Convergence of coordinate ascent variational inference for log-concave measures via optimal transport

arXiv:2404.08792v1 Announce Type: cross
Abstract: Mean field variational inference (VI) is the problem of finding the closest product (factorized) measure, in the sense of relative entropy, to a given high-dimensional probability measure $\rho$. The well known Coordinate Ascent Variational Inference (CAVI) algorithm aims to approximate this product measure by iteratively optimizing over one coordinate (factor) at a time, which can be done explicitly. Despite its popularity, the convergence of CAVI remains poorly understood. In this paper, we prove the convergence …

abstract algorithm arxiv convergence cs.lg entropy inference math.oc math.pr math.st mean probability product sense stat.ml stat.th transport type via