STAT 37797: Syllabus

A tentative one:

1. Spectral methods

   1. Classic L2 matrix perturbation theory

   2. Matrix concentration inequalities

   3. Applications of spectral methods (L2 theory)

   4. Linf matrix perturbation theory

   5. Applications of spectral methods (Linf theory)

2. Nonconvex optimization

   1. Basic optimization theory

   2. Generic local analysis for regularized gradient descent (GD)

   3. Refined local analysis for vanilla GD

   4. Global landscape analysis

   5. Gradient descent with random initialization

3. Convex relaxation

   1. Compressed sensing and sparse recovery

   2. Phase transition and convex geometry

   3. Low-rank matrix recovery

   4. Robust principal component analysis

4. Minimax lower bounds