Robust and Scalable Bayes via a Median of Subset Posterior Measures

TL;DR

This paper introduces a robust Bayesian method that splits data into subgroups, computes individual posteriors, and combines them using a median-based aggregation, offering robustness to outliers and computational benefits.

Contribution

The paper presents a novel median-based aggregation technique for combining subset posteriors, enhancing robustness and efficiency in Bayesian analysis.

Findings

Improved robustness to outliers in Bayesian inference.

Enhanced computational efficiency over traditional methods.

Theoretical guarantees and numerical validation of the approach.

Abstract

We propose a novel approach to Bayesian analysis that is provably robust to outliers in the data and often has computational advantages over standard methods. Our technique is based on splitting the data into non-overlapping subgroups, evaluating the posterior distribution given each independent subgroup, and then combining the resulting measures. The main novelty of our approach is the proposed aggregation step, which is based on the evaluation of a median in the space of probability measures equipped with a suitable collection of distances that can be quickly and efficiently evaluated in practice. We present both theoretical and numerical evidence illustrating the improvements achieved by our method.