Parallel Discrete Sampling via Continuous Walks

Explore a groundbreaking framework for sampling from discrete distributions on the hypercube through continuous distributions in this 57-minute lecture by Nima Anari from Stanford University. Delve into the process of convolving discrete distributions with spherical Gaussians to yield well-conditioned log-concave distributions. Learn about the novel discretization of the stochastic localization process, enabling high accuracy and parallelism in sampling. Discover how this approach resolves open questions on parallel sampling of distributions that allow parallel counting, leading to the first polylogarithmic-time sampling algorithms for determinantal point processes, directed Eulerian tours, and more.