Brief Description: This is a class on the precise analysis of high-dimensional optimization problems arising from statistics, learning, and other areas using probabilistic tools. A main conceptual focus is the relationship between computational/constructive vs statistical/existential tractability. Techniques related to statistical physics (e.g. AMP), combinatorial and nonconvex optimization, and gaussian processes will be covered.
Prerequisites: mathematical maturity, foundational knowledge of probability (e.g. martingales). Additional background from e.g. optimization, algorithms, complexity, high-dimensional statistics helpful but not strictly required.