Alpha-Beta Divergence For Variational Inference

TL;DR

This paper proposes a new variational inference framework using the scale invariant Alpha-Beta divergence, enabling flexible trade-offs between different divergence properties and improving Bayesian regression models.

Contribution

Introduces the sAB divergence as a unified variational objective with interpretable control parameters, allowing direct optimization and broader divergence exploration.

Findings

Enhanced robustness to outliers in Bayesian models

Flexible interpolation between divergence measures

Improved variational inference performance

Abstract

This paper introduces a variational approximation framework using direct optimization of what is known as the {\it scale invariant Alpha-Beta divergence} (sAB divergence). This new objective encompasses most variational objectives that use the Kullback-Leibler, the R{\'e}nyi or the gamma divergences. It also gives access to objective functions never exploited before in the context of variational inference. This is achieved via two easy to interpret control parameters, which allow for a smooth interpolation over the divergence space while trading-off properties such as mass-covering of a target distribution and robustness to outliers in the data. Furthermore, the sAB variational objective can be optimized directly by repurposing existing methods for Monte Carlo computation of complex variational objectives, leading to estimates of the divergence instead of variational lower bounds. We show the advantages of this objective on Bayesian models for regression problems.