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High-dimensional Probability and Statistics (2025) - История изменений
2026-06-06T12:14:02Z
История изменений этой страницы в вики
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imported>Fedor.Noskov: Migrated current public revision from wiki.cs.hse.ru
2025-06-04T16:46:08Z
<p>Migrated current public revision from wiki.cs.hse.ru</p>
<p><b>Новая страница</b></p><div>= Classes =<br />
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Wednesdays 13:00–16:00, in room G110. <br />
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Teachers: [https://www.hse.ru/en/org/persons/510369027 Fedor Noskov], [https://www.hse.ru/en/org/persons/133709471 Quentin Paris]<br />
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Teaching Assistant: [https://t.me/teddy_nos Fedor Noskov]<br />
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= Lecture/Seminar content =<br />
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=== Probability === <br />
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* (15.01.24) Chapter 3.1, Examples 3.5 and 3.14 from [[#blm|[BLM]]]<br />
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* (22.01.24) 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 />
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* (29.01.24) Chapter 2.1.2, Proposition 2.14 from [[#wainwright|[Wainwright]]]. Concentration of order statistics (folklore).<br />
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* (05.02.24) Chapter 2.2 from [[#wainwright|[Wainwright]]].<br />
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* (12.02.24) Chapter 2.1.3 from [[#wainwright|[Wainwright]]]. Orlicz norms, see Chapter 2.5 from [[#vershynin|[Vershynin]]].<br />
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* (19.02.24) Orlicz norms, see Chapter 2.5 from [[#vershynin|[Vershynin]]]. Sanov's theorem and KL-divergence, Chapter 6.2 from [[#Weissman |[Weissman]]].<br />
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* (26.02.24) 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]]]). Concentration of Gaussian Lipschitz functions.<br />
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* (05.03.24) Uniform Johnson-Lindenstrauss lemma (Theorem 5.10 from [[#blm|[BLM]]]). A modified logarithmic Sobolev inequality (Theorem 6.7 from [[#blm|[BLM]]]).<br />
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* (12.03.24) 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 />
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* (17.03.24) Matrix Chernoff from PSD matrices (Theorem 5.1.1 from [[#Tropp |[Tropp]]]). Application to graph sparsifying (Chapter 32 from [[#Spielman | [Spielman]]]).<br />
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== Grading ==<br />
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The final grade is obtained as follows:<br />
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0.2 HW HDP + 0.3 Midterm HDP + 0.2 HW HDS + 0.3 Exam HDS,<br />
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where HW stands for home assignment, HDP stands for High-Dimensional Probability, HDS stands for High-Dimensional Statistics.<br />
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== Midterm ==<br />
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See the midterm program [https://disk.yandex.ru/i/Xd6yWNDGpXRu8Q here].<br />
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== Home assignments ==<br />
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Please, send your solutions to [https://classroom.google.com/c/NzQ3Njg2NjQ0NTc2?cjc=h6qefgx Google classroom].<br />
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* [https://classroom.google.com/c/NzQ3Njg2NjQ0NTc2/a/NzQ5NjY1OTM0Nzg0/details Optional home assignment I]. The deadline is April, 6, 23:59.<br />
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* [https://classroom.google.com/c/NzQ3Njg2NjQ0NTc2/a/NzYyNTY4MzE1OTU3/details Obligatory home assignment I]. The deadline is March 30, 23:59.<br />
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* [https://classroom.google.com/c/NzQ3Njg2NjQ0NTc2/a/NzY2NzM4MTgxNTIz/details Obligatory home assignment II]. The deadline is June 22, 23:59.<br />
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= References =<br />
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<b>links are available via hse accounts</b><br />
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<span id="van_handel">[van Handel]</span> [https://disk.yandex.ru/i/GPfpvZt7lSf7Bg Ramon van Handel. Probability in High Dimensions, Lecture Notes]<br />
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<span id="vershynin">[Vershynin]</span> [https://disk.yandex.ru/i/ci_c_FW5-eXH-A R. Vershynin. High-Dimensional Probability]<br />
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<span id="wainwright">[Wainwright]</span> [https://disk.yandex.ru/i/4RUmUDj3--sNOQ M.J. Wainwright. High-Dimensional Statistics]<br />
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<span id="blm">[BLM]</span> [https://disk.yandex.ru/i/7GOknoh1HYGEJQ Boucheron et al. Concentration inequalities]<br />
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<span id="rigollet">[Rigollet]</span> [https://disk.yandex.ru/i/GW7kFWmdsrfClA Philippe Rigollet and Jan-Christian H¨utter. High-Dimensional Statistics. Lecture Notes]<br />
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<span id="paris">[Paris]</span> [https://disk.yandex.ru/i/CeIEx0MW2hpbrw Quentin Paris. Statistical Learning Theory. Lecture Notes]<br />
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<span id="EvansPDE">[EvansPDE]</span> [https://disk.yandex.ru/i/cCHL2bbbr0V-7Q Lawrence Evans. Partial Differential Equations]<br />
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<span id="Ziemer">[Ziemer]</span> [https://disk.yandex.ru/i/1aMzdRyaMZixCQ William Ziemer. Weakly Differentiable Equations]<br />
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<span id="Weissman">[Weissman]</span> [https://disk.yandex.ru/i/OPDZenkw-OPSAA Tsachy Weissman. Information theory, Lecture notes]<br />
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<span id="Tropp">[Tropp]</span> [https://disk.yandex.ru/i/nzHbi_l_SALkew Joel Tropp. An Introduction to Matrix Concentration Inequalities]<br />
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<span id="Spielman">[Spielman]</span> [https://disk.yandex.ru/i/BIqcuUz1yZb0Cg Daniel Spielman. Spectral and Algebraic Graph Theory]</div>
imported>Fedor.Noskov