Split Variational Inference

Abstract

We propose a deterministic method to evaluate the integral of a positive function based on soft-binning functions that smoothly cut the integral into smaller integrals that are easier to approximate. The use of mean-field approximations for each individual sub-part leads to a tractable algorithm that alternates between the optimization of the bins and the approximation of the local integrals. We introduce suitable choices for the binning functions such that a standard mean field approximation can be extended to a split mean field approximation without the need for extra derivations. The method can be seen as a revival of the ideas underlying the mixture mean field approach. We discuss the relation between the two algorithms.