Constructing Bayesian Pseudo-Coresets using Contrastive Divergence

Bayesian Pseudo-Coreset (BPC) and Dataset Condensation are two parallel streams of work that construct a synthetic set such that, a model trained independently on this synthetic set, yields the same performance as training on the original training set. While dataset condensation methods use non-bayesian, heuristic ways to construct such a synthetic set, BPC methods take a bayesian approach and formulate the problem as divergence minimization between posteriors associated with original data and synthetic data. However, BPC methods generally rely on distributional assumptions on these posteriors which makes them less flexible and hinders their performance. In this work, we propose to solve these issues by modeling the posterior associated with synthetic data by an energy-based distribution. We derive a contrastive-divergence-like loss function to learn the synthetic set and show a simple and efficient way to estimate this loss. Further, we perform rigorous experiments pertaining to the proposed method. Our experiments on multiple datasets show that the proposed method not only outperforms previous BPC methods but also gives performance comparable to dataset condensation counterparts.