-
Notifications
You must be signed in to change notification settings - Fork 2
/
Copy pathdistributions.html
5899 lines (5181 loc) · 741 KB
/
distributions.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>
<!--[if IE 8]><html class="no-js lt-ie9" lang="en" > <![endif]-->
<!--[if gt IE 8]><!--> <html class="no-js" lang="en" > <!--<![endif]-->
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Probability distributions - torch.distributions — PyTorch 2.2 documentation</title>
<link rel="canonical" href="https://pytorch.org/docs/stable/distributions.html"/>
<link rel="stylesheet" href="_static/css/theme.css" type="text/css" />
<!-- <link rel="stylesheet" href="_static/pygments.css" type="text/css" /> -->
<link rel="stylesheet" href="_static/pygments.css" type="text/css" />
<link rel="stylesheet" href="_static/css/theme.css" type="text/css" />
<link rel="stylesheet" href="_static/copybutton.css" type="text/css" />
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/katex.min.css" type="text/css" />
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/katex.min.css" type="text/css" />
<link rel="stylesheet" href="_static/katex-math.css" type="text/css" />
<link rel="stylesheet" href="_static/sphinx-dropdown.css" type="text/css" />
<link rel="stylesheet" href="_static/panels-bootstrap.min.css" type="text/css" />
<link rel="stylesheet" href="_static/css/jit.css" type="text/css" />
<link rel="index" title="Index" href="genindex.html" />
<link rel="search" title="Search" href="search.html" />
<link rel="next" title="torch.compiler" href="torch.compiler.html" />
<link rel="prev" title="Distributed Checkpoint - torch.distributed.checkpoint" href="distributed.checkpoint.html" />
<!-- Google Tag Manager -->
<script>(function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':
new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],
j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src=
'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);
})(window,document,'script','dataLayer','GTM-T8XT4PS');</script>
<!-- End Google Tag Manager -->
<script src="_static/js/modernizr.min.js"></script>
<!-- Preload the theme fonts -->
<link rel="preload" href="_static/fonts/FreightSans/freight-sans-book.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="_static/fonts/FreightSans/freight-sans-medium.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="_static/fonts/IBMPlexMono/IBMPlexMono-Medium.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="_static/fonts/FreightSans/freight-sans-bold.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="_static/fonts/FreightSans/freight-sans-medium-italic.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="_static/fonts/IBMPlexMono/IBMPlexMono-SemiBold.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<!-- Preload the katex fonts -->
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Math-Italic.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Main-Regular.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Main-Bold.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Size1-Regular.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Size4-Regular.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Size2-Regular.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Size3-Regular.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="preload" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/fonts/KaTeX_Caligraphic-Regular.woff2" as="font" type="font/woff2" crossorigin="anonymous">
<link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.15.2/css/all.css" integrity="sha384-vSIIfh2YWi9wW0r9iZe7RJPrKwp6bG+s9QZMoITbCckVJqGCCRhc+ccxNcdpHuYu" crossorigin="anonymous">
</head>
<div class="container-fluid header-holder tutorials-header" id="header-holder">
<div class="container">
<div class="header-container">
<a class="header-logo" href="https://pytorch.org/" aria-label="PyTorch"></a>
<div class="main-menu">
<ul>
<li>
<a href="https://pytorch.org/get-started">Get Started</a>
</li>
<li>
<a href="https://pytorch.org/ecosystem">Ecosystem</a>
</li>
<li>
<div id="resourcesDropdownButton" data-toggle="resources-dropdown" class="resources-dropdown">
<a class="resource-option with-down-arrow">
Edge
</a>
<div class="resources-dropdown-menu">
<a class="nav-dropdown-item" href="https://pytorch.org/edge">
<span class="dropdown-title">About PyTorch Edge</span>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/executorch">
<span class="dropdown-title">ExecuTorch</span>
</a>
</div>
</div>
</li>
<li>
<a href="https://pytorch.org/blog/">Blog</a>
</li>
<li>
<a href="https://pytorch.org/tutorials">Tutorials</a>
</li>
<li class="active docs-active">
<div id="resourcesDropdownButton" data-toggle="resources-dropdown" class="resources-dropdown">
<a class="resource-option with-down-orange-arrow">
Docs
</a>
<div class="resources-dropdown-menu">
<a class="doc-dropdown-option nav-dropdown-item" href="https://pytorch.org/docs/stable/index.html">
<span class="dropdown-title">PyTorch</span>
<p></p>
</a>
<a class="doc-dropdown-option nav-dropdown-item" href="https://pytorch.org/audio/stable/index.html">
<span class="dropdown-title">torchaudio</span>
<p></p>
</a>
<a class="doc-dropdown-option nav-dropdown-item" href="https://pytorch.org/text/stable/index.html">
<span class="dropdown-title">torchtext</span>
<p></p>
</a>
<a class="doc-dropdown-option nav-dropdown-item" href="https://pytorch.org/vision/stable/index.html">
<span class="dropdown-title">torchvision</span>
<p></p>
</a>
<a class="doc-dropdown-option nav-dropdown-item" href="https://pytorch.org/torcharrow">
<span class="dropdown-title">torcharrow</span>
<p></p>
</a>
<a class="doc-dropdown-option nav-dropdown-item" href="https://pytorch.org/data">
<span class="dropdown-title">TorchData</span>
<p></p>
</a>
<a class="doc-dropdown-option nav-dropdown-item" href="https://pytorch.org/torchrec">
<span class="dropdown-title">TorchRec</span>
<p></p>
</a>
<a class="doc-dropdown-option nav-dropdown-item" href="https://pytorch.org/serve/">
<span class="dropdown-title">TorchServe</span>
<p></p>
</a>
<a class="doc-dropdown-option nav-dropdown-item" href="https://pytorch.org/torchx/">
<span class="dropdown-title">TorchX</span>
<p></p>
</a>
<a class="doc-dropdown-option nav-dropdown-item" href="https://pytorch.org/xla">
<span class="dropdown-title">PyTorch on XLA Devices</span>
<p></p>
</a>
</div>
</li>
<li>
<div id="resourcesDropdownButton" data-toggle="resources-dropdown" class="resources-dropdown">
<a class="resource-option with-down-arrow">
Resources
</a>
<div class="resources-dropdown-menu">
<a class="nav-dropdown-item" href="https://pytorch.org/features">
<span class="dropdown-title">About</span>
<p>Learn about PyTorch’s features and capabilities</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/foundation">
<span class="dropdown-title">PyTorch Foundation</span>
<p>Learn about the PyTorch foundation</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/#community-module">
<span class="dropdown-title">Community</span>
<p>Join the PyTorch developer community to contribute, learn, and get your questions answered.</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/community-stories">
<span class="dropdown-title">Community Stories</span>
<p>Learn how our community solves real, everyday machine learning problems with PyTorch.</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/resources">
<span class="dropdown-title">Developer Resources</span>
<p>Find resources and get questions answered</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/events">
<span class="dropdown-title">Events</span>
<p>Find events, webinars, and podcasts</p>
</a>
<a class="nav-dropdown-item" href="https://discuss.pytorch.org/" target="_blank">
<span class="dropdown-title">Forums</span>
<p>A place to discuss PyTorch code, issues, install, research</p>
</a>
<a class="nav-dropdown-item" href="https://pytorch.org/hub">
<span class="dropdown-title">Models (Beta)</span>
<p>Discover, publish, and reuse pre-trained models</p>
</a>
</div>
</div>
</li>
<li>
<a href="https://github.com/pytorch/pytorch">GitHub</a>
</li>
</ul>
</div>
<a class="main-menu-open-button" href="#" data-behavior="open-mobile-menu"></a>
</div>
</div>
</div>
<body class="pytorch-body">
<div class="table-of-contents-link-wrapper">
<span>Table of Contents</span>
<a href="#" class="toggle-table-of-contents" data-behavior="toggle-table-of-contents"></a>
</div>
<nav data-toggle="wy-nav-shift" class="pytorch-left-menu" id="pytorch-left-menu">
<div class="pytorch-side-scroll">
<div class="pytorch-menu pytorch-menu-vertical" data-spy="affix" role="navigation" aria-label="main navigation">
<div class="pytorch-left-menu-search">
<div class="version">
<a href='https://pytorch.org/docs/versions.html'>2.2 ▼</a>
</div>
<div role="search">
<form id="rtd-search-form" class="wy-form" action="search.html" method="get">
<input type="text" name="q" placeholder="Search Docs" />
<input type="hidden" name="check_keywords" value="yes" />
<input type="hidden" name="area" value="default" />
</form>
</div>
</div>
<p class="caption" role="heading"><span class="caption-text">Community</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="community/build_ci_governance.html">PyTorch Governance | Build + CI</a></li>
<li class="toctree-l1"><a class="reference internal" href="community/contribution_guide.html">PyTorch Contribution Guide</a></li>
<li class="toctree-l1"><a class="reference internal" href="community/design.html">PyTorch Design Philosophy</a></li>
<li class="toctree-l1"><a class="reference internal" href="community/governance.html">PyTorch Governance | Mechanics</a></li>
<li class="toctree-l1"><a class="reference internal" href="community/persons_of_interest.html">PyTorch Governance | Maintainers</a></li>
</ul>
<p class="caption" role="heading"><span class="caption-text">Developer Notes</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="notes/amp_examples.html">CUDA Automatic Mixed Precision examples</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/autograd.html">Autograd mechanics</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/broadcasting.html">Broadcasting semantics</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/cpu_threading_torchscript_inference.html">CPU threading and TorchScript inference</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/cuda.html">CUDA semantics</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/ddp.html">Distributed Data Parallel</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/extending.html">Extending PyTorch</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/extending.func.html">Extending torch.func with autograd.Function</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/faq.html">Frequently Asked Questions</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/gradcheck.html">Gradcheck mechanics</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/hip.html">HIP (ROCm) semantics</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/large_scale_deployments.html">Features for large-scale deployments</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/modules.html">Modules</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/mps.html">MPS backend</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/multiprocessing.html">Multiprocessing best practices</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/numerical_accuracy.html">Numerical accuracy</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/randomness.html">Reproducibility</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/serialization.html">Serialization semantics</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes/windows.html">Windows FAQ</a></li>
</ul>
<p class="caption" role="heading"><span class="caption-text">Language Bindings</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="cpp_index.html">C++</a></li>
<li class="toctree-l1"><a class="reference external" href="https://pytorch.org/javadoc/">Javadoc</a></li>
<li class="toctree-l1"><a class="reference internal" href="deploy.html">torch::deploy</a></li>
</ul>
<p class="caption" role="heading"><span class="caption-text">Python API</span></p>
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="torch.html">torch</a></li>
<li class="toctree-l1"><a class="reference internal" href="nn.html">torch.nn</a></li>
<li class="toctree-l1"><a class="reference internal" href="nn.functional.html">torch.nn.functional</a></li>
<li class="toctree-l1"><a class="reference internal" href="tensors.html">torch.Tensor</a></li>
<li class="toctree-l1"><a class="reference internal" href="tensor_attributes.html">Tensor Attributes</a></li>
<li class="toctree-l1"><a class="reference internal" href="tensor_view.html">Tensor Views</a></li>
<li class="toctree-l1"><a class="reference internal" href="amp.html">torch.amp</a></li>
<li class="toctree-l1"><a class="reference internal" href="autograd.html">torch.autograd</a></li>
<li class="toctree-l1"><a class="reference internal" href="library.html">torch.library</a></li>
<li class="toctree-l1"><a class="reference internal" href="cpu.html">torch.cpu</a></li>
<li class="toctree-l1"><a class="reference internal" href="cuda.html">torch.cuda</a></li>
<li class="toctree-l1"><a class="reference internal" href="torch_cuda_memory.html">Understanding CUDA Memory Usage</a></li>
<li class="toctree-l1"><a class="reference internal" href="torch_cuda_memory.html#generating-a-snapshot">Generating a Snapshot</a></li>
<li class="toctree-l1"><a class="reference internal" href="torch_cuda_memory.html#using-the-visualizer">Using the visualizer</a></li>
<li class="toctree-l1"><a class="reference internal" href="torch_cuda_memory.html#snapshot-api-reference">Snapshot API Reference</a></li>
<li class="toctree-l1"><a class="reference internal" href="mps.html">torch.mps</a></li>
<li class="toctree-l1"><a class="reference internal" href="backends.html">torch.backends</a></li>
<li class="toctree-l1"><a class="reference internal" href="export.html">torch.export</a></li>
<li class="toctree-l1"><a class="reference internal" href="distributed.html">torch.distributed</a></li>
<li class="toctree-l1"><a class="reference internal" href="distributed.algorithms.join.html">torch.distributed.algorithms.join</a></li>
<li class="toctree-l1"><a class="reference internal" href="distributed.elastic.html">torch.distributed.elastic</a></li>
<li class="toctree-l1"><a class="reference internal" href="fsdp.html">torch.distributed.fsdp</a></li>
<li class="toctree-l1"><a class="reference internal" href="distributed.optim.html">torch.distributed.optim</a></li>
<li class="toctree-l1"><a class="reference internal" href="distributed.tensor.parallel.html">torch.distributed.tensor.parallel</a></li>
<li class="toctree-l1"><a class="reference internal" href="distributed.checkpoint.html">torch.distributed.checkpoint</a></li>
<li class="toctree-l1 current"><a class="current reference internal" href="#">torch.distributions</a></li>
<li class="toctree-l1"><a class="reference internal" href="torch.compiler.html">torch.compiler</a></li>
<li class="toctree-l1"><a class="reference internal" href="fft.html">torch.fft</a></li>
<li class="toctree-l1"><a class="reference internal" href="func.html">torch.func</a></li>
<li class="toctree-l1"><a class="reference internal" href="futures.html">torch.futures</a></li>
<li class="toctree-l1"><a class="reference internal" href="fx.html">torch.fx</a></li>
<li class="toctree-l1"><a class="reference internal" href="hub.html">torch.hub</a></li>
<li class="toctree-l1"><a class="reference internal" href="jit.html">torch.jit</a></li>
<li class="toctree-l1"><a class="reference internal" href="linalg.html">torch.linalg</a></li>
<li class="toctree-l1"><a class="reference internal" href="monitor.html">torch.monitor</a></li>
<li class="toctree-l1"><a class="reference internal" href="signal.html">torch.signal</a></li>
<li class="toctree-l1"><a class="reference internal" href="special.html">torch.special</a></li>
<li class="toctree-l1"><a class="reference internal" href="torch.overrides.html">torch.overrides</a></li>
<li class="toctree-l1"><a class="reference internal" href="package.html">torch.package</a></li>
<li class="toctree-l1"><a class="reference internal" href="profiler.html">torch.profiler</a></li>
<li class="toctree-l1"><a class="reference internal" href="nn.init.html">torch.nn.init</a></li>
<li class="toctree-l1"><a class="reference internal" href="onnx.html">torch.onnx</a></li>
<li class="toctree-l1"><a class="reference internal" href="optim.html">torch.optim</a></li>
<li class="toctree-l1"><a class="reference internal" href="complex_numbers.html">Complex Numbers</a></li>
<li class="toctree-l1"><a class="reference internal" href="ddp_comm_hooks.html">DDP Communication Hooks</a></li>
<li class="toctree-l1"><a class="reference internal" href="pipeline.html">Pipeline Parallelism</a></li>
<li class="toctree-l1"><a class="reference internal" href="quantization.html">Quantization</a></li>
<li class="toctree-l1"><a class="reference internal" href="rpc.html">Distributed RPC Framework</a></li>
<li class="toctree-l1"><a class="reference internal" href="random.html">torch.random</a></li>
<li class="toctree-l1"><a class="reference internal" href="masked.html">torch.masked</a></li>
<li class="toctree-l1"><a class="reference internal" href="nested.html">torch.nested</a></li>
<li class="toctree-l1"><a class="reference internal" href="sparse.html">torch.sparse</a></li>
<li class="toctree-l1"><a class="reference internal" href="storage.html">torch.Storage</a></li>
<li class="toctree-l1"><a class="reference internal" href="testing.html">torch.testing</a></li>
<li class="toctree-l1"><a class="reference internal" href="utils.html">torch.utils</a></li>
<li class="toctree-l1"><a class="reference internal" href="benchmark_utils.html">torch.utils.benchmark</a></li>
<li class="toctree-l1"><a class="reference internal" href="bottleneck.html">torch.utils.bottleneck</a></li>
<li class="toctree-l1"><a class="reference internal" href="checkpoint.html">torch.utils.checkpoint</a></li>
<li class="toctree-l1"><a class="reference internal" href="cpp_extension.html">torch.utils.cpp_extension</a></li>
<li class="toctree-l1"><a class="reference internal" href="data.html">torch.utils.data</a></li>
<li class="toctree-l1"><a class="reference internal" href="deterministic.html">torch.utils.deterministic</a></li>
<li class="toctree-l1"><a class="reference internal" href="jit_utils.html">torch.utils.jit</a></li>
<li class="toctree-l1"><a class="reference internal" href="dlpack.html">torch.utils.dlpack</a></li>
<li class="toctree-l1"><a class="reference internal" href="mobile_optimizer.html">torch.utils.mobile_optimizer</a></li>
<li class="toctree-l1"><a class="reference internal" href="model_zoo.html">torch.utils.model_zoo</a></li>
<li class="toctree-l1"><a class="reference internal" href="tensorboard.html">torch.utils.tensorboard</a></li>
<li class="toctree-l1"><a class="reference internal" href="type_info.html">Type Info</a></li>
<li class="toctree-l1"><a class="reference internal" href="named_tensor.html">Named Tensors</a></li>
<li class="toctree-l1"><a class="reference internal" href="name_inference.html">Named Tensors operator coverage</a></li>
<li class="toctree-l1"><a class="reference internal" href="config_mod.html">torch.__config__</a></li>
<li class="toctree-l1"><a class="reference internal" href="logging.html">torch._logging</a></li>
</ul>
<p class="caption" role="heading"><span class="caption-text">Libraries</span></p>
<ul>
<li class="toctree-l1"><a class="reference external" href="https://pytorch.org/audio/stable">torchaudio</a></li>
<li class="toctree-l1"><a class="reference external" href="https://pytorch.org/data">TorchData</a></li>
<li class="toctree-l1"><a class="reference external" href="https://pytorch.org/torchrec">TorchRec</a></li>
<li class="toctree-l1"><a class="reference external" href="https://pytorch.org/serve">TorchServe</a></li>
<li class="toctree-l1"><a class="reference external" href="https://pytorch.org/text/stable">torchtext</a></li>
<li class="toctree-l1"><a class="reference external" href="https://pytorch.org/vision/stable">torchvision</a></li>
<li class="toctree-l1"><a class="reference external" href="https://pytorch.org/xla/">PyTorch on XLA Devices</a></li>
</ul>
</div>
</div>
</nav>
<div class="pytorch-container">
<div class="pytorch-page-level-bar" id="pytorch-page-level-bar">
<div class="pytorch-breadcrumbs-wrapper">
<div role="navigation" aria-label="breadcrumbs navigation">
<ul class="pytorch-breadcrumbs">
<li>
<a href="index.html">
Docs
</a> >
</li>
<li>Probability distributions - torch.distributions</li>
<li class="pytorch-breadcrumbs-aside">
<a href="_sources/distributions.rst.txt" rel="nofollow"><img src="_static/images/view-page-source-icon.svg"></a>
</li>
</ul>
</div>
</div>
<div class="pytorch-shortcuts-wrapper" id="pytorch-shortcuts-wrapper">
Shortcuts
</div>
</div>
<section data-toggle="wy-nav-shift" id="pytorch-content-wrap" class="pytorch-content-wrap">
<div class="pytorch-content-left">
<!-- Google Tag Manager (noscript) -->
<noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-T8XT4PS"
height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
<!-- End Google Tag Manager (noscript) -->
<div class="rst-content">
<div role="main" class="main-content" itemscope="itemscope" itemtype="http://schema.org/Article">
<article itemprop="articleBody" id="pytorch-article" class="pytorch-article">
<div class="section" id="module-torch.distributions">
<span id="probability-distributions-torch-distributions"></span><h1>Probability distributions - torch.distributions<a class="headerlink" href="#module-torch.distributions" title="Permalink to this heading">¶</a></h1>
<p>The <code class="docutils literal notranslate"><span class="pre">distributions</span></code> package contains parameterizable probability distributions
and sampling functions. This allows the construction of stochastic computation
graphs and stochastic gradient estimators for optimization. This package
generally follows the design of the <a class="reference external" href="https://arxiv.org/abs/1711.10604">TensorFlow Distributions</a> package.</p>
<p>It is not possible to directly backpropagate through random samples. However,
there are two main methods for creating surrogate functions that can be
backpropagated through. These are the score function estimator/likelihood ratio
estimator/REINFORCE and the pathwise derivative estimator. REINFORCE is commonly
seen as the basis for policy gradient methods in reinforcement learning, and the
pathwise derivative estimator is commonly seen in the reparameterization trick
in variational autoencoders. Whilst the score function only requires the value
of samples <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">f(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></span>, the pathwise derivative requires the derivative
<span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>f</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">f'(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0019em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></span>. The next sections discuss these two in a reinforcement learning
example. For more details see
<a class="reference external" href="https://arxiv.org/abs/1506.05254">Gradient Estimation Using Stochastic Computation Graphs</a> .</p>
<div class="section" id="score-function">
<h2>Score function<a class="headerlink" href="#score-function" title="Permalink to this heading">¶</a></h2>
<p>When the probability density function is differentiable with respect to its
parameters, we only need <code class="xref py py-meth docutils literal notranslate"><span class="pre">sample()</span></code> and
<code class="xref py py-meth docutils literal notranslate"><span class="pre">log_prob()</span></code> to implement REINFORCE:</p>
<div class="math">
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>θ</mi><mo>=</mo><mi>α</mi><mi>r</mi><mfrac><mrow><mi mathvariant="normal">∂</mi><mi>log</mi><mo></mo><mi>p</mi><mo stretchy="false">(</mo><mi>a</mi><mi mathvariant="normal">∣</mi><msup><mi>π</mi><mi>θ</mi></msup><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="normal">∂</mi><mi>θ</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\Delta\theta = \alpha r \frac{\partial\log p(a|\pi^\theta(s))}{\partial\theta}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">Δ</span><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.2121em;vertical-align:-0.686em;"></span><span class="mord mathnormal" style="margin-right:0.0037em;">α</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5261em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord" style="margin-right:0.05556em;">∂</span><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord" style="margin-right:0.05556em;">∂</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mord">∣</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">s</span><span class="mclose">))</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>where <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>θ</mi></mrow><annotation encoding="application/x-tex">\theta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span></span></span></span></span> are the parameters, <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>α</mi></mrow><annotation encoding="application/x-tex">\alpha</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.0037em;">α</span></span></span></span></span> is the learning rate,
<span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi></mrow><annotation encoding="application/x-tex">r</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span></span></span></span></span> is the reward and <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo stretchy="false">(</mo><mi>a</mi><mi mathvariant="normal">∣</mi><msup><mi>π</mi><mi>θ</mi></msup><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">p(a|\pi^\theta(s))</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0991em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mord">∣</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">s</span><span class="mclose">))</span></span></span></span></span> is the probability of
taking action <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi></mrow><annotation encoding="application/x-tex">a</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">a</span></span></span></span></span> in state <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>s</mi></mrow><annotation encoding="application/x-tex">s</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">s</span></span></span></span></span> given policy <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>π</mi><mi>θ</mi></msup></mrow><annotation encoding="application/x-tex">\pi^\theta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8491em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span></span></span></span></span></span></span></span></span></span></span></span>.</p>
<p>In practice we would sample an action from the output of a network, apply this
action in an environment, and then use <code class="docutils literal notranslate"><span class="pre">log_prob</span></code> to construct an equivalent
loss function. Note that we use a negative because optimizers use gradient
descent, whilst the rule above assumes gradient ascent. With a categorical
policy, the code for implementing REINFORCE would be as follows:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">probs</span> <span class="o">=</span> <span class="n">policy_network</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
<span class="c1"># Note that this is equivalent to what used to be called multinomial</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">Categorical</span><span class="p">(</span><span class="n">probs</span><span class="p">)</span>
<span class="n">action</span> <span class="o">=</span> <span class="n">m</span><span class="o">.</span><span class="n">sample</span><span class="p">()</span>
<span class="n">next_state</span><span class="p">,</span> <span class="n">reward</span> <span class="o">=</span> <span class="n">env</span><span class="o">.</span><span class="n">step</span><span class="p">(</span><span class="n">action</span><span class="p">)</span>
<span class="n">loss</span> <span class="o">=</span> <span class="o">-</span><span class="n">m</span><span class="o">.</span><span class="n">log_prob</span><span class="p">(</span><span class="n">action</span><span class="p">)</span> <span class="o">*</span> <span class="n">reward</span>
<span class="n">loss</span><span class="o">.</span><span class="n">backward</span><span class="p">()</span>
</pre></div>
</div>
</div>
<div class="section" id="pathwise-derivative">
<h2>Pathwise derivative<a class="headerlink" href="#pathwise-derivative" title="Permalink to this heading">¶</a></h2>
<p>The other way to implement these stochastic/policy gradients would be to use the
reparameterization trick from the
<code class="xref py py-meth docutils literal notranslate"><span class="pre">rsample()</span></code> method, where the
parameterized random variable can be constructed via a parameterized
deterministic function of a parameter-free random variable. The reparameterized
sample therefore becomes differentiable. The code for implementing the pathwise
derivative would be as follows:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">params</span> <span class="o">=</span> <span class="n">policy_network</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">Normal</span><span class="p">(</span><span class="o">*</span><span class="n">params</span><span class="p">)</span>
<span class="c1"># Any distribution with .has_rsample == True could work based on the application</span>
<span class="n">action</span> <span class="o">=</span> <span class="n">m</span><span class="o">.</span><span class="n">rsample</span><span class="p">()</span>
<span class="n">next_state</span><span class="p">,</span> <span class="n">reward</span> <span class="o">=</span> <span class="n">env</span><span class="o">.</span><span class="n">step</span><span class="p">(</span><span class="n">action</span><span class="p">)</span> <span class="c1"># Assuming that reward is differentiable</span>
<span class="n">loss</span> <span class="o">=</span> <span class="o">-</span><span class="n">reward</span>
<span class="n">loss</span><span class="o">.</span><span class="n">backward</span><span class="p">()</span>
</pre></div>
</div>
</div>
<div class="section" id="distribution">
<h2><span class="hidden-section">Distribution</span><a class="headerlink" href="#distribution" title="Permalink to this heading">¶</a></h2>
<dl class="py class">
<dt class="sig sig-object py" id="torch.distributions.distribution.Distribution">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">torch.distributions.distribution.</span></span><span class="sig-name descname"><span class="pre">Distribution</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">batch_shape</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">torch.Size([])</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">event_shape</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">torch.Size([])</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">validate_args</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/distribution.html#Distribution"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.distribution.Distribution" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a></p>
<p>Distribution is the abstract base class for probability distributions.</p>
<dl class="field-list simple">
</dl>
<dl class="py property">
<dt class="sig sig-object py" id="torch.distributions.distribution.Distribution.arg_constraints">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">arg_constraints</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Dict" title="(in Python v3.12)"><span class="pre">Dict</span></a><span class="p"><span class="pre">[</span></span><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.12)"><span class="pre">str</span></a><span class="p"><span class="pre">,</span></span><span class="w"> </span><a class="reference internal" href="#torch.distributions.constraints.Constraint" title="torch.distributions.constraints.Constraint"><span class="pre">Constraint</span></a><span class="p"><span class="pre">]</span></span></em><a class="headerlink" href="#torch.distributions.distribution.Distribution.arg_constraints" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a dictionary from argument names to
<a class="reference internal" href="#torch.distributions.constraints.Constraint" title="torch.distributions.constraints.Constraint"><code class="xref py py-class docutils literal notranslate"><span class="pre">Constraint</span></code></a> objects that
should be satisfied by each argument of this distribution. Args that
are not tensors need not appear in this dict.</p>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="torch.distributions.distribution.Distribution.batch_shape">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">batch_shape</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">Size</span></em><a class="headerlink" href="#torch.distributions.distribution.Distribution.batch_shape" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the shape over which parameters are batched.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="torch.distributions.distribution.Distribution.cdf">
<span class="sig-name descname"><span class="pre">cdf</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">value</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/distribution.html#Distribution.cdf"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.distribution.Distribution.cdf" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the cumulative density/mass function evaluated at
<cite>value</cite>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>value</strong> (<a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – </p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p><a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="torch.distributions.distribution.Distribution.entropy">
<span class="sig-name descname"><span class="pre">entropy</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/distribution.html#Distribution.entropy"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.distribution.Distribution.entropy" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns entropy of distribution, batched over batch_shape.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>Tensor of shape batch_shape.</p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p><a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="torch.distributions.distribution.Distribution.enumerate_support">
<span class="sig-name descname"><span class="pre">enumerate_support</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">expand</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/distribution.html#Distribution.enumerate_support"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.distribution.Distribution.enumerate_support" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns tensor containing all values supported by a discrete
distribution. The result will enumerate over dimension 0, so the shape
of the result will be <cite>(cardinality,) + batch_shape + event_shape</cite>
(where <cite>event_shape = ()</cite> for univariate distributions).</p>
<p>Note that this enumerates over all batched tensors in lock-step
<cite>[[0, 0], [1, 1], …]</cite>. With <cite>expand=False</cite>, enumeration happens
along dim 0, but with the remaining batch dimensions being
singleton dimensions, <cite>[[0], [1], ..</cite>.</p>
<p>To iterate over the full Cartesian product use
<cite>itertools.product(m.enumerate_support())</cite>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>expand</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.12)"><em>bool</em></a>) – whether to expand the support over the
batch dims to match the distribution’s <cite>batch_shape</cite>.</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>Tensor iterating over dimension 0.</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p><a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="torch.distributions.distribution.Distribution.event_shape">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">event_shape</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">Size</span></em><a class="headerlink" href="#torch.distributions.distribution.Distribution.event_shape" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the shape of a single sample (without batching).</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="torch.distributions.distribution.Distribution.expand">
<span class="sig-name descname"><span class="pre">expand</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">batch_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">_instance</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/distribution.html#Distribution.expand"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.distribution.Distribution.expand" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a new distribution instance (or populates an existing instance
provided by a derived class) with batch dimensions expanded to
<cite>batch_shape</cite>. This method calls <a class="reference internal" href="generated/torch.Tensor.expand.html#torch.Tensor.expand" title="torch.Tensor.expand"><code class="xref py py-class docutils literal notranslate"><span class="pre">expand</span></code></a> on
the distribution’s parameters. As such, this does not allocate new
memory for the expanded distribution instance. Additionally,
this does not repeat any args checking or parameter broadcasting in
<cite>__init__.py</cite>, when an instance is first created.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>batch_shape</strong> (<em>torch.Size</em>) – the desired expanded size.</p></li>
<li><p><strong>_instance</strong> – new instance provided by subclasses that
need to override <cite>.expand</cite>.</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>New distribution instance with batch dimensions expanded to
<cite>batch_size</cite>.</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="torch.distributions.distribution.Distribution.icdf">
<span class="sig-name descname"><span class="pre">icdf</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">value</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/distribution.html#Distribution.icdf"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.distribution.Distribution.icdf" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the inverse cumulative density/mass function evaluated at
<cite>value</cite>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>value</strong> (<a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – </p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p><a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="torch.distributions.distribution.Distribution.log_prob">
<span class="sig-name descname"><span class="pre">log_prob</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">value</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/distribution.html#Distribution.log_prob"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.distribution.Distribution.log_prob" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the log of the probability density/mass function evaluated at
<cite>value</cite>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>value</strong> (<a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – </p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p><a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="torch.distributions.distribution.Distribution.mean">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">mean</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><span class="pre">Tensor</span></a></em><a class="headerlink" href="#torch.distributions.distribution.Distribution.mean" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the mean of the distribution.</p>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="torch.distributions.distribution.Distribution.mode">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">mode</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><span class="pre">Tensor</span></a></em><a class="headerlink" href="#torch.distributions.distribution.Distribution.mode" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the mode of the distribution.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="torch.distributions.distribution.Distribution.perplexity">
<span class="sig-name descname"><span class="pre">perplexity</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/distribution.html#Distribution.perplexity"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.distribution.Distribution.perplexity" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns perplexity of distribution, batched over batch_shape.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>Tensor of shape batch_shape.</p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p><a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="torch.distributions.distribution.Distribution.rsample">
<span class="sig-name descname"><span class="pre">rsample</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sample_shape</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">torch.Size([])</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/distribution.html#Distribution.rsample"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.distribution.Distribution.rsample" title="Permalink to this definition">¶</a></dt>
<dd><p>Generates a sample_shape shaped reparameterized sample or sample_shape
shaped batch of reparameterized samples if the distribution parameters
are batched.</p>
<dl class="field-list simple">
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p><a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="torch.distributions.distribution.Distribution.sample">
<span class="sig-name descname"><span class="pre">sample</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sample_shape</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">torch.Size([])</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/distribution.html#Distribution.sample"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.distribution.Distribution.sample" title="Permalink to this definition">¶</a></dt>
<dd><p>Generates a sample_shape shaped sample or sample_shape shaped batch of
samples if the distribution parameters are batched.</p>
<dl class="field-list simple">
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p><a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="torch.distributions.distribution.Distribution.sample_n">
<span class="sig-name descname"><span class="pre">sample_n</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/distribution.html#Distribution.sample_n"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.distribution.Distribution.sample_n" title="Permalink to this definition">¶</a></dt>
<dd><p>Generates n samples or n batches of samples if the distribution
parameters are batched.</p>
<dl class="field-list simple">
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p><a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="torch.distributions.distribution.Distribution.set_default_validate_args">
<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">set_default_validate_args</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">value</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/distribution.html#Distribution.set_default_validate_args"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.distribution.Distribution.set_default_validate_args" title="Permalink to this definition">¶</a></dt>
<dd><p>Sets whether validation is enabled or disabled.</p>
<p>The default behavior mimics Python’s <code class="docutils literal notranslate"><span class="pre">assert</span></code> statement: validation
is on by default, but is disabled if Python is run in optimized mode
(via <code class="docutils literal notranslate"><span class="pre">python</span> <span class="pre">-O</span></code>). Validation may be expensive, so you may want to
disable it once a model is working.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>value</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.12)"><em>bool</em></a>) – Whether to enable validation.</p>
</dd>
</dl>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="torch.distributions.distribution.Distribution.stddev">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">stddev</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><span class="pre">Tensor</span></a></em><a class="headerlink" href="#torch.distributions.distribution.Distribution.stddev" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the standard deviation of the distribution.</p>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="torch.distributions.distribution.Distribution.support">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">support</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Optional" title="(in Python v3.12)"><span class="pre">Optional</span></a><span class="p"><span class="pre">[</span></span><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.12)"><span class="pre">Any</span></a><span class="p"><span class="pre">]</span></span></em><a class="headerlink" href="#torch.distributions.distribution.Distribution.support" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a <a class="reference internal" href="#torch.distributions.constraints.Constraint" title="torch.distributions.constraints.Constraint"><code class="xref py py-class docutils literal notranslate"><span class="pre">Constraint</span></code></a> object
representing this distribution’s support.</p>
</dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="torch.distributions.distribution.Distribution.variance">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">variance</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><span class="pre">Tensor</span></a></em><a class="headerlink" href="#torch.distributions.distribution.Distribution.variance" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the variance of the distribution.</p>
</dd></dl>
</dd></dl>
</div>
<div class="section" id="exponentialfamily">
<h2><span class="hidden-section">ExponentialFamily</span><a class="headerlink" href="#exponentialfamily" title="Permalink to this heading">¶</a></h2>
<dl class="py class">
<dt class="sig sig-object py" id="torch.distributions.exp_family.ExponentialFamily">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">torch.distributions.exp_family.</span></span><span class="sig-name descname"><span class="pre">ExponentialFamily</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">batch_shape</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">torch.Size([])</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">event_shape</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">torch.Size([])</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">validate_args</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/exp_family.html#ExponentialFamily"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.exp_family.ExponentialFamily" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference internal" href="#torch.distributions.distribution.Distribution" title="torch.distributions.distribution.Distribution"><code class="xref py py-class docutils literal notranslate"><span class="pre">Distribution</span></code></a></p>
<p>ExponentialFamily is the abstract base class for probability distributions belonging to an
exponential family, whose probability mass/density function has the form is defined below</p>
<div class="math">
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>p</mi><mi>F</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">;</mo><mi>θ</mi><mo stretchy="false">)</mo><mo>=</mo><mi>exp</mi><mo></mo><mo stretchy="false">(</mo><mo stretchy="false">⟨</mo><mi>t</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo separator="true">,</mo><mi>θ</mi><mo stretchy="false">⟩</mo><mo>−</mo><mi>F</mi><mo stretchy="false">(</mo><mi>θ</mi><mo stretchy="false">)</mo><mo>+</mo><mi>k</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">p_{F}(x; \theta) = \exp(\langle t(x), \theta\rangle - F(\theta) + k(x))</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">F</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">exp</span><span class="mopen">(⟨</span><span class="mord mathnormal">t</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span><span class="mclose">⟩</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">))</span></span></span></span></span></div><p>where <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>θ</mi></mrow><annotation encoding="application/x-tex">\theta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span></span></span></span></span> denotes the natural parameters, <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">t(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">t</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></span> denotes the sufficient statistic,
<span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>θ</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F(\theta)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span><span class="mclose">)</span></span></span></span></span> is the log normalizer function for a given family and <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">k(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></span> is the carrier
measure.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>This class is an intermediary between the <cite>Distribution</cite> class and distributions which belong
to an exponential family mainly to check the correctness of the <cite>.entropy()</cite> and analytic KL
divergence methods. We use this class to compute the entropy and KL divergence using the AD
framework and Bregman divergences (courtesy of: Frank Nielsen and Richard Nock, Entropies and
Cross-entropies of Exponential Families).</p>
</div>
<dl class="field-list simple">
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="torch.distributions.exp_family.ExponentialFamily.entropy">
<span class="sig-name descname"><span class="pre">entropy</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/exp_family.html#ExponentialFamily.entropy"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.exp_family.ExponentialFamily.entropy" title="Permalink to this definition">¶</a></dt>
<dd><p>Method to compute the entropy using Bregman divergence of the log normalizer.</p>
</dd></dl>
</dd></dl>
</div>
<div class="section" id="bernoulli">
<h2><span class="hidden-section">Bernoulli</span><a class="headerlink" href="#bernoulli" title="Permalink to this heading">¶</a></h2>
<dl class="py class">
<dt class="sig sig-object py" id="torch.distributions.bernoulli.Bernoulli">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">torch.distributions.bernoulli.</span></span><span class="sig-name descname"><span class="pre">Bernoulli</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">probs</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">logits</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">validate_args</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/bernoulli.html#Bernoulli"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.bernoulli.Bernoulli" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference internal" href="#torch.distributions.exp_family.ExponentialFamily" title="torch.distributions.exp_family.ExponentialFamily"><code class="xref py py-class docutils literal notranslate"><span class="pre">ExponentialFamily</span></code></a></p>
<p>Creates a Bernoulli distribution parameterized by <a class="reference internal" href="#torch.distributions.bernoulli.Bernoulli.probs" title="torch.distributions.bernoulli.Bernoulli.probs"><code class="xref py py-attr docutils literal notranslate"><span class="pre">probs</span></code></a>
or <a class="reference internal" href="#torch.distributions.bernoulli.Bernoulli.logits" title="torch.distributions.bernoulli.Bernoulli.logits"><code class="xref py py-attr docutils literal notranslate"><span class="pre">logits</span></code></a> (but not both).</p>
<p>Samples are binary (0 or 1). They take the value <cite>1</cite> with probability <cite>p</cite>
and <cite>0</cite> with probability <cite>1 - p</cite>.</p>
<p>Example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">m</span> <span class="o">=</span> <span class="n">Bernoulli</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">tensor</span><span class="p">([</span><span class="mf">0.3</span><span class="p">]))</span>
<span class="gp">>>> </span><span class="n">m</span><span class="o">.</span><span class="n">sample</span><span class="p">()</span> <span class="c1"># 30% chance 1; 70% chance 0</span>
<span class="go">tensor([ 0.])</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>probs</strong> (<em>Number</em><em>, </em><a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – the probability of sampling <cite>1</cite></p></li>
<li><p><strong>logits</strong> (<em>Number</em><em>, </em><a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – the log-odds of sampling <cite>1</cite></p></li>
</ul>
</dd>
</dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="torch.distributions.bernoulli.Bernoulli.arg_constraints">
<span class="sig-name descname"><span class="pre">arg_constraints</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">{'logits':</span> <span class="pre">Real(),</span> <span class="pre">'probs':</span> <span class="pre">Interval(lower_bound=0.0,</span> <span class="pre">upper_bound=1.0)}</span></em><a class="headerlink" href="#torch.distributions.bernoulli.Bernoulli.arg_constraints" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="torch.distributions.bernoulli.Bernoulli.entropy">
<span class="sig-name descname"><span class="pre">entropy</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/bernoulli.html#Bernoulli.entropy"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.bernoulli.Bernoulli.entropy" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="torch.distributions.bernoulli.Bernoulli.enumerate_support">
<span class="sig-name descname"><span class="pre">enumerate_support</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">expand</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/bernoulli.html#Bernoulli.enumerate_support"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.bernoulli.Bernoulli.enumerate_support" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="torch.distributions.bernoulli.Bernoulli.expand">
<span class="sig-name descname"><span class="pre">expand</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">batch_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">_instance</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/bernoulli.html#Bernoulli.expand"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.bernoulli.Bernoulli.expand" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="torch.distributions.bernoulli.Bernoulli.has_enumerate_support">
<span class="sig-name descname"><span class="pre">has_enumerate_support</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">True</span></em><a class="headerlink" href="#torch.distributions.bernoulli.Bernoulli.has_enumerate_support" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="torch.distributions.bernoulli.Bernoulli.log_prob">
<span class="sig-name descname"><span class="pre">log_prob</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">value</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/bernoulli.html#Bernoulli.log_prob"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.bernoulli.Bernoulli.log_prob" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="torch.distributions.bernoulli.Bernoulli.logits">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">logits</span></span><a class="headerlink" href="#torch.distributions.bernoulli.Bernoulli.logits" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="torch.distributions.bernoulli.Bernoulli.mean">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">mean</span></span><a class="headerlink" href="#torch.distributions.bernoulli.Bernoulli.mean" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="torch.distributions.bernoulli.Bernoulli.mode">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">mode</span></span><a class="headerlink" href="#torch.distributions.bernoulli.Bernoulli.mode" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="torch.distributions.bernoulli.Bernoulli.param_shape">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">param_shape</span></span><a class="headerlink" href="#torch.distributions.bernoulli.Bernoulli.param_shape" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="torch.distributions.bernoulli.Bernoulli.probs">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">probs</span></span><a class="headerlink" href="#torch.distributions.bernoulli.Bernoulli.probs" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="torch.distributions.bernoulli.Bernoulli.sample">
<span class="sig-name descname"><span class="pre">sample</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sample_shape</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">torch.Size([])</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/bernoulli.html#Bernoulli.sample"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.bernoulli.Bernoulli.sample" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="torch.distributions.bernoulli.Bernoulli.support">
<span class="sig-name descname"><span class="pre">support</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">Boolean()</span></em><a class="headerlink" href="#torch.distributions.bernoulli.Bernoulli.support" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="torch.distributions.bernoulli.Bernoulli.variance">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">variance</span></span><a class="headerlink" href="#torch.distributions.bernoulli.Bernoulli.variance" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
</dd></dl>
</div>
<div class="section" id="beta">
<h2><span class="hidden-section">Beta</span><a class="headerlink" href="#beta" title="Permalink to this heading">¶</a></h2>
<dl class="py class">
<dt class="sig sig-object py" id="torch.distributions.beta.Beta">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">torch.distributions.beta.</span></span><span class="sig-name descname"><span class="pre">Beta</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">concentration1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">concentration0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">validate_args</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/beta.html#Beta"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.beta.Beta" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference internal" href="#torch.distributions.exp_family.ExponentialFamily" title="torch.distributions.exp_family.ExponentialFamily"><code class="xref py py-class docutils literal notranslate"><span class="pre">ExponentialFamily</span></code></a></p>
<p>Beta distribution parameterized by <a class="reference internal" href="#torch.distributions.beta.Beta.concentration1" title="torch.distributions.beta.Beta.concentration1"><code class="xref py py-attr docutils literal notranslate"><span class="pre">concentration1</span></code></a> and <a class="reference internal" href="#torch.distributions.beta.Beta.concentration0" title="torch.distributions.beta.Beta.concentration0"><code class="xref py py-attr docutils literal notranslate"><span class="pre">concentration0</span></code></a>.</p>
<p>Example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">m</span> <span class="o">=</span> <span class="n">Beta</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">tensor</span><span class="p">([</span><span class="mf">0.5</span><span class="p">]),</span> <span class="n">torch</span><span class="o">.</span><span class="n">tensor</span><span class="p">([</span><span class="mf">0.5</span><span class="p">]))</span>
<span class="gp">>>> </span><span class="n">m</span><span class="o">.</span><span class="n">sample</span><span class="p">()</span> <span class="c1"># Beta distributed with concentration concentration1 and concentration0</span>
<span class="go">tensor([ 0.1046])</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>concentration1</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em> or </em><a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – 1st concentration parameter of the distribution
(often referred to as alpha)</p></li>
<li><p><strong>concentration0</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em> or </em><a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a>) – 2nd concentration parameter of the distribution
(often referred to as beta)</p></li>
</ul>
</dd>
</dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="torch.distributions.beta.Beta.arg_constraints">
<span class="sig-name descname"><span class="pre">arg_constraints</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">{'concentration0':</span> <span class="pre">GreaterThan(lower_bound=0.0),</span> <span class="pre">'concentration1':</span> <span class="pre">GreaterThan(lower_bound=0.0)}</span></em><a class="headerlink" href="#torch.distributions.beta.Beta.arg_constraints" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="torch.distributions.beta.Beta.concentration0">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">concentration0</span></span><a class="headerlink" href="#torch.distributions.beta.Beta.concentration0" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="torch.distributions.beta.Beta.concentration1">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">concentration1</span></span><a class="headerlink" href="#torch.distributions.beta.Beta.concentration1" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="torch.distributions.beta.Beta.entropy">
<span class="sig-name descname"><span class="pre">entropy</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/beta.html#Beta.entropy"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.beta.Beta.entropy" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="torch.distributions.beta.Beta.expand">
<span class="sig-name descname"><span class="pre">expand</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">batch_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">_instance</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/beta.html#Beta.expand"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.beta.Beta.expand" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="torch.distributions.beta.Beta.has_rsample">
<span class="sig-name descname"><span class="pre">has_rsample</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">True</span></em><a class="headerlink" href="#torch.distributions.beta.Beta.has_rsample" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="torch.distributions.beta.Beta.log_prob">
<span class="sig-name descname"><span class="pre">log_prob</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">value</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/beta.html#Beta.log_prob"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.beta.Beta.log_prob" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="torch.distributions.beta.Beta.mean">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">mean</span></span><a class="headerlink" href="#torch.distributions.beta.Beta.mean" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="torch.distributions.beta.Beta.mode">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">mode</span></span><a class="headerlink" href="#torch.distributions.beta.Beta.mode" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="torch.distributions.beta.Beta.rsample">
<span class="sig-name descname"><span class="pre">rsample</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sample_shape</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">()</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/beta.html#Beta.rsample"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.beta.Beta.rsample" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="torch.distributions.beta.Beta.support">
<span class="sig-name descname"><span class="pre">support</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">Interval(lower_bound=0.0,</span> <span class="pre">upper_bound=1.0)</span></em><a class="headerlink" href="#torch.distributions.beta.Beta.support" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py property">
<dt class="sig sig-object py" id="torch.distributions.beta.Beta.variance">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">variance</span></span><a class="headerlink" href="#torch.distributions.beta.Beta.variance" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
</dd></dl>
</div>
<div class="section" id="binomial">
<h2><span class="hidden-section">Binomial</span><a class="headerlink" href="#binomial" title="Permalink to this heading">¶</a></h2>
<dl class="py class">
<dt class="sig sig-object py" id="torch.distributions.binomial.Binomial">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">torch.distributions.binomial.</span></span><span class="sig-name descname"><span class="pre">Binomial</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">total_count</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">probs</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">logits</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">validate_args</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/distributions/binomial.html#Binomial"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#torch.distributions.binomial.Binomial" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference internal" href="#torch.distributions.distribution.Distribution" title="torch.distributions.distribution.Distribution"><code class="xref py py-class docutils literal notranslate"><span class="pre">Distribution</span></code></a></p>
<p>Creates a Binomial distribution parameterized by <code class="xref py py-attr docutils literal notranslate"><span class="pre">total_count</span></code> and
either <a class="reference internal" href="#torch.distributions.binomial.Binomial.probs" title="torch.distributions.binomial.Binomial.probs"><code class="xref py py-attr docutils literal notranslate"><span class="pre">probs</span></code></a> or <a class="reference internal" href="#torch.distributions.binomial.Binomial.logits" title="torch.distributions.binomial.Binomial.logits"><code class="xref py py-attr docutils literal notranslate"><span class="pre">logits</span></code></a> (but not both). <code class="xref py py-attr docutils literal notranslate"><span class="pre">total_count</span></code> must be
broadcastable with <a class="reference internal" href="#torch.distributions.binomial.Binomial.probs" title="torch.distributions.binomial.Binomial.probs"><code class="xref py py-attr docutils literal notranslate"><span class="pre">probs</span></code></a>/<a class="reference internal" href="#torch.distributions.binomial.Binomial.logits" title="torch.distributions.binomial.Binomial.logits"><code class="xref py py-attr docutils literal notranslate"><span class="pre">logits</span></code></a>.</p>
<p>Example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">m</span> <span class="o">=</span> <span class="n">Binomial</span><span class="p">(</span><span class="mi">100</span><span class="p">,</span> <span class="n">torch</span><span class="o">.</span><span class="n">tensor</span><span class="p">([</span><span class="mi">0</span> <span class="p">,</span> <span class="mf">.2</span><span class="p">,</span> <span class="mf">.8</span><span class="p">,</span> <span class="mi">1</span><span class="p">]))</span>
<span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">m</span><span class="o">.</span><span class="n">sample</span><span class="p">()</span>
<span class="go">tensor([ 0., 22., 71., 100.])</span>
<span class="gp">>>> </span><span class="n">m</span> <span class="o">=</span> <span class="n">Binomial</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">tensor</span><span class="p">([[</span><span class="mf">5.</span><span class="p">],</span> <span class="p">[</span><span class="mf">10.</span><span class="p">]]),</span> <span class="n">torch</span><span class="o">.</span><span class="n">tensor</span><span class="p">([</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.8</span><span class="p">]))</span>
<span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">m</span><span class="o">.</span><span class="n">sample</span><span class="p">()</span>
<span class="go">tensor([[ 4., 5.],</span>
<span class="go"> [ 7., 6.]])</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">