High Dimensional Probability

Time: Tuesday, Thursday 10:30am - 11:45am

Location: Maxwell Dworkin 119

TA: Jarosław Błasiok (jblasiok (at) g.harvard.edu)

Course Description

CS 229 is a graduate course in probability theory. The primary focus will be on concentration of measure, random matrices and their applications to computer science and statistics.


I have decided to type up some lecture notes so that you can focus on the material in class rather than scrambling to write everything on the board. I will make the corresponding notes available after each lecture.

Lecture Notes

  • Lecture 1 (Introduction) 1/29/2019
  • Lecture 2 (Proofs of the Central Limit Theorem) 1/31/2019
  • Lecture 3 (Proofs of the Central Limit Theorem II- Stein's Method) 2/5/2019
  • Lecture 4 (Subgaussian Random Variables) 2/7/2019
  • Lecture 5 (Anti-concentration I) 2/12/2019
  • Lecture 6 (Anti-concentration II) 2/14/2019
  • Lecture 7 (Norm of a Random Matrix) 2/19/2019
  • Lecture 8 (Condition Number of Random Matrices) 2/21/2019
  • Lecture 9 (Martingales, Bounded Differences & Talagrand's Inequality) 2/26/2019
  • Lecture 10 (Applications) 2/28/2019
  • Lecture 11 (Empirical Processes) 3/5/2019
  • Lecture 12 (Chaining) 3/7/2019
  • Lecture 13 (Compressed Sensing) (3/12/2019)
  • Lecture 14 (Subsampling Fourier Matrices) (3/14/2019)
  • Lecture 15 (Simplicity of Spectrum and Graph Isomorphism) (3/26/2019)
  • Lecture 16 (Sums of Random Matrices) (3/28 /2019)
  • Lecture 17 (Basic Tensor Theory) (4/2/2019)
  • Lecture 18 (Basic Tensory Theory II) (4/4/2019) Notes coming soon!
  • Lecture 19 (Guest Lecture: Prayaag Venkat on Mean Estimation) (4/9/2019)
  • Lecture 20 (Polynomial Threshold Functions and Random Tensors) (4/11/2019)


Homework Assignments