Abstract

Efficient sampling from complex non-log-concave distributions is a cornerstone of statistical computing and machine learning, yet it is challenged by stringent isoperimetric conditions and high computational costs. Traditional methods often suffer from exponential gradient complexity, limiting their applicability to a broad array of problems.  In this talk, we present RS-DMC, a novel advancement in Diffusion-based Monte Carlo (DMC) algorithms that transcends these limitations by introducing a recursive score estimation technique.  By dissecting the diffusion process into manageable segments, RS-DMC addresses sampling through interconnected mean estimation and sampling subproblems, each efficiently solvable under strongly log-concave distributions. This methodological innovation not only significantly reduces the gradient complexity to a quasi-polynomial dependency on the error tolerance $\epsilon$, but also establishes a new benchmark in sampling efficiency for distributions without isoperimetry condition, which is commonly required in previous works. This talk will delve into the algorithm's design and the rigorous proof details that underpin our theoretical framework, and introduces some new directions that can be explored accordingly.

Time

2024-04-15  15:30 - 16:30   

Speaker

Difan Zou, The University of Hong Kong

Room

Room 308