Parallelizing MCMC with Random Partition Trees
This addresses the problem of scalable Bayesian inference for large datasets, representing an incremental improvement over existing EP-MCMC methods.
The authors tackled the computational expense of MCMC for large datasets by proposing a new embarrassingly parallel MCMC algorithm called PART, which uses random partition trees to combine subset posterior draws, resulting in improved approximation accuracy and easier resampling as demonstrated in experiments.
The modern scale of data has brought new challenges to Bayesian inference. In particular, conventional MCMC algorithms are computationally very expensive for large data sets. A promising approach to solve this problem is embarrassingly parallel MCMC (EP-MCMC), which first partitions the data into multiple subsets and runs independent sampling algorithms on each subset. The subset posterior draws are then aggregated via some combining rules to obtain the final approximation. Existing EP-MCMC algorithms are limited by approximation accuracy and difficulty in resampling. In this article, we propose a new EP-MCMC algorithm PART that solves these problems. The new algorithm applies random partition trees to combine the subset posterior draws, which is distribution-free, easy to resample from and can adapt to multiple scales. We provide theoretical justification and extensive experiments illustrating empirical performance.