6.S891: Algorithmic Counting and Sampling

Fall 2023, Graduate special topics course

This course introduces the modern theory of algorithms for sampling from high-dimensional probability distributions and estimating their partition functions. These fundamental algorithmic primitives lie at the foundation of statistics, physics, and machine learning. We will study a diverse set of algorithmic paradigms for solving these problems based on Markov chains, decay of correlations, geometry of polynomials, and more. We will further study the rich set of analytic, probabilistic, and algebraic tools used to give performance guarantees to these algorithms.