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Recent Advances in Non-log-concave and Heavy-tailed Sampling

Krishna Balasubramanian – Assistant Professor, UC Davis

Thu, 19-Jan-2023 / 4:00pm / Packard 202

Abstract

This talk will be about recent advances in the complexity of sampling from non-log-concave and heavy-tailed densities.Taking motivation from the theory of non-convex optimization, first, a framework for establishing the iteration complexity of sampling of the Langevin Monte Carlo (LMC) when the non-log-concave target density satisfies only the relatively milder Holder-smoothness assumption will be discussed. In particular, this approach yields a new state-of-the-art guarantee for sampling with LMC from distributions which satisfy a Poincare inequality. Next, the complexity of sampling from a class of heavy-tailed distributions by discretizing a natural class of Ito diffusions associated with weighted Poincare inequalities will be discussed. Based on a mean-square analysis, we obtain the iteration complexity in the Wasserstein-2 metric for sampling from a class of heavy-tailed target distributions. Our approach takes the mean-square analysis to its limits, i.e., we invariably only require that the target density has finite variance, the minimal requirement for a mean-square analysis.

Bio

Krishna Balasubramanian is an assistant professor in the Department of Statistics, University of California, Davis. His research interests include stochastic optimization and sampling, geometric and topological statistics, and theoretical machine learning. His research was/is supported by a Facebook PhD fellowship, and CeDAR and NSF grants.