PageSourceSearch

https://stephane-v-boucheron.fr/publication/ps-2022/

html stephane-v-boucheron.fr collected 2026-10-01 15:35:09 UTC 18,629 bytes, 1,302 lines download raw bytes

1<!DOCTYPE html>
2<!-- This site was created with Hugo Blox. https://hugoblox.com -->
3<!-- Last Published: January 8, 2024 --><html lang="en-us" >
4
5
6<head>
7  <meta charset="utf-8" />
8  <meta name="viewport" content="width=device-width, initial-scale=1" />
9  <meta http-equiv="X-UA-Compatible" content="IE=edge" />
10  
11  
12  
13    <meta name="generator" content="Hugo Blox Builder 5.9.6" />
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  <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin />
53  
54
55  
56  
57  
58    
59      
60      <link rel="preload" as="style" href="https://fonts.googleapis.com/css2?family=Montserrat:wght@400;700&family=Roboto+Mono&family=Roboto:wght@400;700&display=swap">
61      <link rel="stylesheet" href="https://fonts.googleapis.com/css2?family=Montserrat:wght@400;700&family=Roboto+Mono&family=Roboto:wght@400;700&display=swap" media="print" onload="this.media='all'">
62    
63  
64
65  
66  
67
68  
69  
70
71  
72
73  <link rel="stylesheet" href="/css/vendor-bundle.min.047268c6dd09ad74ba54a0ba71837064.css" media="print" onload="this.media='all'">
74
75  
76  
77  
78    
79    
80      <link rel="stylesheet" href="https://cdn.jsdelivr.net/gh/jpswalsh/[email protected]/css/academicons.min.css" integrity="sha512-IW0nhlW5MgNydsXJO40En2EoCkTTjZhI3yuODrZIc8cQ4h1XcF53PsqDHa09NqnkXuIe0Oiyyj171BqZFwISBw==" crossorigin="anonymous" media="print" onload="this.media='all'">
81    
82
83    
84    
85    
86    
87      
88      
89    
90    
91    
92
93    
94    
95    
96      <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/leaflet.min.css" integrity="" crossorigin="anonymous" media="print" onload="this.media='all'">
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  <link rel="stylesheet" href="/css/wowchemy.6002c9f97f17b88101644d5bbb659351.css" />
218
219  
220  
221  
222
223  
224  
225  
226  
227  
228  
229  
230    
231    
232    <link rel="stylesheet" href="/css/libs/chroma/github-light.min.css" title="hl-light" media="print" onload="this.media='all'" >
233    <link rel="stylesheet" href="/css/libs/chroma/dracula.min.css" title="hl-dark" media="print" onload="this.media='all'" disabled>
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<meta name="description" content="" />
277
278
279
280<link rel="alternate" hreflang="en-us" href="https://stephane-v-boucheron.fr/publication/ps-2022/" />
281<link rel="canonical" href="https://stephane-v-boucheron.fr/publication/ps-2022/" />
282
283
284
285  <link rel="manifest" href="/manifest.webmanifest" />
286
287
288
289<link rel="icon" type="image/png" href="/media/icon_hu0b7a4cb9992c9ac0e91bd28ffd38dd00_9727_32x32_fill_lanczos_center_3.png" />
290<link rel="apple-touch-icon" type="image/png" href="/media/icon_hu0b7a4cb9992c9ac0e91bd28ffd38dd00_9727_180x180_fill_lanczos_center_3.png" />
291
292<meta name="theme-color" content="#1565c0" />
293
294
295
296
297
298
299
300
301
302
303  
304  
305
306
307
308
309
310
311<meta property="twitter:card" content="summary" />
312
313  <meta property="twitter:site" content="@GetResearchDev" />
314  <meta property="twitter:creator" content="@GetResearchDev" />
315<meta property="twitter:image" content="https://stephane-v-boucheron.fr/media/icon_hu0b7a4cb9992c9ac0e91bd28ffd38dd00_9727_512x512_fill_lanczos_center_3.png" />
316
317
318
319  
320
321<meta property="og:type" content="article" />
322<meta property="og:site_name" content="Stéphane Boucheron" />
323<meta property="og:url" content="https://stephane-v-boucheron.fr/publication/ps-2022/" />
324<meta property="og:title" content="Topics in Statistical Learning Theory | Stéphane Boucheron" />
325<meta property="og:description" content="" /><meta property="og:image" content="https://stephane-v-boucheron.fr/media/icon_hu0b7a4cb9992c9ac0e91bd28ffd38dd00_9727_512x512_fill_lanczos_center_3.png" /><meta property="og:locale" content="en-us" />
326
327  
328    <meta
329      property="article:published_time"
330      content="2022-06-01T00:00:00&#43;00:00"
331    />
332  
333  
334    <meta property="article:modified_time" content="2022-06-01T00:00:00&#43;00:00">
335  
336
337
338
339
340
341
342    
343
344
345
346
347
348
349
350
351
352<script type="application/ld+json">
353{
354  "@context": "https://schema.org",
355  "@type": "Article",
356  "mainEntityOfPage": {
357    "@type": "WebPage",
358    "@id": "https://stephane-v-boucheron.fr/publication/ps-2022/"
359  },
360  "headline": "Topics in Statistical Learning Theory",
361  
362  "datePublished": "2022-06-01T00:00:00Z",
363  "dateModified": "2022-06-01T00:00:00Z",
364  
365  "author": {
366    "@type": "Person",
367    "name": "Peter L. Bartlett"
368  },
369  
370  "publisher": {
371    "@type": "Organization",
372    "name": "Stéphane Boucheron",
373    "logo": {
374      "@type": "ImageObject",
375      "url": "https://stephane-v-boucheron.fr/media/icon_hu0b7a4cb9992c9ac0e91bd28ffd38dd00_9727_192x192_fill_lanczos_center_3.png"
376    }
377  },
378  "description": ""
379}
380</script>
380
381
382  
383
384  
385
386
387
388
389  
390  
391  
392
393  
394  
395
396  
397
398
399  
400  <title>Topics in Statistical Learning Theory | Stéphane Boucheron</title>
401
402  
403  
404  
405  
406
407
408
409
410
411
412
413
414
415
416
417</head>
418
419
420<body id="top" data-spy="scroll" data-offset="70" data-target="#TableOfContents" class="page-wrapper   " data-wc-page-id="5d60448532b29a52853557d6fc3d3079" >
421
422  
423  
424  
425  
426  
427  
428  
429  
430  
431  
431<script src="/js/wowchemy-init.min.3a6bdbdff5d8a89d6e651adb3deec035.js"></script>
431
432
433  
434
435
436<aside class="search-modal" id="search">
437  <div class="container">
438    <section class="search-header">
439
440      <div class="row no-gutters justify-content-between mb-3">
441        <div class="col-6">
442          <h1>Search</h1>
443        </div>
444        <div class="col-6 col-search-close">
445          <a class="js-search" href="#" aria-label="Close"><i class="fas fa-times-circle text-muted" aria-hidden="true"></i></a>
446        </div>
447      </div>
448
449      <div id="search-box">
450        
451        <input name="q" id="search-query" placeholder="Search..." autocapitalize="off"
452        autocomplete="off" autocorrect="off" spellcheck="false" type="search" class="form-control"
453        aria-label="Search...">
454        
455      </div>
456
457      
458      
459
460      
461
462    </section>
463    <section class="section-search-results">
464
465      <div id="search-hits">
466        
467      </div>
468
469    </section>
470  </div>
471</aside>
472
473
474
475  <div class="page-header header--fixed">
476  
477  
478  
479  
480  
481
482
483
484
485
486
487
488
489
490
491
492
493<header>
494  <nav class="navbar navbar-expand-lg navbar-light compensate-for-scrollbar" id="navbar-main">
495    <div class="container-xl">
496
497      
498      <div class="d-none d-lg-inline-flex">
499        <a class="navbar-brand" href="/">Stéphane Boucheron</a>
500      </div>
501      
502
503      
504      <button type="button" class="navbar-toggler" data-toggle="collapse"
505              data-target="#navbar-content" aria-controls="navbar-content" aria-expanded="false" aria-label="Toggle navigation">
506      <span><i class="fas fa-bars"></i></span>
507      </button>
508      
509
510      
511      <div class="navbar-brand-mobile-wrapper d-inline-flex d-lg-none">
512        <a class="navbar-brand" href="/">Stéphane Boucheron</a>
513      </div>
514      
515
516      
517      
518      <div class="navbar-collapse main-menu-item collapse justify-content-end" id="navbar-content">
519
520        
521        <ul class="navbar-nav d-md-inline-flex">
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          <li class="nav-item">
555            <a class="nav-link " href="/#about"><span>Home</span></a>
556          </li>
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          <li class="nav-item">
592            <a class="nav-link " href="/#publications"><span>Publications</span></a>
593          </li>
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          <li class="nav-item">
622            <a class="nav-link " href="/courses/"><span>Courses</span></a>
623          </li>
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          <li class="nav-item">
659            <a class="nav-link " href="/#contact"><span>Contact</span></a>
660          </li>
661
662          
663          
664
665        
666
667          
668        </ul>
669      </div>
670
671      <ul class="nav-icons navbar-nav flex-row ml-auto d-flex pl-md-2">
672
673        
674        
675
676        
677        
678        
679        <li class="nav-item">
680          <a class="nav-link js-search" href="#" aria-label="Search"><i class="fas fa-search" aria-hidden="true"></i></a>
681        </li>
682        
683
684        
685        
686        
687        <li class="nav-item dropdown theme-dropdown">
688          <a href="#" class="nav-link" data-toggle="dropdown" aria-haspopup="true" aria-label="Display preferences">
689            <i class="fas fa-moon" aria-hidden="true"></i>
690          </a>
691          <div class="dropdown-menu">
692            <a href="#" class="dropdown-item js-set-theme-light">
693              <span>Light</span>
694            </a>
695            <a href="#" class="dropdown-item js-set-theme-dark">
696              <span>Dark</span>
697            </a>
698            <a href="#" class="dropdown-item js-set-theme-auto">
699              <span>Automatic</span>
700            </a>
701          </div>
702        </li>
703        
704
705        
706        
707
708      </ul>
709
710    </div>
711  </nav>
712</header>
713
714
715  </div>
716
717  <div class="page-body">
718    
719    
720    
721
722    
723
724
725  
726    
727    
728  
729
730
731<div class="pub">
732
733  
734
735
736
737
738
739
740
741
742
743
744
745
746
747  
748
749  
750  
751  
752<div class="article-container pt-3">
753  <h1>Topics in Statistical Learning Theory</h1>
754
755  
756
757  
758    
759
760
761<div class="article-metadata">
762
763  
764  
765  
766  
767  <div>
768    
769
770  <span >
771      Peter L. Bartlett</span>, <span >
772      Sanjoy Dasgupta</span>
773  </div>
774  
775  
776
777  
778  <span class="article-date">
779    
780    
781      
782    
783    June, 2022
784  </span>
785  
786
787  
788
789  
790
791  
792  
793  
794  
795
796  
797  
798
799</div>
800
801    
802
803
804
805
806<div class="btn-links mb-3">
807  
808  
809
810
811
812
813
814
815
816
817  
818    
819  
820
821
822
823<a class="btn btn-outline-primary btn-page-header" href="https://bookstore.ams.org/view?ProductCode=PASY/57" target="_blank" rel="noopener">
824  PDF
825</a>
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843</div>
844
845
846  
847</div>
848
849
850
851  <div class="article-container">
852
853    
854
855    
856    
857    <div class="row">
858      <div class="col-md-1"></div>
859      <div class="col-md-10">
860        <div class="row">
861          <div class="col-12 col-md-3 pub-row-heading">Type</div>
862          <div class="col-12 col-md-9">
863            <a href="/publication/#5">
864              5
865            </a>
866          </div>
867        </div>
868      </div>
869      <div class="col-md-1"></div>
870    </div>
871    <div class="d-md-none space-below"></div>
872    
873
874    
875    <div class="row">
876      <div class="col-md-1"></div>
877      <div class="col-md-10">
878        <div class="row">
879          <div class="col-12 col-md-3 pub-row-heading">Publication</div>
880          <div class="col-12 col-md-9"><em>Panoramas et Synthèses</em></div>
881        </div>
882      </div>
883      <div class="col-md-1"></div>
884    </div>
885    <div class="d-md-none space-below"></div>
886    
887
888    <div class="space-below"></div>
889
890    <div class="article-style"></div>
891
892    
893
894
895
896
897
898
899
900<div class="share-box">
901  <ul class="share">
902    
903      
904      
905      
906        
907      
908      
909      
910      
911      
912      
913      
914      <li>
915        <a href="https://twitter.com/intent/tweet?url=https%3A%2F%2Fstephane-v-boucheron.fr%2Fpublication%2Fps-2022%2F&amp;text=Topics&#43;in&#43;Statistical&#43;Learning&#43;Theory" target="_blank" rel="noopener" class="share-btn-twitter" aria-label="twitter">
916          <i class="fab fa-twitter"></i>
917        </a>
918      </li>
919    
920      
921      
922      
923        
924      
925      
926      
927      
928      
929      
930      
931      <li>
932        <a href="https://www.facebook.com/sharer.php?u=https%3A%2F%2Fstephane-v-boucheron.fr%2Fpublication%2Fps-2022%2F&amp;t=Topics&#43;in&#43;Statistical&#43;Learning&#43;Theory" target="_blank" rel="noopener" class="share-btn-facebook" aria-label="facebook">
933          <i class="fab fa-facebook"></i>
934        </a>
935      </li>
936    
937      
938      
939      
940        
941      
942      
943      
944      
945      
946      
947      
948        
949      
950      <li>
951        <a href="mailto:?subject=Topics%20in%20Statistical%20Learning%20Theory&amp;body=https%3A%2F%2Fstephane-v-boucheron.fr%2Fpublication%2Fps-2022%2F" target="_blank" rel="noopener" class="share-btn-email" aria-label="envelope">
952          <i class="fas fa-envelope"></i>
953        </a>
954      </li>
955    
956      
957      
958      
959        
960      
961      
962      
963      
964      
965      
966      
967      <li>
968        <a href="https://www.linkedin.com/shareArticle?url=https%3A%2F%2Fstephane-v-boucheron.fr%2Fpublication%2Fps-2022%2F&amp;title=Topics&#43;in&#43;Statistical&#43;Learning&#43;Theory" target="_blank" rel="noopener" class="share-btn-linkedin" aria-label="linkedin-in">
969          <i class="fab fa-linkedin-in"></i>
970        </a>
971      </li>
972    
973      
974      
975      
976        
977      
978      
979      
980      
981      
982      
983      
984      <li>
985        <a href="whatsapp://send?text=Topics&#43;in&#43;Statistical&#43;Learning&#43;Theory%20https%3A%2F%2Fstephane-v-boucheron.fr%2Fpublication%2Fps-2022%2F" target="_blank" rel="noopener" class="share-btn-whatsapp" aria-label="whatsapp">
986          <i class="fab fa-whatsapp"></i>
987        </a>
988      </li>
989    
990      
991      
992      
993        
994      
995      
996      
997      
998      
999      
1000      
1001      <li>
1002        <a href="https://service.weibo.com/share/share.php?url=https%3A%2F%2Fstephane-v-boucheron.fr%2Fpublication%2Fps-2022%2F&amp;title=Topics&#43;in&#43;Statistical&#43;Learning&#43;Theory" target="_blank" rel="noopener" class="share-btn-weibo" aria-label="weibo">
1003          <i class="fab fa-weibo"></i>
1004        </a>
1005      </li>
1006    
1007  </ul>
1008</div>
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020  
1021  
1022    
1023
1024
1025
1026
1027  
1028    
1029
1030
1031
1032
1033  
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050  </div>
1051</div>
1052  </div>
1053
1054  <div class="page-footer">
1055    
1056    
1057    <div class="container">
1058      <footer class="site-footer">
1059
1060  
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073  
1074  
1075  
1076  
1077  
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091  
1092  
1093  
1094
1095  
1096  
1097    
1098  
1099  
1100    
1101  
1102
1103  
1104
1105  
1106  <p class="powered-by copyright-license-text">
1107    © 2024 Me. This work is licensed under <a href="https://creativecommons.org/licenses/by-nc-nd/4.0" rel="noopener noreferrer" target="_blank">CC BY NC ND 4.0</a>
1108  </p>
1109  
1110
1111  <p class="powered-by footer-license-icons">
1112    <a href="https://creativecommons.org/licenses/by-nc-nd/4.0" rel="noopener noreferrer" target="_blank" aria-label="Creative 
1112Commons">
1113      <i class="fab fa-creative-commons fa-2x" aria-hidden="true"></i>
1114      <i class="fab fa-creative-commons-by fa-2x" aria-hidden="true"></i>
1115      
1116        <i class="fab fa-creative-commons-nc fa-2x" aria-hidden="true"></i>
1117      
1118      
1119        <i class="fab fa-creative-commons-nd fa-2x" aria-hidden="true"></i>
1120      
1121    </a>
1122  </p>
1123
1124
1125
1126
1127
1128  <p class="powered-by">
1129    
1130    
1131    
1132      
1133      
1134      
1135      
1136      
1137      
1138      Published with <a href="https://hugoblox.com/?utm_campaign=poweredby" target="_blank" rel="noopener">Hugo Blox Builder</a> — the free, <a href="https://github.com/HugoBlox/hugo-blox-builder" target="_blank" rel="noopener">open source</a> website builder that empowers creators.
1139    
1140  </p>
1141</footer>
1142
1143    </div>
1144    
1145  </div>
1146
1147  
1148
1149
1150<script src="/js/vendor-bundle.min.938a3a7554cd9f6602290411f64d2617.js"></script>
1150
1151
1152
1153
1154
1155  
1156
1157  
1158  
1159
1160  
1161
1162
1163
1164
1165
1166
1167  
1167<script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/leaflet.min.js" integrity="" crossorigin="anonymous"></script>
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176  
1177  
1177<script id="search-hit-fuse-template" type="text/x-template">
1178    <div class="search-hit" id="summary-{{key}}">
1179      <div class="search-hit-content">
1180        <div class="search-hit-name">
1181          <a href="{{relpermalink}}">{{title}}</a>
1182          <div class="article-metadata search-hit-type">{{type}}</div>
1183          <p class="search-hit-description">{{snippet}}</p>
1184        </div>
1185      </div>
1186    </div>
1187  </script>
1187
1188  
1189    
1189<script src="https://cdn.jsdelivr.net/gh/krisk/[email protected]/dist/fuse.min.js" integrity="sha512-o38bmzBGX+hD3JHWUFCDA09btWaqrNmoJ3RXLlrysA7PP01Kgs4UlE4MhelE1v5dJR3+cxlR4qQlotsW7jKsnw==" crossorigin="anonymous"></script>
1189
1190    
1190<script src="https://cdn.jsdelivr.net/gh/julmot/[email protected]/dist/jquery.mark.min.js" integrity="sha512-mhbv5DqBMgrWL+32MmsDOt/OAvqr/cHimk6B8y/bx/xS88MVkYGPiVv2ixKVrkywF2qHplNRUvFsAHUdxZ3Krg==" crossorigin="anonymous"></script>
1190
1191  
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204  
1205  
1206  
1207  
1208  
1209  
1210  
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228<script id="page-data" type="application/json">{"use_headroom":true}</script>
1228
1229
1230
1231  
1231<script src="/js/wowchemy-headroom.db4755770454eb63685f8de785c0a172.js" type="module"></script>
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241  
1242  
1243
1244
1245<script src="/en/js/wowchemy.min.62586ca65ca61821fe707eb9fa6268b7.js"></script>
1245
1246
1247
1248
1249  
1249<script src="/js/wowchemy-map.a26e9d2f7238ba5b868384f1c5bc6477.js" type="module"></script>
1249
1250
1251
1252
1253
1254  
1255<div id="modal" class="modal fade" role="dialog">
1256  <div class="modal-dialog">
1257    <div class="modal-content">
1258      <div class="modal-header">
1259        <h5 class="modal-title">Cite</h5>
1260        <button type="button" class="close" data-dismiss="modal" aria-label="Close">
1261          <span aria-hidden="true">&times;</span>
1262        </button>
1263      </div>
1264      <div class="modal-body">
1265        
1266        <pre><code></code></pre>
1267      </div>
1268      <div class="modal-footer">
1269        <a class="btn btn-outline-primary my-1 js-copy-cite" href="#" target="_blank">
1270          <i class="fas fa-copy"></i> Copy
1271        </a>
1272        <a class="btn btn-outline-primary my-1 js-download-cite" href="#" target="_blank">
1273          <i class="fas fa-download"></i> Download
1274        </a>
1275        <div id="modal-error"></div>
1276      </div>
1277    </div>
1278  </div>
1279</div>
1280
1281
1282  
1282<script src="/js/wowchemy-publication.9137013a66774049159934c29c3f0205.js" type="module"></script>
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301</body>
1302</html>

Line numbers count LF bytes from the start of the resource, as the search results do. Vendor segments are library code the classifier recognised; they are stored but not indexed. Bytes are shown as Latin1 characters, one per byte.