Embarrassingly parallel MCMC using deep invertible transformations

TL;DR

This paper introduces a novel embarrassingly parallel MCMC method that uses deep invertible transformations to efficiently approximate subposteriors, enabling scalable Bayesian inference with limited communication and high accuracy.

Contribution

The authors propose a new approach employing deep invertible transformations to approximate subposteriors, improving aggregation efficiency and accuracy in parallel MCMC.

Findings

Outperforms state-of-the-art methods in high-dimensional scenarios

Maintains low communication costs while achieving accurate approximations

Effective for heterogeneous and complex subposterior distributions

Abstract

While MCMC methods have become a main work-horse for Bayesian inference, scaling them to large distributed datasets is still a challenge. Embarrassingly parallel MCMC strategies take a divide-and-conquer stance to achieve this by writing the target posterior as a product of subposteriors, running MCMC for each of them in parallel and subsequently combining the results. The challenge then lies in devising efficient aggregation strategies. Current strategies trade-off between approximation quality, and costs of communication and computation. In this work, we introduce a novel method that addresses these issues simultaneously. Our key insight is to introduce a deep invertible transformation to approximate each of the subposteriors. These approximations can be made accurate even for complex distributions and serve as intermediate representations, keeping the total communication cost limited. Moreover, they enable us to sample from the product of the subposteriors using an efficient and stable importance sampling scheme. We demonstrate the approach outperforms available state-of-the-art methods in a range of challenging scenarios, including high-dimensional and heterogeneous subposteriors.