On Divergence Measures for Bayesian Pseudocoresets
This work addresses the scalability of Bayesian inference for practitioners in machine learning, though it is incremental as it builds on existing dataset distillation and pseudocoreset methods.
The paper tackles the problem of constructing Bayesian pseudocoresets for scalable inference in high-dimensional settings, such as image classification with deep neural networks, by unifying dataset distillation methods under divergence measures and proposing a new algorithm based on forward KL divergence, with empirical results showing that these pseudocoresets accurately reflect the true posterior.
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.