High-dimensional Probability and Statistics
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Версия от 15:26, 21 марта 2024; Fedor.Noskov (обсуждение | вклад)
Содержание
Classes
Wednesdays 16:20–17:40, in room R307.
Teachers: Alexey Naumov, Quentin Paris
Teaching Assistant: Fedor Noskov
Lecture content
- (17.01.24) Chapter 1 from [van Handel]
Seminar content
- (17.01.24) Example 2.4 from [Wainwright], Lemma 2.2 from [BLM]
- (24.01.24) Appendix A and Exercise 2.2 of the second chapter of [Wainwright], Section 2.5.1 from [Vershynin]
- (31.01.24) Section 2.1.3 and Example 2.12 from [Wainwright]
- (07.02.24) Section 2.3 from [Wainwright]
- (24.02.24) Herbst's argument (Proposition 3.2 from [Wainwright]), Sub-additivity of the entropy (Theorem 4.22 from [BLM]), logorithmic Sobolev inequality for Gaussian random variables (Theorem 5.5 from [BLM])
- (07.03.24) PAC-Bayesian inequality. (Lemma 2.1 from [Zhivotovsky])
- (14.03.24) Dimension-free concentration of sample covariance matrix in the spectral norm (Theorem 1.2 of [Zhivotovsky])
- (21.03.24) Theorem 1.2 of [Zhivotovsky], Concentration of Lipshitz and separately convex function of bounded random variables (Theorem 6.10 from [BLM]), Concentration of the supremum of an empirical process (Section 3.4 of [Wainwright])
References
links are available via hse accounts
[van Handel] Ramon van Handel. Probability in High Dimensions, Lecture Notes
[Vershynin] R. Vershynin. High-Dimensional Probability
[Wainwright] M.J. Wainwright. High-Dimensional Statistics