Approximate Decentralized Bayesian Inference

TL;DR

This paper introduces an approximate decentralized Bayesian inference method that improves computational efficiency and predictive accuracy by accounting for broken dependencies during local posterior combination in a network of agents.

Contribution

It proposes a novel optimization step in combining local posteriors to preserve dependencies, enhancing decentralized Bayesian inference accuracy.

Findings

Outperforms previous methods in predictive test likelihood.

Reduces computational costs compared to batch and distributed approaches.

Effective on both synthetic and real datasets.

Abstract

This paper presents an approximate method for performing Bayesian inference in models with conditional independence over a decentralized network of learning agents. The method first employs variational inference on each individual learning agent to generate a local approximate posterior, the agents transmit their local posteriors to other agents in the network, and finally each agent combines its set of received local posteriors. The key insight in this work is that, for many Bayesian models, approximate inference schemes destroy symmetry and dependencies in the model that are crucial to the correct application of Bayes' rule when combining the local posteriors. The proposed method addresses this issue by including an additional optimization step in the combination procedure that accounts for these broken dependencies. Experiments on synthetic and real data demonstrate that the decentralized method provides advantages in computational performance and predictive test likelihood over previous batch and distributed methods.