https://wiki.cs.hse.ru/index.php?action=history&feed=atom&title=High-dimensional_Probability_and_Statistics_%282026%29 2026-09-21T21:23:46Z История изменений этой страницы в вики MediaWiki 1.43.9 https://wiki.cs.hse.ru/index.php?title=High-dimensional_Probability_and_Statistics_(2026)&diff=95578&oldid=prev 2026-02-27T10:11:11Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="ru"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Предыдущая версия</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Версия от 10:11, 27 февраля 2026</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l17">Строка 17:</td> <td colspan="2" class="diff-lineno">Строка 17:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* (04.02.2026) Chapter 2.1.2, Proposition 2.14 from [[#wainwright|[Wainwright]]]. Concentration of order statistics (folklore).</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* (04.02.2026) Chapter 2.1.2, Proposition 2.14 from [[#wainwright|[Wainwright]]]. Concentration of order statistics (folklore).</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Chapter 2.2 from [[#wainwright|[Wainwright]]].</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* <ins style="font-weight: bold; text-decoration: none;">(11.02.2026) </ins>Chapter 2.2 from [[#wainwright|[Wainwright<ins style="font-weight: bold; text-decoration: none;">]]]. Chapter 2.1.3 from [[#wainwright|[Wainwright]]]. Orlicz norms, see Chapter 2.5 from  [[#vershynin|[Vershynin</ins>]]].</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Chapter 2.<del style="font-weight: bold; text-decoration: none;">1</del>.3 from [[#wainwright|[Wainwright]]]. <del style="font-weight: bold; text-decoration: none;">Orlicz norms, see Chapter 2</del>.<del style="font-weight: bold; text-decoration: none;">5 </del>from <del style="font-weight: bold; text-decoration: none;"> </del>[[#<del style="font-weight: bold; text-decoration: none;">vershynin</del>|[<del style="font-weight: bold; text-decoration: none;">Vershynin</del>]]].</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* <ins style="font-weight: bold; text-decoration: none;">(18.02.2026) Orlicz norms, see </ins>Chapter 2.<ins style="font-weight: bold; text-decoration: none;">5 from  [[#vershynin|[Vershynin]]]. Sanov's theorem and KL-divergence, Chapter 6.2 from [[#Weissman |[Weissman]]]. KL-divergence. Definition of entropy</ins>. <ins style="font-weight: bold; text-decoration: none;">Herbst's argument (Proposition </ins>3<ins style="font-weight: bold; text-decoration: none;">.2 </ins>from [[#wainwright|[Wainwright]]]<ins style="font-weight: bold; text-decoration: none;">)</ins>. <ins style="font-weight: bold; text-decoration: none;">Gaussian Logarithmic Sobolev inequality (Theorem 5</ins>.<ins style="font-weight: bold; text-decoration: none;">4 </ins>from [[#<ins style="font-weight: bold; text-decoration: none;">blm|[BLM]]]). Sub-additivity of the entropy (Section 4.13 [[#blm</ins>|[<ins style="font-weight: bold; text-decoration: none;">BLM</ins>]]]<ins style="font-weight: bold; text-decoration: none;">)</ins>.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* <del style="font-weight: bold; text-decoration: none;">Orlicz norms, see Chapter 2.5 from  [[#vershynin|[Vershynin]]]. Sanov's theorem and KL-divergence, Chapter 6.2 from [[#Weissman |[Weissman]]].</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Concentration of Gaussian Lipschitz functions.</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">* KL-divergence. Definition of entropy. Herbst's argument (Proposition 3.2 from [[#wainwright|[Wainwright]]]). Gaussian Logarithmic Sobolev inequality (Theorem 5.4 from [[#blm|[BLM]]]). Sub-additivity of the entropy (Section 4.13 [[#blm|[BLM]]]). </del>Concentration of Gaussian Lipschitz functions.</div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Uniform Johnson-Lindenstrauss lemma (Theorem 5.10 from [[#blm|[BLM]]]). A modified logarithmic Sobolev inequality (Theorem 6.7 from [[#blm|[BLM]]]).</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Uniform Johnson-Lindenstrauss lemma (Theorem 5.10 from [[#blm|[BLM]]]). A modified logarithmic Sobolev inequality (Theorem 6.7 from [[#blm|[BLM]]]).</div></td></tr> </table>

Fedor.Noskov https://wiki.cs.hse.ru/index.php?title=High-dimensional_Probability_and_Statistics_(2026)&diff=95223&oldid=prev 2026-02-07T22:24:50Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="ru"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Предыдущая версия</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Версия от 22:24, 7 февраля 2026</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l13">Строка 13:</td> <td colspan="2" class="diff-lineno">Строка 13:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* (21.01.2026) Chapter 3.1, Examples 3.5 and 3.14 from [[#blm|[BLM]]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* (21.01.2026) Chapter 3.1, Examples 3.5 and 3.14 from [[#blm|[BLM]]]</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Chapters 3.6-3.7 from [[#blm|[BLM]]]. For the Sobolev spaces, weak derivatives and the approximation argument, see Chapters 5.2-5.3 [[#EvansPDE | [EvansPDE]]]. See also Chapters 2.1-2.3 of [[#Ziemer | [Ziemer]]].</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* <ins style="font-weight: bold; text-decoration: none;">(28.01.2026) </ins>Chapters 3.6-3.7 from [[#blm|[BLM]]]. For the Sobolev spaces, weak derivatives and the approximation argument, see Chapters 5.2-5.3 [[#EvansPDE | [EvansPDE]]]. See also Chapters 2.1-2.3 of [[#Ziemer | [Ziemer]]].</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Chapter 2.1.2, Proposition 2.14 from [[#wainwright|[Wainwright]]]. Concentration of order statistics (folklore).</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* <ins style="font-weight: bold; text-decoration: none;">(04.02.2026) </ins>Chapter 2.1.2, Proposition 2.14 from [[#wainwright|[Wainwright]]]. Concentration of order statistics (folklore).</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Chapter 2.2 from [[#wainwright|[Wainwright]]].</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Chapter 2.2 from [[#wainwright|[Wainwright]]].</div></td></tr> </table>

Fedor.Noskov https://wiki.cs.hse.ru/index.php?title=High-dimensional_Probability_and_Statistics_(2026)&diff=94838&oldid=prev 2026-01-22T13:20:42Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="ru"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Предыдущая версия</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Версия от 13:20, 22 января 2026</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l11">Строка 11:</td> <td colspan="2" class="diff-lineno">Строка 11:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Probability ===  </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== Probability ===  </div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Chapter 3.1, Examples 3.5 and 3.14 from [[#blm|[BLM]]]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* <ins style="font-weight: bold; text-decoration: none;">(21.01.2026) </ins>Chapter 3.1, Examples 3.5 and 3.14 from [[#blm|[BLM]]]</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Chapters 3.6-3.7 from [[#blm|[BLM]]]. For the Sobolev spaces, weak derivatives and the approximation argument, see Chapters 5.2-5.3 [[#EvansPDE | [EvansPDE]]]. See also Chapters 2.1-2.3 of [[#Ziemer | [Ziemer]]].</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Chapters 3.6-3.7 from [[#blm|[BLM]]]. For the Sobolev spaces, weak derivatives and the approximation argument, see Chapters 5.2-5.3 [[#EvansPDE | [EvansPDE]]]. See also Chapters 2.1-2.3 of [[#Ziemer | [Ziemer]]].</div></td></tr> </table>

Fedor.Noskov https://wiki.cs.hse.ru/index.php?title=High-dimensional_Probability_and_Statistics_(2026)&diff=94837&oldid=prev 2026-01-22T13:20:13Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="ru"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Предыдущая версия</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Версия от 13:20, 22 января 2026</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l42">Строка 42:</td> <td colspan="2" class="diff-lineno">Строка 42:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Midterm =</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Midterm =</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">TBA</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Home assignments =</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Home assignments =</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">TBA</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= References =</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= References =</div></td></tr> </table>

Fedor.Noskov https://wiki.cs.hse.ru/index.php?title=High-dimensional_Probability_and_Statistics_(2026)&diff=94836&oldid=prev 2026-01-22T13:19:52Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="ru"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Предыдущая версия</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Версия от 13:19, 22 января 2026</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l31">Строка 31:</td> <td colspan="2" class="diff-lineno">Строка 31:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Matrix Chernoff from PSD matrices (Theorem 5.1.1 from [[#Tropp |[Tropp]]]). Application to graph sparsifying (Chapter 32 from [[#Spielman | [Spielman]]]).</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Matrix Chernoff from PSD matrices (Theorem 5.1.1 from [[#Tropp |[Tropp]]]). Application to graph sparsifying (Chapter 32 from [[#Spielman | [Spielman]]]).</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">=</del>= Grading <del style="font-weight: bold; text-decoration: none;">=</del>=</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>= Grading =</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The final grade is obtained as follows:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The final grade is obtained as follows:</div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l40">Строка 40:</td> <td colspan="2" class="diff-lineno">Строка 40:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">=</del>= Midterm <del style="font-weight: bold; text-decoration: none;">=</del>=</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>= Midterm =</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">=</del>= Home assignments <del style="font-weight: bold; text-decoration: none;">=</del>=</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>= Home assignments =</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> </table>

Fedor.Noskov https://wiki.cs.hse.ru/index.php?title=High-dimensional_Probability_and_Statistics_(2026)&diff=94835&oldid=prev 2026-01-22T13:19:21Z

<p>создание страницы курса</p> <p><b>Новая страница</b></p><div>= Classes =<br /> <br /> Wednesdays 14:40–17:40, in room G410. <br /> <br /> Teachers: [https://www.hse.ru/en/org/persons/510369027 Fedor Noskov], [https://www.hse.ru/en/org/persons/133709471 Quentin Paris]<br /> <br /> Teaching Assistant: [https://t.me/teddy_nos Fedor Noskov]<br /> <br /> = Lecture/Seminar content =<br /> <br /> === Probability === <br /> <br /> * Chapter 3.1, Examples 3.5 and 3.14 from [[#blm|[BLM]]]<br /> <br /> * Chapters 3.6-3.7 from [[#blm|[BLM]]]. For the Sobolev spaces, weak derivatives and the approximation argument, see Chapters 5.2-5.3 [[#EvansPDE | [EvansPDE]]]. See also Chapters 2.1-2.3 of [[#Ziemer | [Ziemer]]].<br /> <br /> * Chapter 2.1.2, Proposition 2.14 from [[#wainwright|[Wainwright]]]. Concentration of order statistics (folklore).<br /> <br /> * Chapter 2.2 from [[#wainwright|[Wainwright]]].<br /> <br /> * Chapter 2.1.3 from [[#wainwright|[Wainwright]]]. Orlicz norms, see Chapter 2.5 from [[#vershynin|[Vershynin]]].<br /> <br /> * Orlicz norms, see Chapter 2.5 from [[#vershynin|[Vershynin]]]. Sanov&#039;s theorem and KL-divergence, Chapter 6.2 from [[#Weissman |[Weissman]]].<br /> <br /> * KL-divergence. Definition of entropy. Herbst&#039;s argument (Proposition 3.2 from [[#wainwright|[Wainwright]]]). Gaussian Logarithmic Sobolev inequality (Theorem 5.4 from [[#blm|[BLM]]]). Sub-additivity of the entropy (Section 4.13 [[#blm|[BLM]]]). Concentration of Gaussian Lipschitz functions.<br /> <br /> * Uniform Johnson-Lindenstrauss lemma (Theorem 5.10 from [[#blm|[BLM]]]). A modified logarithmic Sobolev inequality (Theorem 6.7 from [[#blm|[BLM]]]).<br /> <br /> * Functional Hoeffding inequality (Theorem 3.26 from [[#wainwright|[Wainwright]]]). Largest eigenvalue of a random symmetric matrix (Example 6.8 from [[#blm|[BLM]]]). Matrix Chernoff bound (Lemma 6.12 from [[#wainwright|[Wainwright]]].<br /> <br /> * Matrix Chernoff from PSD matrices (Theorem 5.1.1 from [[#Tropp |[Tropp]]]). Application to graph sparsifying (Chapter 32 from [[#Spielman | [Spielman]]]).<br /> <br /> == Grading ==<br /> <br /> The final grade is obtained as follows:<br /> <br /> 0.2 HW HDP + 0.3 Midterm HDP + 0.2 HW HDS + 0.3 Exam HDS,<br /> <br /> where HW stands for home assignment, HDP stands for High-Dimensional Probability, HDS stands for High-Dimensional Statistics.<br /> <br /> <br /> == Midterm ==<br /> <br /> <br /> <br /> == Home assignments ==<br /> <br /> <br /> <br /> = References =<br /> <br /> &lt;b&gt;links are available via hse accounts&lt;/b&gt;<br /> <br /> &lt;span id=&quot;van_handel&quot;&gt;[van Handel]&lt;/span&gt; [https://disk.yandex.ru/i/GPfpvZt7lSf7Bg Ramon van Handel. Probability in High Dimensions, Lecture Notes]<br /> <br /> &lt;span id=&quot;vershynin&quot;&gt;[Vershynin]&lt;/span&gt; [https://disk.yandex.ru/i/ci_c_FW5-eXH-A R. Vershynin. High-Dimensional Probability]<br /> <br /> &lt;span id=&quot;wainwright&quot;&gt;[Wainwright]&lt;/span&gt; [https://disk.yandex.ru/i/4RUmUDj3--sNOQ M.J. Wainwright. High-Dimensional Statistics]<br /> <br /> &lt;span id=&quot;blm&quot;&gt;[BLM]&lt;/span&gt; [https://disk.yandex.ru/i/7GOknoh1HYGEJQ Boucheron et al. Concentration inequalities]<br /> <br /> &lt;span id=&quot;rigollet&quot;&gt;[Rigollet]&lt;/span&gt; [https://disk.yandex.ru/i/GW7kFWmdsrfClA Philippe Rigollet and Jan-Christian H¨utter. High-Dimensional Statistics. Lecture Notes]<br /> <br /> &lt;span id=&quot;paris&quot;&gt;[Paris]&lt;/span&gt; [https://disk.yandex.ru/i/CeIEx0MW2hpbrw Quentin Paris. Statistical Learning Theory. Lecture Notes]<br /> <br /> &lt;span id=&quot;EvansPDE&quot;&gt;[EvansPDE]&lt;/span&gt; [https://disk.yandex.ru/i/cCHL2bbbr0V-7Q Lawrence Evans. Partial Differential Equations]<br /> <br /> &lt;span id=&quot;Ziemer&quot;&gt;[Ziemer]&lt;/span&gt; [https://disk.yandex.ru/i/1aMzdRyaMZixCQ William Ziemer. Weakly Differentiable Equations]<br /> <br /> &lt;span id=&quot;Weissman&quot;&gt;[Weissman]&lt;/span&gt; [https://disk.yandex.ru/i/OPDZenkw-OPSAA Tsachy Weissman. Information theory, Lecture notes]<br /> <br /> &lt;span id=&quot;Tropp&quot;&gt;[Tropp]&lt;/span&gt; [https://disk.yandex.ru/i/nzHbi_l_SALkew Joel Tropp. An Introduction to Matrix Concentration Inequalities]<br /> <br /> &lt;span id=&quot;Spielman&quot;&gt;[Spielman]&lt;/span&gt; [https://disk.yandex.ru/i/BIqcuUz1yZb0Cg Daniel Spielman. Spectral and Algebraic Graph Theory]</div>

Fedor.Noskov