Extending Mean-Field Variational Inference via Entropic Regularization: Theory and Computation

arXiv:2404.09113v1 Announce Type: cross
Abstract: Variational inference (VI) has emerged as a popular method for approximate inference for high-dimensional Bayesian models. In this paper, we propose a novel VI method that extends the naive mean field via entropic regularization, referred to as $\Xi$-variational inference ($\Xi$-VI). $\Xi$-VI has a close connection to the entropic optimal transport problem and benefits from the computationally efficient Sinkhorn algorithm. We show that $\Xi$-variational posteriors effectively recover the true posterior dependency, where the dependence is downweighted …

abstract approximate inference arxiv bayesian computation cs.lg inference math.st mean novel paper popular regularization stat.ml stat.th theory type via