Bayesian Pseudo-Coresets via Contrastive Divergence

TL;DR

This paper introduces a new method for constructing Bayesian pseudo-coresets using contrastive divergence, which simplifies the process and improves efficiency by avoiding approximations and enabling finite-step MCMC sampling.

Contribution

The paper proposes a novel contrastive divergence-based approach for building pseudo-coresets, eliminating the need for approximate distributions and enabling faster MCMC sampling in high-dimensional spaces.

Findings

Outperforms existing Bayesian pseudo-coreset methods in experiments

Reduces inference time significantly

Maintains high posterior approximation accuracy

Abstract

Bayesian methods provide an elegant framework for estimating parameter posteriors and quantification of uncertainty associated with probabilistic models. However, they often suffer from slow inference times. To address this challenge, Bayesian Pseudo-Coresets (BPC) have emerged as a promising solution. BPC methods aim to create a small synthetic dataset, known as pseudo-coresets, that approximates the posterior inference achieved with the original dataset. This approximation is achieved by optimizing a divergence measure between the true posterior and the pseudo-coreset posterior. Various divergence measures have been proposed for constructing pseudo-coresets, with forward Kullback-Leibler (KL) divergence being the most successful. However, using forward KL divergence necessitates sampling from the pseudo-coreset posterior, often accomplished through approximate Gaussian variational distributions. Alternatively, one could employ Markov Chain Monte Carlo (MCMC) methods for sampling, but this becomes challenging in high-dimensional parameter spaces due to slow mixing. In this study, we introduce a novel approach for constructing pseudo-coresets by utilizing contrastive divergence. Importantly, optimizing contrastive divergence eliminates the need for approximations in the pseudo-coreset construction process. Furthermore, it enables the use of finite-step MCMC methods, alleviating the requirement for extensive mixing to reach a stationary distribution. To validate our method's effectiveness, we conduct extensive experiments on multiple datasets, demonstrating its superiority over existing BPC techniques.