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 | |
| 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.) | |
| 22-24 |
Student presentation |
| Homework 1 | due in class on | Tuesday, 10 February |
| Homework 2 | Tuesday, 10 March | |
| Homework 3 | Tuesday, 7 April |