Boosting Variational Inference

TL;DR

Boosting Variational Inference (BVI) introduces a flexible mixture-based approach that iteratively enhances posterior approximations, capturing complex distributions more effectively than traditional VI methods.

Contribution

The paper proposes BVI, a novel gradient boosting-inspired algorithm that improves variational inference by using mixture models to better approximate complex posteriors.

Findings

BVI captures multimodal posteriors effectively.

BVI outperforms mean-field VI in complex distribution scenarios.

Progressively improves approximation quality with more iterations.

Abstract

Variational inference (VI) provides fast approximations of a Bayesian posterior in part because it formulates posterior approximation as an optimization problem: to find the closest distribution to the exact posterior over some family of distributions. For practical reasons, the family of distributions in VI is usually constrained so that it does not include the exact posterior, even as a limit point. Thus, no matter how long VI is run, the resulting approximation will not approach the exact posterior. We propose to instead consider a more flexible approximating family consisting of all possible finite mixtures of a parametric base distribution (e.g., Gaussian). For efficient inference, we borrow ideas from gradient boosting to develop an algorithm we call boosting variational inference (BVI). BVI iteratively improves the current approximation by mixing it with a new component from the base distribution family and thereby yields progressively more accurate posterior approximations as more computing time is spent. Unlike a number of common VI variants including mean-field VI, BVI is able to capture multimodality, general posterior covariance, and nonstandard posterior shapes.