A1311
Title: Robust variational Bayes by min-max median aggregation
Authors: Jiyuan Tu - Shanghai University of Finance and Economics (China) [presenting]
Abstract: A robust and scalable variational Bayes (VB) framework is proposed that is designed to effectively handle contamination and outliers in datasets. The approach partitions the data into m disjoint subsets and formulates a joint optimization problem based on robust aggregation principles. A key insight is that the full posterior distribution is equivalent to the minimizer of the mean Kullback-Leibler (KL) divergence from the m-powered local posterior distributions. To enhance robustness, the mean KL divergence is replaced with a min-max median formulation. A notable discrepancy is observed in the m-powered marginal log likelihood function contingent on the presence of local latent variables. To address this, these two scenarios are treated separately to guarantee the consistency of the aggregated variational posterior. Specifically, when local latent variables are present, an aggregate-and-rescale strategy is introduced. Theoretically, a refined analysis of Bernstein-von Mises (BvM) theorem is provided to accommodate a diverging number of subsets m. The findings indicate that the two-stage approach yields a smaller approximation error compared to directly aggregating the m-powered local posteriors. Furthermore, a nearly optimal statistical rate for the mean of the proposed posterior is established, advancing existing theories related to min-max median estimators. The efficacy of the method is demonstrated through extensive simulation studies.
