A Forest Mixture Bound for Block-Free Parallel Inference

TL;DR

This paper introduces the forest mixture bound, a novel lower bound for variational inference that enables stable, block-free parallel inference in deep exponential families, improving convergence speed especially for forest-like models.

Contribution

It proposes a new forest mixture bound that allows parallel inference without variable partitioning, enhancing stability and speed in deep exponential family models.

Findings

Faster convergence for forest-like models.

Stable parallel inference without variable partitioning.

Effective in Gaussian variable cases.

Abstract

Coordinate ascent variational inference is an important algorithm for inference in probabilistic models, but it is slow because it updates only a single variable at a time. Block coordinate methods perform inference faster by updating blocks of variables in parallel. However, the speed and stability of these algorithms depends on how the variables are partitioned into blocks. In this paper, we give a stable parallel algorithm for inference in deep exponential families that doesn't require the variables to be partitioned into blocks. We achieve this by lower bounding the ELBO by a new objective we call the forest mixture bound (FM bound) that separates the inference problem for variables within a hidden layer. We apply this to the simple case when all random variables are Gaussian and show empirically that the algorithm converges faster for models that are inherently more forest-like.