Bayesian Pseudo-Coresets via Contrastive Divergence
Piyush Tiwary, Kumar Shubham, Vivek V. Kashyap, Prathosh A. P
TL;DR
The paper tackles slow Bayesian inference on large datasets by proposing Bayesian Pseudo-Coresets (BPC) learned via contrastive divergence. This approach eliminates the need to approximate the pseudo-coreset posterior and enables finite-step MCMC during learning, improving efficiency and posterior fidelity. Empirical results across six datasets show substantial improvements over state-of-the-art BPC methods in accuracy, NLL, and posterior calibration, including robustness to distribution shifts and cross-architecture generalization. The work advances scalable, privacy-friendly Bayesian inference with practical impact for large-scale probabilistic modeling.
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.