-
Notifications
You must be signed in to change notification settings - Fork 81
/
Copy pathimpute.html
1217 lines (981 loc) · 83.9 KB
/
impute.html
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
<!DOCTYPE html>
<html lang="en" data-content_root="../" >
<head>
<meta charset="utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="viewport" content="width=device-width, initial-scale=1" />
<meta property="og:title" content="6.4. Imputation of missing values" />
<meta property="og:type" content="website" />
<meta property="og:url" content="https://scikit-learn/stable/modules/impute.html" />
<meta property="og:site_name" content="scikit-learn" />
<meta property="og:description" content="For various reasons, many real world datasets contain missing values, often encoded as blanks, NaNs or other placeholders. Such datasets however are incompatible with scikit-learn estimators which ..." />
<meta property="og:image" content="https://scikit-learn.org/stable/_static/scikit-learn-logo-small.png" />
<meta property="og:image:alt" content="scikit-learn" />
<meta name="description" content="For various reasons, many real world datasets contain missing values, often encoded as blanks, NaNs or other placeholders. Such datasets however are incompatible with scikit-learn estimators which ..." />
<title>6.4. Imputation of missing values — scikit-learn 1.5.2 documentation</title>
<script data-cfasync="false">
document.documentElement.dataset.mode = localStorage.getItem("mode") || "";
document.documentElement.dataset.theme = localStorage.getItem("theme") || "";
</script>
<!-- Loaded before other Sphinx assets -->
<link href="../_static/styles/theme.css?digest=dfe6caa3a7d634c4db9b" rel="stylesheet" />
<link href="../_static/styles/bootstrap.css?digest=dfe6caa3a7d634c4db9b" rel="stylesheet" />
<link href="../_static/styles/pydata-sphinx-theme.css?digest=dfe6caa3a7d634c4db9b" rel="stylesheet" />
<link href="../_static/vendor/fontawesome/6.5.2/css/all.min.css?digest=dfe6caa3a7d634c4db9b" rel="stylesheet" />
<link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.5.2/webfonts/fa-solid-900.woff2" />
<link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.5.2/webfonts/fa-brands-400.woff2" />
<link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.5.2/webfonts/fa-regular-400.woff2" />
<link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=a746c00c" />
<link rel="stylesheet" type="text/css" href="../_static/copybutton.css?v=76b2166b" />
<link rel="stylesheet" type="text/css" href="../_static/plot_directive.css" />
<link rel="stylesheet" type="text/css" href="https://fonts.googleapis.com/css?family=Vibur" />
<link rel="stylesheet" type="text/css" href="../_static/jupyterlite_sphinx.css?v=ca70e7f1" />
<link rel="stylesheet" type="text/css" href="../_static/sg_gallery.css?v=d2d258e8" />
<link rel="stylesheet" type="text/css" href="../_static/sg_gallery-binder.css?v=f4aeca0c" />
<link rel="stylesheet" type="text/css" href="../_static/sg_gallery-dataframe.css?v=2082cf3c" />
<link rel="stylesheet" type="text/css" href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
<link rel="stylesheet" type="text/css" href="../_static/sphinx-design.min.css?v=95c83b7e" />
<link rel="stylesheet" type="text/css" href="../_static/styles/colors.css?v=cc94ab7d" />
<link rel="stylesheet" type="text/css" href="../_static/styles/custom.css?v=e4cb1417" />
<!-- Pre-loaded scripts that we'll load fully later -->
<link rel="preload" as="script" href="../_static/scripts/bootstrap.js?digest=dfe6caa3a7d634c4db9b" />
<link rel="preload" as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=dfe6caa3a7d634c4db9b" />
<script src="../_static/vendor/fontawesome/6.5.2/js/all.min.js?digest=dfe6caa3a7d634c4db9b"></script>
<script src="../_static/documentation_options.js?v=73275c37"></script>
<script src="../_static/doctools.js?v=9a2dae69"></script>
<script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
<script src="../_static/clipboard.min.js?v=a7894cd8"></script>
<script src="../_static/copybutton.js?v=97f0b27d"></script>
<script src="../_static/jupyterlite_sphinx.js?v=d6bdf5f8"></script>
<script src="../_static/design-tabs.js?v=f930bc37"></script>
<script data-domain="scikit-learn.org" defer="defer" src="https://views.scientific-python.org/js/script.js"></script>
<script>DOCUMENTATION_OPTIONS.pagename = 'modules/impute';</script>
<script>
DOCUMENTATION_OPTIONS.theme_version = '0.15.4';
DOCUMENTATION_OPTIONS.theme_switcher_json_url = 'https://scikit-learn.org/dev/_static/versions.json';
DOCUMENTATION_OPTIONS.theme_switcher_version_match = '1.5.2';
DOCUMENTATION_OPTIONS.show_version_warning_banner = true;
</script>
<script src="../_static/scripts/dropdown.js?v=e2048168"></script>
<script src="../_static/scripts/version-switcher.js?v=a6dd8357"></script>
<link rel="canonical" href="https://scikit-learn.org/stable/modules/impute.html" />
<link rel="icon" href="../_static/favicon.ico"/>
<link rel="author" title="About these documents" href="../about.html" />
<link rel="search" title="Search" href="../search.html" />
<link rel="next" title="6.5. Unsupervised dimensionality reduction" href="unsupervised_reduction.html" />
<link rel="prev" title="6.3. Preprocessing data" href="preprocessing.html" />
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<meta name="docsearch:language" content="en"/>
</head>
<body data-bs-spy="scroll" data-bs-target=".bd-toc-nav" data-offset="180" data-bs-root-margin="0px 0px -60%" data-default-mode="">
<div id="pst-skip-link" class="skip-link d-print-none"><a href="#main-content">Skip to main content</a></div>
<div id="pst-scroll-pixel-helper"></div>
<button type="button" class="btn rounded-pill" id="pst-back-to-top">
<i class="fa-solid fa-arrow-up"></i>Back to top</button>
<input type="checkbox"
class="sidebar-toggle"
id="pst-primary-sidebar-checkbox"/>
<label class="overlay overlay-primary" for="pst-primary-sidebar-checkbox"></label>
<input type="checkbox"
class="sidebar-toggle"
id="pst-secondary-sidebar-checkbox"/>
<label class="overlay overlay-secondary" for="pst-secondary-sidebar-checkbox"></label>
<div class="search-button__wrapper">
<div class="search-button__overlay"></div>
<div class="search-button__search-container">
<form class="bd-search d-flex align-items-center"
action="../search.html"
method="get">
<i class="fa-solid fa-magnifying-glass"></i>
<input type="search"
class="form-control"
name="q"
id="search-input"
placeholder="Search the docs ..."
aria-label="Search the docs ..."
autocomplete="off"
autocorrect="off"
autocapitalize="off"
spellcheck="false"/>
<span class="search-button__kbd-shortcut"><kbd class="kbd-shortcut__modifier">Ctrl</kbd>+<kbd>K</kbd></span>
</form></div>
</div>
<div class="pst-async-banner-revealer d-none">
<aside id="bd-header-version-warning" class="d-none d-print-none" aria-label="Version warning"></aside>
</div>
<header class="bd-header navbar navbar-expand-lg bd-navbar d-print-none">
<div class="bd-header__inner bd-page-width">
<button class="pst-navbar-icon sidebar-toggle primary-toggle" aria-label="Site navigation">
<span class="fa-solid fa-bars"></span>
</button>
<div class=" navbar-header-items__start">
<div class="navbar-item">
<a class="navbar-brand logo" href="../index.html">
<img src="../_static/scikit-learn-logo-small.png" class="logo__image only-light" alt="scikit-learn homepage"/>
<script>document.write(`<img src="../_static/scikit-learn-logo-small.png" class="logo__image only-dark" alt="scikit-learn homepage"/>`);</script>
</a></div>
</div>
<div class=" navbar-header-items">
<div class="me-auto navbar-header-items__center">
<div class="navbar-item">
<nav>
<ul class="bd-navbar-elements navbar-nav">
<li class="nav-item ">
<a class="nav-link nav-internal" href="../install.html">
Install
</a>
</li>
<li class="nav-item current active">
<a class="nav-link nav-internal" href="../user_guide.html">
User Guide
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../api/index.html">
API
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../auto_examples/index.html">
Examples
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-external" href="https://blog.scikit-learn.org/">
Community
</a>
</li>
<li class="nav-item dropdown">
<button class="btn dropdown-toggle nav-item" type="button" data-bs-toggle="dropdown" aria-expanded="false" aria-controls="pst-nav-more-links">
More
</button>
<ul id="pst-nav-more-links" class="dropdown-menu">
<li class=" ">
<a class="nav-link dropdown-item nav-internal" href="../getting_started.html">
Getting Started
</a>
</li>
<li class=" ">
<a class="nav-link dropdown-item nav-internal" href="../whats_new.html">
Release History
</a>
</li>
<li class=" ">
<a class="nav-link dropdown-item nav-internal" href="../glossary.html">
Glossary
</a>
</li>
<li class=" ">
<a class="nav-link dropdown-item nav-external" href="https://scikit-learn.org/dev/developers/index.html">
Development
</a>
</li>
<li class=" ">
<a class="nav-link dropdown-item nav-internal" href="../faq.html">
FAQ
</a>
</li>
<li class=" ">
<a class="nav-link dropdown-item nav-internal" href="../support.html">
Support
</a>
</li>
<li class=" ">
<a class="nav-link dropdown-item nav-internal" href="../related_projects.html">
Related Projects
</a>
</li>
<li class=" ">
<a class="nav-link dropdown-item nav-internal" href="../roadmap.html">
Roadmap
</a>
</li>
<li class=" ">
<a class="nav-link dropdown-item nav-internal" href="../governance.html">
Governance
</a>
</li>
<li class=" ">
<a class="nav-link dropdown-item nav-internal" href="../about.html">
About us
</a>
</li>
</ul>
</li>
</ul>
</nav></div>
</div>
<div class="navbar-header-items__end">
<div class="navbar-item navbar-persistent--container">
<script>
document.write(`
<button class="btn btn-sm pst-navbar-icon search-button search-button__button" title="Search" aria-label="Search" data-bs-placement="bottom" data-bs-toggle="tooltip">
<i class="fa-solid fa-magnifying-glass fa-lg"></i>
</button>
`);
</script>
</div>
<div class="navbar-item">
<script>
document.write(`
<button class="btn btn-sm nav-link pst-navbar-icon theme-switch-button" title="light/dark" aria-label="light/dark" data-bs-placement="bottom" data-bs-toggle="tooltip">
<i class="theme-switch fa-solid fa-sun fa-lg" data-mode="light"></i>
<i class="theme-switch fa-solid fa-moon fa-lg" data-mode="dark"></i>
<i class="theme-switch fa-solid fa-circle-half-stroke fa-lg" data-mode="auto"></i>
</button>
`);
</script></div>
<div class="navbar-item"><ul class="navbar-icon-links"
aria-label="Icon Links">
<li class="nav-item">
<a href="https://github.com/scikit-learn/scikit-learn" title="GitHub" class="nav-link pst-navbar-icon" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><i class="fa-brands fa-square-github fa-lg" aria-hidden="true"></i>
<span class="sr-only">GitHub</span></a>
</li>
</ul></div>
<div class="navbar-item">
<script>
document.write(`
<div class="version-switcher__container dropdown">
<button id="pst-version-switcher-button-2"
type="button"
class="version-switcher__button btn btn-sm dropdown-toggle"
data-bs-toggle="dropdown"
aria-haspopup="listbox"
aria-controls="pst-version-switcher-list-2"
aria-label="Version switcher list"
>
Choose version <!-- this text may get changed later by javascript -->
<span class="caret"></span>
</button>
<div id="pst-version-switcher-list-2"
class="version-switcher__menu dropdown-menu list-group-flush py-0"
role="listbox" aria-labelledby="pst-version-switcher-button-2">
<!-- dropdown will be populated by javascript on page load -->
</div>
</div>
`);
</script></div>
</div>
</div>
<div class="navbar-persistent--mobile">
<script>
document.write(`
<button class="btn btn-sm pst-navbar-icon search-button search-button__button" title="Search" aria-label="Search" data-bs-placement="bottom" data-bs-toggle="tooltip">
<i class="fa-solid fa-magnifying-glass fa-lg"></i>
</button>
`);
</script>
</div>
<button class="pst-navbar-icon sidebar-toggle secondary-toggle" aria-label="On this page">
<span class="fa-solid fa-outdent"></span>
</button>
</div>
</header>
<div class="bd-container">
<div class="bd-container__inner bd-page-width">
<div class="bd-sidebar-primary bd-sidebar">
<div class="sidebar-header-items sidebar-primary__section">
<div class="sidebar-header-items__center">
<div class="navbar-item">
<nav>
<ul class="bd-navbar-elements navbar-nav">
<li class="nav-item ">
<a class="nav-link nav-internal" href="../install.html">
Install
</a>
</li>
<li class="nav-item current active">
<a class="nav-link nav-internal" href="../user_guide.html">
User Guide
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../api/index.html">
API
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../auto_examples/index.html">
Examples
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-external" href="https://blog.scikit-learn.org/">
Community
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../getting_started.html">
Getting Started
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../whats_new.html">
Release History
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../glossary.html">
Glossary
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-external" href="https://scikit-learn.org/dev/developers/index.html">
Development
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../faq.html">
FAQ
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../support.html">
Support
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../related_projects.html">
Related Projects
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../roadmap.html">
Roadmap
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../governance.html">
Governance
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../about.html">
About us
</a>
</li>
</ul>
</nav></div>
</div>
<div class="sidebar-header-items__end">
<div class="navbar-item">
<script>
document.write(`
<button class="btn btn-sm nav-link pst-navbar-icon theme-switch-button" title="light/dark" aria-label="light/dark" data-bs-placement="bottom" data-bs-toggle="tooltip">
<i class="theme-switch fa-solid fa-sun fa-lg" data-mode="light"></i>
<i class="theme-switch fa-solid fa-moon fa-lg" data-mode="dark"></i>
<i class="theme-switch fa-solid fa-circle-half-stroke fa-lg" data-mode="auto"></i>
</button>
`);
</script></div>
<div class="navbar-item"><ul class="navbar-icon-links"
aria-label="Icon Links">
<li class="nav-item">
<a href="https://github.com/scikit-learn/scikit-learn" title="GitHub" class="nav-link pst-navbar-icon" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><i class="fa-brands fa-square-github fa-lg" aria-hidden="true"></i>
<span class="sr-only">GitHub</span></a>
</li>
</ul></div>
<div class="navbar-item">
<script>
document.write(`
<div class="version-switcher__container dropdown">
<button id="pst-version-switcher-button-3"
type="button"
class="version-switcher__button btn btn-sm dropdown-toggle"
data-bs-toggle="dropdown"
aria-haspopup="listbox"
aria-controls="pst-version-switcher-list-3"
aria-label="Version switcher list"
>
Choose version <!-- this text may get changed later by javascript -->
<span class="caret"></span>
</button>
<div id="pst-version-switcher-list-3"
class="version-switcher__menu dropdown-menu list-group-flush py-0"
role="listbox" aria-labelledby="pst-version-switcher-button-3">
<!-- dropdown will be populated by javascript on page load -->
</div>
</div>
`);
</script></div>
</div>
</div>
<div class="sidebar-primary-items__start sidebar-primary__section">
<div class="sidebar-primary-item">
<nav class="bd-docs-nav bd-links"
aria-label="Section Navigation">
<p class="bd-links__title" role="heading" aria-level="1">Section Navigation</p>
<div class="bd-toc-item navbar-nav"><ul class="current nav bd-sidenav">
<li class="toctree-l1 has-children"><a class="reference internal" href="../supervised_learning.html">1. Supervised learning</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="linear_model.html">1.1. Linear Models</a></li>
<li class="toctree-l2"><a class="reference internal" href="lda_qda.html">1.2. Linear and Quadratic Discriminant Analysis</a></li>
<li class="toctree-l2"><a class="reference internal" href="kernel_ridge.html">1.3. Kernel ridge regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="svm.html">1.4. Support Vector Machines</a></li>
<li class="toctree-l2"><a class="reference internal" href="sgd.html">1.5. Stochastic Gradient Descent</a></li>
<li class="toctree-l2"><a class="reference internal" href="neighbors.html">1.6. Nearest Neighbors</a></li>
<li class="toctree-l2"><a class="reference internal" href="gaussian_process.html">1.7. Gaussian Processes</a></li>
<li class="toctree-l2"><a class="reference internal" href="cross_decomposition.html">1.8. Cross decomposition</a></li>
<li class="toctree-l2"><a class="reference internal" href="naive_bayes.html">1.9. Naive Bayes</a></li>
<li class="toctree-l2"><a class="reference internal" href="tree.html">1.10. Decision Trees</a></li>
<li class="toctree-l2"><a class="reference internal" href="ensemble.html">1.11. Ensembles: Gradient boosting, random forests, bagging, voting, stacking</a></li>
<li class="toctree-l2"><a class="reference internal" href="multiclass.html">1.12. Multiclass and multioutput algorithms</a></li>
<li class="toctree-l2"><a class="reference internal" href="feature_selection.html">1.13. Feature selection</a></li>
<li class="toctree-l2"><a class="reference internal" href="semi_supervised.html">1.14. Semi-supervised learning</a></li>
<li class="toctree-l2"><a class="reference internal" href="isotonic.html">1.15. Isotonic regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="calibration.html">1.16. Probability calibration</a></li>
<li class="toctree-l2"><a class="reference internal" href="neural_networks_supervised.html">1.17. Neural network models (supervised)</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../unsupervised_learning.html">2. Unsupervised learning</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="mixture.html">2.1. Gaussian mixture models</a></li>
<li class="toctree-l2"><a class="reference internal" href="manifold.html">2.2. Manifold learning</a></li>
<li class="toctree-l2"><a class="reference internal" href="clustering.html">2.3. Clustering</a></li>
<li class="toctree-l2"><a class="reference internal" href="biclustering.html">2.4. Biclustering</a></li>
<li class="toctree-l2"><a class="reference internal" href="decomposition.html">2.5. Decomposing signals in components (matrix factorization problems)</a></li>
<li class="toctree-l2"><a class="reference internal" href="covariance.html">2.6. Covariance estimation</a></li>
<li class="toctree-l2"><a class="reference internal" href="outlier_detection.html">2.7. Novelty and Outlier Detection</a></li>
<li class="toctree-l2"><a class="reference internal" href="density.html">2.8. Density Estimation</a></li>
<li class="toctree-l2"><a class="reference internal" href="neural_networks_unsupervised.html">2.9. Neural network models (unsupervised)</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../model_selection.html">3. Model selection and evaluation</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="cross_validation.html">3.1. Cross-validation: evaluating estimator performance</a></li>
<li class="toctree-l2"><a class="reference internal" href="grid_search.html">3.2. Tuning the hyper-parameters of an estimator</a></li>
<li class="toctree-l2"><a class="reference internal" href="classification_threshold.html">3.3. Tuning the decision threshold for class prediction</a></li>
<li class="toctree-l2"><a class="reference internal" href="model_evaluation.html">3.4. Metrics and scoring: quantifying the quality of predictions</a></li>
<li class="toctree-l2"><a class="reference internal" href="learning_curve.html">3.5. Validation curves: plotting scores to evaluate models</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../inspection.html">4. Inspection</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="partial_dependence.html">4.1. Partial Dependence and Individual Conditional Expectation plots</a></li>
<li class="toctree-l2"><a class="reference internal" href="permutation_importance.html">4.2. Permutation feature importance</a></li>
</ul>
</details></li>
<li class="toctree-l1"><a class="reference internal" href="../visualizations.html">5. Visualizations</a></li>
<li class="toctree-l1 current active has-children"><a class="reference internal" href="../data_transforms.html">6. Dataset transformations</a><details open="open"><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul class="current">
<li class="toctree-l2"><a class="reference internal" href="compose.html">6.1. Pipelines and composite estimators</a></li>
<li class="toctree-l2"><a class="reference internal" href="feature_extraction.html">6.2. Feature extraction</a></li>
<li class="toctree-l2"><a class="reference internal" href="preprocessing.html">6.3. Preprocessing data</a></li>
<li class="toctree-l2 current active"><a class="current reference internal" href="#">6.4. Imputation of missing values</a></li>
<li class="toctree-l2"><a class="reference internal" href="unsupervised_reduction.html">6.5. Unsupervised dimensionality reduction</a></li>
<li class="toctree-l2"><a class="reference internal" href="random_projection.html">6.6. Random Projection</a></li>
<li class="toctree-l2"><a class="reference internal" href="kernel_approximation.html">6.7. Kernel Approximation</a></li>
<li class="toctree-l2"><a class="reference internal" href="metrics.html">6.8. Pairwise metrics, Affinities and Kernels</a></li>
<li class="toctree-l2"><a class="reference internal" href="preprocessing_targets.html">6.9. Transforming the prediction target (<code class="docutils literal notranslate"><span class="pre">y</span></code>)</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../datasets.html">7. Dataset loading utilities</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../datasets/toy_dataset.html">7.1. Toy datasets</a></li>
<li class="toctree-l2"><a class="reference internal" href="../datasets/real_world.html">7.2. Real world datasets</a></li>
<li class="toctree-l2"><a class="reference internal" href="../datasets/sample_generators.html">7.3. Generated datasets</a></li>
<li class="toctree-l2"><a class="reference internal" href="../datasets/loading_other_datasets.html">7.4. Loading other datasets</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../computing.html">8. Computing with scikit-learn</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../computing/scaling_strategies.html">8.1. Strategies to scale computationally: bigger data</a></li>
<li class="toctree-l2"><a class="reference internal" href="../computing/computational_performance.html">8.2. Computational Performance</a></li>
<li class="toctree-l2"><a class="reference internal" href="../computing/parallelism.html">8.3. Parallelism, resource management, and configuration</a></li>
</ul>
</details></li>
<li class="toctree-l1"><a class="reference internal" href="../model_persistence.html">9. Model persistence</a></li>
<li class="toctree-l1"><a class="reference internal" href="../common_pitfalls.html">10. Common pitfalls and recommended practices</a></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../dispatching.html">11. Dispatching</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="array_api.html">11.1. Array API support (experimental)</a></li>
</ul>
</details></li>
<li class="toctree-l1"><a class="reference internal" href="../machine_learning_map.html">12. Choosing the right estimator</a></li>
<li class="toctree-l1"><a class="reference internal" href="../presentations.html">13. External Resources, Videos and Talks</a></li>
</ul>
</div>
</nav></div>
</div>
<div class="sidebar-primary-items__end sidebar-primary__section">
</div>
<div id="rtd-footer-container"></div>
</div>
<main id="main-content" class="bd-main" role="main">
<div class="bd-content">
<div class="bd-article-container">
<div class="bd-header-article d-print-none">
<div class="header-article-items header-article__inner">
<div class="header-article-items__start">
<div class="header-article-item">
<nav aria-label="Breadcrumb" class="d-print-none">
<ul class="bd-breadcrumbs">
<li class="breadcrumb-item breadcrumb-home">
<a href="../index.html" class="nav-link" aria-label="Home">
<i class="fa-solid fa-home"></i>
</a>
</li>
<li class="breadcrumb-item"><a href="../user_guide.html" class="nav-link">User Guide</a></li>
<li class="breadcrumb-item"><a href="../data_transforms.html" class="nav-link"><span class="section-number">6. </span>Dataset transformations</a></li>
<li class="breadcrumb-item active" aria-current="page"><span...</li>
</ul>
</nav>
</div>
</div>
</div>
</div>
<div id="searchbox"></div>
<article class="bd-article">
<section id="imputation-of-missing-values">
<span id="impute"></span><h1><span class="section-number">6.4. </span>Imputation of missing values<a class="headerlink" href="#imputation-of-missing-values" title="Link to this heading">#</a></h1>
<p>For various reasons, many real world datasets contain missing values, often
encoded as blanks, NaNs or other placeholders. Such datasets however are
incompatible with scikit-learn estimators which assume that all values in an
array are numerical, and that all have and hold meaning. A basic strategy to
use incomplete datasets is to discard entire rows and/or columns containing
missing values. However, this comes at the price of losing data which may be
valuable (even though incomplete). A better strategy is to impute the missing
values, i.e., to infer them from the known part of the data. See the
glossary entry on <a class="reference internal" href="../glossary.html#term-imputation"><span class="xref std std-term">imputation</span></a>.</p>
<section id="univariate-vs-multivariate-imputation">
<h2><span class="section-number">6.4.1. </span>Univariate vs. Multivariate Imputation<a class="headerlink" href="#univariate-vs-multivariate-imputation" title="Link to this heading">#</a></h2>
<p>One type of imputation algorithm is univariate, which imputes values in the
i-th feature dimension using only non-missing values in that feature dimension
(e.g. <a class="reference internal" href="generated/sklearn.impute.SimpleImputer.html#sklearn.impute.SimpleImputer" title="sklearn.impute.SimpleImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">SimpleImputer</span></code></a>). By contrast, multivariate imputation
algorithms use the entire set of available feature dimensions to estimate the
missing values (e.g. <a class="reference internal" href="generated/sklearn.impute.IterativeImputer.html#sklearn.impute.IterativeImputer" title="sklearn.impute.IterativeImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">IterativeImputer</span></code></a>).</p>
</section>
<section id="univariate-feature-imputation">
<span id="single-imputer"></span><h2><span class="section-number">6.4.2. </span>Univariate feature imputation<a class="headerlink" href="#univariate-feature-imputation" title="Link to this heading">#</a></h2>
<p>The <a class="reference internal" href="generated/sklearn.impute.SimpleImputer.html#sklearn.impute.SimpleImputer" title="sklearn.impute.SimpleImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">SimpleImputer</span></code></a> class provides basic strategies for imputing missing
values. Missing values can be imputed with a provided constant value, or using
the statistics (mean, median or most frequent) of each column in which the
missing values are located. This class also allows for different missing values
encodings.</p>
<p>The following snippet demonstrates how to replace missing values,
encoded as <code class="docutils literal notranslate"><span class="pre">np.nan</span></code>, using the mean value of the columns (axis 0)
that contain the missing values:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.impute</span> <span class="kn">import</span> <span class="n">SimpleImputer</span>
<span class="gp">>>> </span><span class="n">imp</span> <span class="o">=</span> <span class="n">SimpleImputer</span><span class="p">(</span><span class="n">missing_values</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="n">strategy</span><span class="o">=</span><span class="s1">'mean'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">imp</span><span class="o">.</span><span class="n">fit</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">6</span><span class="p">]])</span>
<span class="go">SimpleImputer()</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="p">[[</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">6</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">],</span> <span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">6</span><span class="p">]]</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">imp</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X</span><span class="p">))</span>
<span class="go">[[4. 2. ]</span>
<span class="go"> [6. 3.666...]</span>
<span class="go"> [7. 6. ]]</span>
</pre></div>
</div>
<p>The <a class="reference internal" href="generated/sklearn.impute.SimpleImputer.html#sklearn.impute.SimpleImputer" title="sklearn.impute.SimpleImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">SimpleImputer</span></code></a> class also supports sparse matrices:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">scipy.sparse</span> <span class="k">as</span> <span class="nn">sp</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">csc_matrix</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">8</span><span class="p">,</span> <span class="mi">4</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">imp</span> <span class="o">=</span> <span class="n">SimpleImputer</span><span class="p">(</span><span class="n">missing_values</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span> <span class="n">strategy</span><span class="o">=</span><span class="s1">'mean'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">imp</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="go">SimpleImputer(missing_values=-1)</span>
<span class="gp">>>> </span><span class="n">X_test</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">csc_matrix</span><span class="p">([[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">6</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">6</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">imp</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span><span class="o">.</span><span class="n">toarray</span><span class="p">())</span>
<span class="go">[[3. 2.]</span>
<span class="go"> [6. 3.]</span>
<span class="go"> [7. 6.]]</span>
</pre></div>
</div>
<p>Note that this format is not meant to be used to implicitly store missing
values in the matrix because it would densify it at transform time. Missing
values encoded by 0 must be used with dense input.</p>
<p>The <a class="reference internal" href="generated/sklearn.impute.SimpleImputer.html#sklearn.impute.SimpleImputer" title="sklearn.impute.SimpleImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">SimpleImputer</span></code></a> class also supports categorical data represented as
string values or pandas categoricals when using the <code class="docutils literal notranslate"><span class="pre">'most_frequent'</span></code> or
<code class="docutils literal notranslate"><span class="pre">'constant'</span></code> strategy:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="gp">>>> </span><span class="n">df</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">([[</span><span class="s2">"a"</span><span class="p">,</span> <span class="s2">"x"</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="s2">"a"</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="s2">"b"</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">]],</span> <span class="n">dtype</span><span class="o">=</span><span class="s2">"category"</span><span class="p">)</span>
<span class="gp">...</span>
<span class="gp">>>> </span><span class="n">imp</span> <span class="o">=</span> <span class="n">SimpleImputer</span><span class="p">(</span><span class="n">strategy</span><span class="o">=</span><span class="s2">"most_frequent"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">imp</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">df</span><span class="p">))</span>
<span class="go">[['a' 'x']</span>
<span class="go"> ['a' 'y']</span>
<span class="go"> ['a' 'y']</span>
<span class="go"> ['b' 'y']]</span>
</pre></div>
</div>
<p>For another example on usage, see <a class="reference internal" href="../auto_examples/impute/plot_missing_values.html#sphx-glr-auto-examples-impute-plot-missing-values-py"><span class="std std-ref">Imputing missing values before building an estimator</span></a>.</p>
</section>
<section id="multivariate-feature-imputation">
<span id="iterative-imputer"></span><h2><span class="section-number">6.4.3. </span>Multivariate feature imputation<a class="headerlink" href="#multivariate-feature-imputation" title="Link to this heading">#</a></h2>
<p>A more sophisticated approach is to use the <a class="reference internal" href="generated/sklearn.impute.IterativeImputer.html#sklearn.impute.IterativeImputer" title="sklearn.impute.IterativeImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">IterativeImputer</span></code></a> class,
which models each feature with missing values as a function of other features,
and uses that estimate for imputation. It does so in an iterated round-robin
fashion: at each step, a feature column is designated as output <code class="docutils literal notranslate"><span class="pre">y</span></code> and the
other feature columns are treated as inputs <code class="docutils literal notranslate"><span class="pre">X</span></code>. A regressor is fit on <code class="docutils literal notranslate"><span class="pre">(X,</span>
<span class="pre">y)</span></code> for known <code class="docutils literal notranslate"><span class="pre">y</span></code>. Then, the regressor is used to predict the missing values
of <code class="docutils literal notranslate"><span class="pre">y</span></code>. This is done for each feature in an iterative fashion, and then is
repeated for <code class="docutils literal notranslate"><span class="pre">max_iter</span></code> imputation rounds. The results of the final
imputation round are returned.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>This estimator is still <strong>experimental</strong> for now: default parameters or
details of behaviour might change without any deprecation cycle. Resolving
the following issues would help stabilize <a class="reference internal" href="generated/sklearn.impute.IterativeImputer.html#sklearn.impute.IterativeImputer" title="sklearn.impute.IterativeImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">IterativeImputer</span></code></a>:
convergence criteria (<a class="reference external" href="https://github.com/scikit-learn/scikit-learn/issues/14338">#14338</a>), default estimators (<a class="reference external" href="https://github.com/scikit-learn/scikit-learn/issues/13286">#13286</a>),
and use of random state (<a class="reference external" href="https://github.com/scikit-learn/scikit-learn/issues/15611">#15611</a>). To use it, you need to explicitly
import <code class="docutils literal notranslate"><span class="pre">enable_iterative_imputer</span></code>.</p>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.experimental</span> <span class="kn">import</span> <span class="n">enable_iterative_imputer</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.impute</span> <span class="kn">import</span> <span class="n">IterativeImputer</span>
<span class="gp">>>> </span><span class="n">imp</span> <span class="o">=</span> <span class="n">IterativeImputer</span><span class="p">(</span><span class="n">max_iter</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">imp</span><span class="o">.</span><span class="n">fit</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">6</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">8</span><span class="p">],</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">]])</span>
<span class="go">IterativeImputer(random_state=0)</span>
<span class="gp">>>> </span><span class="n">X_test</span> <span class="o">=</span> <span class="p">[[</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">6</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">],</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="mi">6</span><span class="p">]]</span>
<span class="gp">>>> </span><span class="c1"># the model learns that the second feature is double the first</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">round</span><span class="p">(</span><span class="n">imp</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_test</span><span class="p">)))</span>
<span class="go">[[ 1. 2.]</span>
<span class="go"> [ 6. 12.]</span>
<span class="go"> [ 3. 6.]]</span>
</pre></div>
</div>
<p>Both <a class="reference internal" href="generated/sklearn.impute.SimpleImputer.html#sklearn.impute.SimpleImputer" title="sklearn.impute.SimpleImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">SimpleImputer</span></code></a> and <a class="reference internal" href="generated/sklearn.impute.IterativeImputer.html#sklearn.impute.IterativeImputer" title="sklearn.impute.IterativeImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">IterativeImputer</span></code></a> can be used in a
Pipeline as a way to build a composite estimator that supports imputation.
See <a class="reference internal" href="../auto_examples/impute/plot_missing_values.html#sphx-glr-auto-examples-impute-plot-missing-values-py"><span class="std std-ref">Imputing missing values before building an estimator</span></a>.</p>
<section id="flexibility-of-iterativeimputer">
<h3><span class="section-number">6.4.3.1. </span>Flexibility of IterativeImputer<a class="headerlink" href="#flexibility-of-iterativeimputer" title="Link to this heading">#</a></h3>
<p>There are many well-established imputation packages in the R data science
ecosystem: Amelia, mi, mice, missForest, etc. missForest is popular, and turns
out to be a particular instance of different sequential imputation algorithms
that can all be implemented with <a class="reference internal" href="generated/sklearn.impute.IterativeImputer.html#sklearn.impute.IterativeImputer" title="sklearn.impute.IterativeImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">IterativeImputer</span></code></a> by passing in
different regressors to be used for predicting missing feature values. In the
case of missForest, this regressor is a Random Forest.
See <a class="reference internal" href="../auto_examples/impute/plot_iterative_imputer_variants_comparison.html#sphx-glr-auto-examples-impute-plot-iterative-imputer-variants-comparison-py"><span class="std std-ref">Imputing missing values with variants of IterativeImputer</span></a>.</p>
</section>
<section id="multiple-vs-single-imputation">
<span id="multiple-imputation"></span><h3><span class="section-number">6.4.3.2. </span>Multiple vs. Single Imputation<a class="headerlink" href="#multiple-vs-single-imputation" title="Link to this heading">#</a></h3>
<p>In the statistics community, it is common practice to perform multiple
imputations, generating, for example, <code class="docutils literal notranslate"><span class="pre">m</span></code> separate imputations for a single
feature matrix. Each of these <code class="docutils literal notranslate"><span class="pre">m</span></code> imputations is then put through the
subsequent analysis pipeline (e.g. feature engineering, clustering, regression,
classification). The <code class="docutils literal notranslate"><span class="pre">m</span></code> final analysis results (e.g. held-out validation
errors) allow the data scientist to obtain understanding of how analytic
results may differ as a consequence of the inherent uncertainty caused by the
missing values. The above practice is called multiple imputation.</p>
<p>Our implementation of <a class="reference internal" href="generated/sklearn.impute.IterativeImputer.html#sklearn.impute.IterativeImputer" title="sklearn.impute.IterativeImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">IterativeImputer</span></code></a> was inspired by the R MICE
package (Multivariate Imputation by Chained Equations) <a class="footnote-reference brackets" href="#id3" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>, but differs from
it by returning a single imputation instead of multiple imputations. However,
<a class="reference internal" href="generated/sklearn.impute.IterativeImputer.html#sklearn.impute.IterativeImputer" title="sklearn.impute.IterativeImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">IterativeImputer</span></code></a> can also be used for multiple imputations by applying
it repeatedly to the same dataset with different random seeds when
<code class="docutils literal notranslate"><span class="pre">sample_posterior=True</span></code>. See <a class="footnote-reference brackets" href="#id4" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>, chapter 4 for more discussion on multiple
vs. single imputations.</p>
<p>It is still an open problem as to how useful single vs. multiple imputation is
in the context of prediction and classification when the user is not
interested in measuring uncertainty due to missing values.</p>
<p>Note that a call to the <code class="docutils literal notranslate"><span class="pre">transform</span></code> method of <a class="reference internal" href="generated/sklearn.impute.IterativeImputer.html#sklearn.impute.IterativeImputer" title="sklearn.impute.IterativeImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">IterativeImputer</span></code></a> is
not allowed to change the number of samples. Therefore multiple imputations
cannot be achieved by a single call to <code class="docutils literal notranslate"><span class="pre">transform</span></code>.</p>
</section>
<section id="references">
<h3><span class="section-number">6.4.3.3. </span>References<a class="headerlink" href="#references" title="Link to this heading">#</a></h3>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="id3" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
<p><a class="reference external" href="https://www.jstatsoft.org/article/view/v045i03">Stef van Buuren, Karin Groothuis-Oudshoorn (2011). “mice: Multivariate
Imputation by Chained Equations in R”. Journal of Statistical Software 45:
1-67.</a></p>
</aside>
<aside class="footnote brackets" id="id4" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">2</a><span class="fn-bracket">]</span></span>
<p>Roderick J A Little and Donald B Rubin (1986). “Statistical Analysis
with Missing Data”. John Wiley & Sons, Inc., New York, NY, USA.</p>
</aside>
</aside>
</section>
</section>
<section id="nearest-neighbors-imputation">
<span id="knnimpute"></span><h2><span class="section-number">6.4.4. </span>Nearest neighbors imputation<a class="headerlink" href="#nearest-neighbors-imputation" title="Link to this heading">#</a></h2>
<p>The <a class="reference internal" href="generated/sklearn.impute.KNNImputer.html#sklearn.impute.KNNImputer" title="sklearn.impute.KNNImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">KNNImputer</span></code></a> class provides imputation for filling in missing values
using the k-Nearest Neighbors approach. By default, a euclidean distance metric
that supports missing values,
<a class="reference internal" href="generated/sklearn.metrics.pairwise.nan_euclidean_distances.html#sklearn.metrics.pairwise.nan_euclidean_distances" title="sklearn.metrics.pairwise.nan_euclidean_distances"><code class="xref py py-func docutils literal notranslate"><span class="pre">nan_euclidean_distances</span></code></a>, is used to find the
nearest neighbors. Each missing feature is imputed using values from
<code class="docutils literal notranslate"><span class="pre">n_neighbors</span></code> nearest neighbors that have a value for the feature. The
feature of the neighbors are averaged uniformly or weighted by distance to each
neighbor. If a sample has more than one feature missing, then the neighbors for
that sample can be different depending on the particular feature being imputed.
When the number of available neighbors is less than <code class="docutils literal notranslate"><span class="pre">n_neighbors</span></code> and there are
no defined distances to the training set, the training set average for that
feature is used during imputation. If there is at least one neighbor with a
defined distance, the weighted or unweighted average of the remaining neighbors
will be used during imputation. If a feature is always missing in training, it
is removed during <code class="docutils literal notranslate"><span class="pre">transform</span></code>. For more information on the methodology, see
ref. <a class="reference internal" href="#ol2001" id="id5"><span>[OL2001]</span></a>.</p>
<p>The following snippet demonstrates how to replace missing values,
encoded as <code class="docutils literal notranslate"><span class="pre">np.nan</span></code>, using the mean feature value of the two nearest
neighbors of samples with missing values:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.impute</span> <span class="kn">import</span> <span class="n">KNNImputer</span>
<span class="gp">>>> </span><span class="n">nan</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">nan</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="n">nan</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="p">[</span><span class="mi">8</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">7</span><span class="p">]]</span>
<span class="gp">>>> </span><span class="n">imputer</span> <span class="o">=</span> <span class="n">KNNImputer</span><span class="p">(</span><span class="n">n_neighbors</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">weights</span><span class="o">=</span><span class="s2">"uniform"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">imputer</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="go">array([[1. , 2. , 4. ],</span>
<span class="go"> [3. , 4. , 3. ],</span>
<span class="go"> [5.5, 6. , 5. ],</span>
<span class="go"> [8. , 8. , 7. ]])</span>
</pre></div>
</div>
<p>For another example on usage, see <a class="reference internal" href="../auto_examples/impute/plot_missing_values.html#sphx-glr-auto-examples-impute-plot-missing-values-py"><span class="std std-ref">Imputing missing values before building an estimator</span></a>.</p>
<p class="rubric">References</p>
<div role="list" class="citation-list">
<div class="citation" id="ol2001" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id5">OL2001</a><span class="fn-bracket">]</span></span>
<p><a class="reference external" href="https://academic.oup.com/bioinformatics/article/17/6/520/272365">Olga Troyanskaya, Michael Cantor, Gavin Sherlock, Pat Brown,
Trevor Hastie, Robert Tibshirani, David Botstein and Russ B. Altman,
Missing value estimation methods for DNA microarrays, BIOINFORMATICS
Vol. 17 no. 6, 2001 Pages 520-525.</a></p>
</div>
</div>
</section>
<section id="keeping-the-number-of-features-constant">
<h2><span class="section-number">6.4.5. </span>Keeping the number of features constant<a class="headerlink" href="#keeping-the-number-of-features-constant" title="Link to this heading">#</a></h2>
<p>By default, the scikit-learn imputers will drop fully empty features, i.e.
columns containing only missing values. For instance:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">imputer</span> <span class="o">=</span> <span class="n">SimpleImputer</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="mi">3</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">imputer</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="go">array([[1.],</span>
<span class="go"> [2.],</span>
<span class="go"> [3.]])</span>
</pre></div>
</div>
<p>The first feature in <code class="docutils literal notranslate"><span class="pre">X</span></code> containing only <code class="docutils literal notranslate"><span class="pre">np.nan</span></code> was dropped after the
imputation. While this feature will not help in predictive setting, dropping
the columns will change the shape of <code class="docutils literal notranslate"><span class="pre">X</span></code> which could be problematic when using
imputers in a more complex machine-learning pipeline. The parameter
<code class="docutils literal notranslate"><span class="pre">keep_empty_features</span></code> offers the option to keep the empty features by imputing
with a constant values. In most of the cases, this constant value is zero:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">imputer</span><span class="o">.</span><span class="n">set_params</span><span class="p">(</span><span class="n">keep_empty_features</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="go">SimpleImputer(keep_empty_features=True)</span>
<span class="gp">>>> </span><span class="n">imputer</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="go">array([[0., 1.],</span>
<span class="go"> [0., 2.],</span>
<span class="go"> [0., 3.]])</span>
</pre></div>
</div>
</section>
<section id="marking-imputed-values">
<span id="missing-indicator"></span><h2><span class="section-number">6.4.6. </span>Marking imputed values<a class="headerlink" href="#marking-imputed-values" title="Link to this heading">#</a></h2>
<p>The <a class="reference internal" href="generated/sklearn.impute.MissingIndicator.html#sklearn.impute.MissingIndicator" title="sklearn.impute.MissingIndicator"><code class="xref py py-class docutils literal notranslate"><span class="pre">MissingIndicator</span></code></a> transformer is useful to transform a dataset into
corresponding binary matrix indicating the presence of missing values in the
dataset. This transformation is useful in conjunction with imputation. When
using imputation, preserving the information about which values had been
missing can be informative. Note that both the <a class="reference internal" href="generated/sklearn.impute.SimpleImputer.html#sklearn.impute.SimpleImputer" title="sklearn.impute.SimpleImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">SimpleImputer</span></code></a> and
<a class="reference internal" href="generated/sklearn.impute.IterativeImputer.html#sklearn.impute.IterativeImputer" title="sklearn.impute.IterativeImputer"><code class="xref py py-class docutils literal notranslate"><span class="pre">IterativeImputer</span></code></a> have the boolean parameter <code class="docutils literal notranslate"><span class="pre">add_indicator</span></code>
(<code class="docutils literal notranslate"><span class="pre">False</span></code> by default) which when set to <code class="docutils literal notranslate"><span class="pre">True</span></code> provides a convenient way of
stacking the output of the <a class="reference internal" href="generated/sklearn.impute.MissingIndicator.html#sklearn.impute.MissingIndicator" title="sklearn.impute.MissingIndicator"><code class="xref py py-class docutils literal notranslate"><span class="pre">MissingIndicator</span></code></a> transformer with the
output of the imputer.</p>
<p><code class="docutils literal notranslate"><span class="pre">NaN</span></code> is usually used as the placeholder for missing values. However, it
enforces the data type to be float. The parameter <code class="docutils literal notranslate"><span class="pre">missing_values</span></code> allows to
specify other placeholder such as integer. In the following example, we will
use <code class="docutils literal notranslate"><span class="pre">-1</span></code> as missing values:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.impute</span> <span class="kn">import</span> <span class="n">MissingIndicator</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="mi">8</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">indicator</span> <span class="o">=</span> <span class="n">MissingIndicator</span><span class="p">(</span><span class="n">missing_values</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">mask_missing_values_only</span> <span class="o">=</span> <span class="n">indicator</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">mask_missing_values_only</span>
<span class="go">array([[ True, True, False],</span>
<span class="go"> [False, True, True],</span>
<span class="go"> [False, True, False]])</span>
</pre></div>
</div>
<p>The <code class="docutils literal notranslate"><span class="pre">features</span></code> parameter is used to choose the features for which the mask is
constructed. By default, it is <code class="docutils literal notranslate"><span class="pre">'missing-only'</span></code> which returns the imputer
mask of the features containing missing values at <code class="docutils literal notranslate"><span class="pre">fit</span></code> time:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">indicator</span><span class="o">.</span><span class="n">features_</span>
<span class="go">array([0, 1, 3])</span>
</pre></div>
</div>
<p>The <code class="docutils literal notranslate"><span class="pre">features</span></code> parameter can be set to <code class="docutils literal notranslate"><span class="pre">'all'</span></code> to return all features
whether or not they contain missing values:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">indicator</span> <span class="o">=</span> <span class="n">MissingIndicator</span><span class="p">(</span><span class="n">missing_values</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span> <span class="n">features</span><span class="o">=</span><span class="s2">"all"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">mask_all</span> <span class="o">=</span> <span class="n">indicator</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">mask_all</span>
<span class="go">array([[ True, True, False, False],</span>
<span class="go"> [False, True, False, True],</span>
<span class="go"> [False, True, False, False]])</span>
<span class="gp">>>> </span><span class="n">indicator</span><span class="o">.</span><span class="n">features_</span>