ABSTRACT:

The task of sampling from a given density is a fundamental computational task with numerous applications in machine learning and statistics​. In the last decade, the iteration complexity of sampling from a smooth and (strongly) log-concave density​​ has been well-studied.​However, handling more complex​ multi-model and heavy-tailed densities arising in practice is relatively less understood. In this talk, I will discuss some recent progress in this direction. ​In the first part of this talk, I will discuss a recently proposed framework for establishing the iteration complexity of​the widely used Langevin Monte Carlo ​sampling​algorithm ​when the target density satisfies only the relatively milder Holder-smoothness assumption​​. Motivated by the theory of non-convex optimization, our guarantees are for converging to an appropriately defined first-order stationary solution for sampling. I will also discuss several extensions and applications of our result; in particular, it yields a new state-of-the-art guarantee for sampling from distributions which satisfy a Poincare inequality. ​In the second part of the talk, I will discuss guarantees for appropriately modified versions of the Langevin Monte Carlo ​sampling ​algorithm for sampling from heavy-tailed densities, i.e., densities that decay polynomially at the tails. These guarantees are established for the stronger Renyi metric.

BIO:

Krishna Balasubramanian is an assistant professor in the Department of Statistics, University of California, Davis. His research interests include stochastic optimization and sampling, network analysis, and non-parametric statistics. His research was/is supported by a Facebook PhD fellowship, and CeDAR and NSF grants.

Hosted by Professor Quanquan Gu