Scalable and Robust Bayesian Inference via the Median Posterior

Many Bayesian learning methods for massive data benefit from working with small subsets of observations. In particular, significant progress has been made in scalable Bayesian learning via stochastic approximation. However, Bayesian learning methods in distributed computing environments are often problem- or distributionspecific and use ad hoc techniques. We propose a novel general approach to Bayesian inference that is scalable and robust to corruption in the data. Our technique is based on the idea of splitting the data into several non-overlapping subgroups, evaluating the posterior distribution given each independent subgroup, and then combining the results. Our main contribution is the proposed aggregation step which is based on finding the geometric median of subset posterior distributions. Presented theoretical and numerical results confirm the advantages of our approach.