} else {
familyObj.defaultLink
}
private lazy val familyAndLink = new FamilyAndLink(familyObj, linkObj)
override protected def predict(features: Vector): Double = {
val eta = predictLink(features)
familyAndLink.fitted(eta)
}
/**
* Calculate the link prediction (linear predictor) of the given instance.
*/
private def predictLink(features: Vector): Double = {
BLAS.dot(features, coefficients) + intercept
}
override def transform(dataset: Dataset[_]): DataFrame = {
transformSchema(dataset.schema)
transformImpl(dataset)
}
override protected def transformImpl(dataset: Dataset[_]): DataFrame = {
val predictUDF = udf { (features: Vector) => predict(features) }
val predictLinkUDF = udf { (features: Vector) => predictLink(features) }
var output = dataset
if ($(predictionCol).nonEmpty) {
output = output.withColumn($(predictionCol), predictUDF(col($(featuresCol))))
}
if (hasLinkPredictionCol) {
output = output.withColumn($(linkPredictionCol), predictLinkUDF(col($(featuresCol))))
}
output.toDF()
}
private var trainingSummary: Option[GeneralizedLinearRegressionTrainingSummary] = None
/**
* Gets R-like summary of model on training set. An exception is
* thrown if there is no summary available.
*/
@Since("2.0.0")
def summary: GeneralizedLinearRegressionTrainingSummary = trainingSummary.getOrElse {
throw new SparkException(
"No training summary available for this GeneralizedLinearRegressionModel")
}
/**
* Indicates if [[summary]] is available.
*/
@Since("2.0.0")
def hasSummary: Boolean = trainingSummary.nonEmpty
private[regression]
def setSummary(summary: GeneralizedLinearRegressionTrainingSummary): this.type = {
this.trainingSummary = Some(summary)
this
}
/**
* Evaluate the model on the given dataset, returning a summary of the results.
*/
@Since("2.0.0")
def evaluate(dataset: Dataset[_]): GeneralizedLinearRegressionSummary = {
new GeneralizedLinearRegressionSummary(dataset, this)
}
@Since("2.0.0")
override def copy(extra: ParamMap): GeneralizedLinearRegressionModel = {
copyValues(new GeneralizedLinearRegressionModel(uid, coefficients, intercept), extra)
.setParent(parent)
}
/**
* Returns a [[org.apache.spark.ml.util.MLWriter]] instance for this ML instance.
*
* For [[GeneralizedLinearRegressionModel]], this does NOT currently save the
* training [[summary]]. An option to save [[summary]] may be added in the future.
*
*/
@Since("2.0.0")
override def write: MLWriter =
new GeneralizedLinearRegressionModel.GeneralizedLinearRegressionModelWriter(this)
override val numFeatures: Int = coefficients.size
}
@Since("2.0.0")
object GeneralizedLinearRegressionModel extends MLReadable[GeneralizedLinearRegressionModel] {
@Since("2.0.0")
override def read: MLReader[GeneralizedLinearRegressionModel] =
new GeneralizedLinearRegressionModelReader
@Since("2.0.0")
override def load(path: String): GeneralizedLinearRegressionModel = super.load(path)
/** [[MLWriter]] instance for [[GeneralizedLinearRegressionModel]] */
private[GeneralizedLinearRegressionModel]
class GeneralizedLinearRegressionModelWriter(instance: GeneralizedLinearRegressionModel)
extends MLWriter with Logging {
private case class Data(intercept: Double, coefficients: Vector)
override protected def saveImpl(path: String): Unit = {
// Save metadata and Params
DefaultParamsWriter.saveMetadata(instance, path, sc)
// Save model data: intercept, coefficients
val data = Data(instance.intercept, instance.coefficients)
val dataPath = new Path(path, "data").toString
sparkSession.createDataFrame(Seq(data)).repartition(1).write.parquet(dataPath)
}
}
private class GeneralizedLinearRegressionModelReader
extends MLReader[GeneralizedLinearRegressionModel] {
/** Checked against metadata when loading model */
private val className = classOf[GeneralizedLinearRegressionModel].getName
override def load(path: String): GeneralizedLinearRegressionModel = {
val metadata = DefaultParamsReader.loadMetadata(path, sc, className)
val dataPath = new Path(path, "data").toString
val data = sparkSession.read.parquet(dataPath)
.select("intercept", "coefficients").head()
val intercept = data.getDouble(0)
val coefficients = data.getAs[Vector](1)
val model = new GeneralizedLinearRegressionModel(metadata.uid, coefficients, intercept)
DefaultParamsReader.getAndSetParams(model, metadata)
model
}
}
}
/**
* :: Experimental ::
* Summary of [[GeneralizedLinearRegression]] model and predictions.
*
* @param dataset Dataset to be summarized.
* @param origModel Model to be summarized. This is copied to create an internal
* model which cannot be modified from outside.
*/
@Since("2.0.0")
@Experimental
class GeneralizedLinearRegressionSummary private[regression] (
dataset: Dataset[_],
origModel: GeneralizedLinearRegressionModel) extends Serializable {
import GeneralizedLinearRegression._
/**
* Field in "predictions" which gives the predicted value of each instance.
* This is set to a new column name if the original model's `predictionCol` is not set.
*/
@Since("2.0.0")
val predictionCol: String = {
if (origModel.isDefined(origModel.predictionCol) && origModel.getPredictionCol.nonEmpty) {
origModel.getPredictionCol
} else {
"prediction_" + java.util.UUID.randomUUID.toString
}
}
/**
* Private copy of model to ensure Params are not modified outside this class.
* Coefficients is not a deep copy, but that is acceptable.
*
* NOTE: [[predictionCol]] must be set correctly before the value of [[model]] is set,
* and [[model]] must be set before [[predictions]] is set!
*/
protected val model: GeneralizedLinearRegressionModel =
origModel.copy(ParamMap.empty).setPredictionCol(predictionCol)
/** Predictions output by the model's `transform` method. */
@Since("2.0.0") @transient val predictions: DataFrame = model.transform(dataset)
private[regression] lazy val family: Family = Family.fromName(model.getFamily)
private[regression] lazy val link: Link = if (model.isDefined(model.link)) {
Link.fromName(model.getLink)
} else {
family.defaultLink
}
/** Number of instances in DataFrame predictions. */
private[regression] lazy val numInstances: Long = predictions.count()
/** The numeric rank of the fitted linear model. */
@Since("2.0.0")
lazy val rank: Long = if (model.getFitIntercept) {
model.coefficients.size + 1
} else {
model.coefficients.size
}
/** Degrees of freedom. */
@Since("2.0.0")
lazy val degreesOfFreedom: Long = {
numInstances - rank
}
/** The residual degrees of freedom. */
@Since("2.0.0")
lazy val residualDegreeOfFreedom: Long = degreesOfFreedom
/** The residual degrees of freedom for the null model. */
@Since("2.0.0")
lazy val residualDegreeOfFreedomNull: Long = if (model.getFitIntercept) {
numInstances - 1
} else {
numInstances
}
private def weightCol: Column = {
if (!model.isDefined(model.weightCol) || model.getWeightCol.isEmpty) {
lit(1.0)
} else {
col(model.getWeightCol)
}
}
private[regression] lazy val devianceResiduals: DataFrame = {
val drUDF = udf { (y: Double, mu: Double, weight: Double) =>
val r = math.sqrt(math.max(family.deviance(y, mu, weight), 0.0))
if (y > mu) r else -1.0 * r
}
val w = weightCol
predictions.select(
drUDF(col(model.getLabelCol), col(predictionCol), w).as("devianceResiduals"))
}
private[regression] lazy val pearsonResiduals: DataFrame = {
val prUDF = udf { mu: Double => family.variance(mu) }
val w = weightCol
predictions.select(col(model.getLabelCol).minus(col(predictionCol))
.multiply(sqrt(w)).divide(sqrt(prUDF(col(predictionCol)))).as("pearsonResiduals"))
}
private[regression] lazy val workingResiduals: DataFrame = {
val wrUDF = udf { (y: Double, mu: Double) => (y - mu) * link.deriv(mu) }
predictions.select(wrUDF(col(model.getLabelCol), col(predictionCol)).as("workingResiduals"))
}
private[regression] lazy val responseResiduals: DataFrame = {
predictions.select(col(model.getLabelCol).minus(col(predictionCol)).as("responseResiduals"))
}
/**
* Get the default residuals (deviance residuals) of the fitted model.
*/
@Since("2.0.0")
def residuals(): DataFrame = devianceResiduals
/**
* Get the residuals of the fitted model by type.
*
* @param residualsType The type of residuals which should be returned.
* Supported options: deviance, pearson, working and response.
*/
@Since("2.0.0")
def residuals(residualsType: String): DataFrame = {
residualsType match {
case "deviance" => devianceResiduals
case "pearson" => pearsonResiduals
case "working" => workingResiduals
case "response" => responseResiduals
case other => throw new UnsupportedOperationException(
s"The residuals type $other is not supported by Generalized Linear Regression.")
}
}
/**
* The deviance for the null model.
*/
@Since("2.0.0")
lazy val nullDeviance: Double = {
val w = weightCol
val wtdmu: Double = if (model.getFitIntercept) {
val agg = predictions.agg(sum(w.multiply(col(model.getLabelCol))), sum(w)).first()
agg.getDouble(0) / agg.getDouble(1)
} else {
link.unlink(0.0)
}
predictions.select(col(model.getLabelCol), w).rdd.map {
case Row(y: Double, weight: Double) =>
family.deviance(y, wtdmu, weight)
}.sum()
}
/**
* The deviance for the fitted model.
*/
@Since("2.0.0")
lazy val deviance: Double = {
val w = weightCol
predictions.select(col(model.getLabelCol), col(predictionCol), w).rdd.map {
case Row(label: Double, pred: Double, weight: Double) =>
family.deviance(label, pred, weight)
}.sum()
}
/**
* The dispersion of the fitted model.
* It is taken as 1.0 for the "binomial" and "poisson" families, and otherwise
* estimated by the residual Pearson's Chi-Squared statistic (which is defined as
* sum of the squares of the Pearson residuals) divided by the residual degrees of freedom.
*/
@Since("2.0.0")
lazy val dispersion: Double = if (
model.getFamily == Binomial.name || model.getFamily == Poisson.name) {
1.0
} else {
val rss = pearsonResiduals.agg(sum(pow(col("pearsonResiduals"), 2.0))).first().getDouble(0)
rss / degreesOfFreedom
}
/** Akaike Information Criterion (AIC) for the fitted model. */
@Since("2.0.0")
lazy val aic: Double = {
val w = weightCol
val weightSum = predictions.select(w).agg(sum(w)).first().getDouble(0)
val t = predictions.select(col(model.getLabelCol), col(predictionCol), w).rdd.map {
case Row(label: Double, pred: Double, weight: Double) =>
(label, pred, weight)
}
family.aic(t, deviance, numInstances, weightSum) + 2 * rank
}
}
/**
* :: Experimental ::
* Summary of [[GeneralizedLinearRegression]] fitting and model.
*
* @param dataset Dataset to be summarized.
* @param origModel Model to be summarized. This is copied to create an internal
* model which cannot be modified from outside.
* @param diagInvAtWA diagonal of matrix (A^T * W * A)^-1 in the last iteration
* @param numIterations number of iterations
* @param solver the solver algorithm used for model training
*/
@Since("2.0.0")
@Experimental
class GeneralizedLinearRegressionTrainingSummary private[regression] (
dataset: Dataset[_],
origModel: GeneralizedLinearRegressionModel,
private val diagInvAtWA: Array[Double],
@Since("2.0.0") val numIterations: Int,
@Since("2.0.0") val solver: String)
extends GeneralizedLinearRegressionSummary(dataset, origModel) with Serializable {
import GeneralizedLinearRegression._
/**
* Standard error of estimated coefficients and intercept.
*
* If [[GeneralizedLinearRegression.fitIntercept]] is set to true,
* then the last element returned corresponds to the intercept.
*/
@Since("2.0.0")
lazy val coefficientStandardErrors: Array[Double] = {
diagInvAtWA.map(_ * dispersion).map(math.sqrt)
}
/**
* T-statistic of estimated coefficients and intercept.
*
* If [[GeneralizedLinearRegression.fitIntercept]] is set to true,
* then the last element returned corresponds to the intercept.
*/
@Since("2.0.0")
lazy val tValues: Array[Double] = {
val estimate = if (model.getFitIntercept) {
Array.concat(model.coefficients.toArray, Array(model.intercept))
} else {
model.coefficients.toArray
}
estimate.zip(coefficientStandardErrors).map { x => x._1 / x._2 }
}
/**
* Two-sided p-value of estimated coefficients and intercept.
*
* If [[GeneralizedLinearRegression.fitIntercept]] is set to true,
* then the last element returned corresponds to the intercept.
*/
@Since("2.0.0")
lazy val pValues: Array[Double] = {
if (model.getFamily == Binomial.name || model.getFamily == Poisson.name) {
tValues.map { x => 2.0 * (1.0 - dist.Gaussian(0.0, 1.0).cdf(math.abs(x))) }
} else {
tValues.map { x => 2.0 * (1.0 - dist.StudentsT(degreesOfFreedom.toDouble).cdf(math.abs(x))) }
}
}
}
|