High-dimensional Probability and Statistics (2025)

Classes

Wednesdays 13:00–16:00, in room G110.

Teachers: Fedor Noskov, Quentin Paris

Teaching Assistant: Fedor Noskov

Lecture/Seminar content

Probability

• (15.01.24) Chapter 3.1, Examples 3.5 and 3.14 from [BLM]

• (22.01.24) Chapters 3.6-3.7 from [BLM]. For the Sobolev spaces, weak derivatives and the approximation argument, see Chapters 5.2-5.3 [EvansPDE]. See also Chapters 2.1-2.3 of [Ziemer].

• (29.01.24) Chapter 2.1.2, Proposition 2.14 from [Wainwright]. Concentration of order statistics (folklore).

• (05.02.24) Chapter 2.2 from [Wainwright].

Grading

The final grade is obtained as follows:

0.2 HW HDP + 0.3 Midterm HDP + 0.2 HW HDS + 0.3 Exam HDS,

where HW stands for home assignment, HDP stands for High-Dimensional Probability, HDS stands for High-Dimensional Statistics.

Home assignments

Please, send your solutions to Google classroom.

• Optional home assignment I. The deadline if April, 6, 23:59.

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

[BLM] Boucheron et al. Concentration inequalities

[Rigollet] Philippe Rigollet and Jan-Christian H¨utter. High-Dimensional Statistics. Lecture Notes

[Paris] Quentin Paris. Statistical Learning Theory. Lecture Notes

[EvansPDE] Lawrence Evans. Partial Differential Equations

[Ziemer] William Ziemer. Weakly Differentiable Equations