Diffusion Generative Modelling for Divide-and-Conquer MCMC
This addresses a bottleneck in parallelizing MCMC for large datasets, offering a more efficient merging solution, though it appears incremental as it builds on existing divide-and-conquer frameworks.
The paper tackles the challenge of efficiently merging subposterior distributions in divide-and-conquer MCMC without distributional assumptions, proposing diffusion generative modelling for density approximations, which outperforms existing methods and scales better computationally in high dimensions.
Divide-and-conquer MCMC is a strategy for parallelising Markov Chain Monte Carlo sampling by running independent samplers on disjoint subsets of a dataset and merging their output. An ongoing challenge in the literature is to efficiently perform this merging without imposing distributional assumptions on the posteriors. We propose using diffusion generative modelling to fit density approximations to the subposterior distributions. This approach outperforms existing methods on challenging merging problems, while its computational cost scales more efficiently to high dimensional problems than existing density estimation approaches.