Parallel MCMC Without Embarrassing Failures
This addresses a critical reliability issue in scalable Bayesian inference for large datasets, though it is an incremental improvement over existing parallel MCMC frameworks.
The paper tackles the problem of catastrophic failures in embarrassingly parallel MCMC due to poor subposterior sampling, proposing Parallel Active Inference (PAI) which uses Gaussian Process surrogates and active learning to mitigate these issues. Empirical results show PAI succeeds where previous methods fail, with small communication overhead.
Embarrassingly parallel Markov Chain Monte Carlo (MCMC) exploits parallel computing to scale Bayesian inference to large datasets by using a two-step approach. First, MCMC is run in parallel on (sub)posteriors defined on data partitions. Then, a server combines local results. While efficient, this framework is very sensitive to the quality of subposterior sampling. Common sampling problems such as missing modes or misrepresentation of low-density regions are amplified -- instead of being corrected -- in the combination phase, leading to catastrophic failures. In this work, we propose a novel combination strategy to mitigate this issue. Our strategy, Parallel Active Inference (PAI), leverages Gaussian Process (GP) surrogate modeling and active learning. After fitting GPs to subposteriors, PAI (i) shares information between GP surrogates to cover missing modes; and (ii) uses active sampling to individually refine subposterior approximations. We validate PAI in challenging benchmarks, including heavy-tailed and multi-modal posteriors and a real-world application to computational neuroscience. Empirical results show that PAI succeeds where previous methods catastrophically fail, with a small communication overhead.