On Divergence Measures for Bayesian Pseudocoresets

TL;DR

This paper explores divergence measures for constructing Bayesian pseudocoresets, proposing a new algorithm based on forward KL divergence, and demonstrates their effectiveness in high-dimensional Bayesian inference tasks.

Contribution

It unifies divergence-based approaches for Bayesian pseudocoreset construction and introduces a novel method using forward KL divergence.

Findings

Pseudocoresets reflect the true posterior in high-dimensional problems

Existing divergence measures can be interpreted within a unified framework

The new forward KL-based method performs well in empirical tests

Abstract

A Bayesian pseudocoreset is a small synthetic dataset for which the posterior over parameters approximates that of the original dataset. While promising, the scalability of Bayesian pseudocoresets is not yet validated in realistic problems such as image classification with deep neural networks. On the other hand, dataset distillation methods similarly construct a small dataset such that the optimization using the synthetic dataset converges to a solution with performance competitive with optimization using full data. Although dataset distillation has been empirically verified in large-scale settings, the framework is restricted to point estimates, and their adaptation to Bayesian inference has not been explored. This paper casts two representative dataset distillation algorithms as approximations to methods for constructing pseudocoresets by minimizing specific divergence measures: reverse KL divergence and Wasserstein distance. Furthermore, we provide a unifying view of such divergence measures in Bayesian pseudocoreset construction. Finally, we propose a novel Bayesian pseudocoreset algorithm based on minimizing forward KL divergence. Our empirical results demonstrate that the pseudocoresets constructed from these methods reflect the true posterior even in high-dimensional Bayesian inference problems.