MH7009 High-Dimensional Probability
AY25/26 Semester 2

Some of the lecture notes contain citations, and here is the list of references. Access to lecture notes requires logging with your NTU account.

Lecture Date Content File
1 Jan 12 Introduction, central limit theorem, Berry-Esseen Theorem, exponentiation trick pdf
2 Jan 13 Subgaussian random variables
3 Jan 19 Subgaussian variables (cont.), subexponential variables
4 Jan 20 Subexponential variables (cont.)
5 Jan 26 Concentration of measure on unit sphere, Boolean cube and Gaussian space, concentration of Lipschitz functions
6 Jan 27 Concentraton of Lipschitz functions on unit sphere and Gaussian space without using isoperimetric inequalities
7 Feb 2 Johnson-Lindenstrauss Lemma
8 Feb 3 Isotropic random vectors, subgaussian random vectors
9 Feb 9 Matrix Bernstein inequality
10 Feb 10 Matrix Bernstein inequality (based on Golden-Thompson and Lieb's Inequality)
  Feb 16 Chinese New Year's Eve. No class.
  Feb 17 Chinese New Year. No class.
11 Feb 23 Applications of matrix concentration: covariance estimation, leverage score sampling
12 Feb 24 leverage score sampling (cont.), matrix sparsification
  Mar 2 Recess week. No class.
  Mar 3 Recess week. No class.
13 Mar 9 Non-commutative Khintchine inequality, symmetrization trick
14 Mar 10 Application to covariance matrix estimation
15 Mar 16 Extreme singular values of Gaussian random matrices: comparison inequalities
16 Mar 17 Extreme singular values of Gaussian random matrices: comparison inequalities (cont.)
17 Mar 23 Extreme singular values of random matrices of independent rows: net argument
18 Mar 24 Hanson-Wright inequality: decoupling
19 Mar 30 Dudley's integral, Sudakov's minorization
20 Mar 31 Generic chaining, examples showing that generic chaining is better than Dudley's integral
21 Apr 6 Examples showing that generic chaining is better than Dudley's integral (cont.)
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Student presentation

Homework

Homework 1 due in class on Tuesday, 10 February
Homework 2 Tuesday, 10 March
Homework 3 Tuesday, 7 April