High-dimensional Probability and Statistics — различия между версиями
Материал из Wiki - Факультет компьютерных наук
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* (17.01.24) Example 2.4 from [[#wainwright|[Wainwright]]], Lemma 2.2 from [[#blm|[BLM]]] | * (17.01.24) Example 2.4 from [[#wainwright|[Wainwright]]], Lemma 2.2 from [[#blm|[BLM]]] | ||
− | * (24. | + | * (24.01.24) Appendix A and Exercise 2.2 of the second chapter of [[#wainwright|[Wainwright]]], Section 2.5.1 from [[#vershynin|[Vershynin]]] |
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+ | * (31.01.24) Section 2.1.3 and Example 2.12 from [[#wainwright|[Wainwright]]] | ||
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+ | * (07.02.24) Section 2.3 from [[#wainwright|[Wainwright]]] | ||
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+ | * (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]]]) | ||
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+ | * (07.03.24) PAC-Bayesian inequality. (Lemma 2.1 from [[#zhivotovsky | [Zhivotovsky]]]) | ||
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+ | * (14.03.24) Dimension-free concentration of sample covariance matrix in the spectral norm (Theorem 1.2 of [[#zhivotovsky | [Zhivotovsky]]]) | ||
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+ | * (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]]]) | ||
= References = | = References = | ||
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<span id="blm">[BLM]</span> [https://disk.yandex.ru/i/7GOknoh1HYGEJQ Boucheron et al. Concentration inequalities] | <span id="blm">[BLM]</span> [https://disk.yandex.ru/i/7GOknoh1HYGEJQ Boucheron et al. Concentration inequalities] | ||
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+ | <span id="zhivotovsky">[Zhivotovsky]</span> [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.] |
Текущая версия на 15:26, 21 марта 2024
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