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= Classes =

Wednesdays 16:20–17:40, in room R307.

Teachers: [https://www.hse.ru/en/staff/anaumov Alexey Naumov], [https://www.hse.ru/en/org/persons/133709471 Quentin Paris]

Teaching Assistant: [https://t.me/teddy_nos Fedor Noskov]

= Lecture content =

* (17.01.24) Chapter 1 from [[#van_handel|[van Handel]]]

= Seminar content =

=== Probability ===

* (17.01.24) Example 2.4 from [[#wainwright|[Wainwright]]], Lemma 2.2 from [[#blm|[BLM]]]

* (24.01.24) Appendix A and Exercise 2.2 of the second chapter of [[#wainwright|[Wainwright]]], Section 2.5.1 from [[#vershynin|[Vershynin]]]

* (31.01.24) Section 2.1.3 and Example 2.12 from [[#wainwright|[Wainwright]]]

* (07.02.24) Section 2.3 from [[#wainwright|[Wainwright]]]

* (24.02.24) Herbst's argument (Proposition 3.2 from [[#wainwright|[Wainwright]]]), Sub-additivity of the entropy (Theorem 4.22 from [[#blm|[BLM]]]), logorithmic Sobolev inequality for Gaussian random variables (Theorem 5.5 from [[#blm|[BLM]]])

* (07.03.24) PAC-Bayesian inequality. (Lemma 2.1 from [[#zhivotovsky | [Zhivotovsky]]])

* (14.03.24) Dimension-free concentration of sample covariance matrix in the spectral norm (Theorem 1.2 of [[#zhivotovsky | [Zhivotovsky]]])

* (21.03.24) Theorem 1.2 of [[#zhivotovsky | [Zhivotovsky]]], Concentration of Lipshitz and separately convex function of bounded random variables (Theorem 6.10 from [[#blm|[BLM]]]), Concentration of the supremum of an empirical process (Section 3.4 of [[#wainwright|[Wainwright]]])

=== Statistics ===

* (10.04.24) Linear Regression. Bayesian information criterion. (Theorem 2.4 from [[#rigollet | [Rigollet]]])

* (17.04.24) Restricted isometry property and epsilon-incoherence. (Incoherence section, pp.59-62 of [[#rigollet | [Rigollet]]])

* (24.04.24) Incoherence of a random matrix with independent Rademacher entries (Incoherence section, pp.59-62 of [[#rigollet | [Rigollet]]]). Empirical risk minimization and Rademacher complexity (Sections 4.1-4.2 of [[#wainwright|[Wainwright]]]). Bounds on the Rademacher complexity of finite and finite-dimensional classes can be found in [[#paris | [Paris]]], Theorems 6.1 and 6.3.

* (15.05.24) VC-dimension, Sauer's lemma. (Section 4.3 of [[#wainwright|[Wainwright]]]).

* (22.05.24) Packing-covering duality. (Lemma 5.12 of [[#van_handel|[van Handel]]]). Uniform bound on the metric entropy via VC-dimension (Theorem 7.16 of [[#van_handel|[van Handel]]])

* (29.05.24) Uniform bound on the metric entropy via VC-dimension (Theorem 7.16 of [[#van_handel|[van Handel]]])

* (05.06.24) Offset Rademacher Complexity (some parts of [[#puchkin|[Puchkin]]])

= References =

links are available via hse accounts

[van Handel] [https://disk.yandex.ru/i/GPfpvZt7lSf7Bg Ramon van Handel. Probability in High Dimensions, Lecture Notes]

[Vershynin] [https://disk.yandex.ru/i/ci_c_FW5-eXH-A R. Vershynin. High-Dimensional Probability]

[Wainwright] [https://disk.yandex.ru/i/4RUmUDj3--sNOQ M.J. Wainwright. High-Dimensional Statistics]

[BLM] [https://disk.yandex.ru/i/7GOknoh1HYGEJQ Boucheron et al. Concentration inequalities]

[Zhivotovsky] [https://disk.yandex.ru/i/3yAKKiHc73ZSZQ Nikita Zhivotovskiy. Dimension-free bounds for sums of independent matrices and simple tensors via the variational principle. Electron. J. Probab. vol. 29 (2024), article no. 13, 1–28.]

[Rigollet] [https://disk.yandex.ru/i/GW7kFWmdsrfClA Philippe Rigollet and Jan-Christian H¨utter. High-Dimensional Statistics. Lecture Notes]

[Paris] [https://disk.yandex.ru/i/CeIEx0MW2hpbrw Quentin Paris. Statistical Learning Theory. Lecture Notes]

[Puchkin] [https://proceedings.mlr.press/v195/puchkin23a.html Nikita Puchkin, Nikita Zhivotovskiy. Exploring Local Norms in Exp-concave Statistical Learning. COLT 2023]

High-dimensional Probability and Statistics - История изменений

imported>Fedor.Noskov: Migrated current public revision from wiki.cs.hse.ru