Bayesian cross-validation by parallel Markov Chain Monte Carlo

TL;DR

This paper introduces a parallel MCMC-based cross-validation method for Bayesian models that leverages GPU hardware to significantly reduce computation time, enabling scalable and flexible model assessment.

Contribution

It presents a novel parallel MCMC approach for Bayesian cross-validation that is fast, flexible, and scalable, with new diagnostics for MCMC convergence and stationarity.

Findings

Parallel MCMC can match the speed of a single model fit.

The method supports various data partitioning schemes and scoring rules.

Online algorithms enable scaling to large datasets on memory-limited hardware.

Abstract

Brute force cross-validation (CV) is a method for predictive assessment and model selection that is general and applicable to a wide range of Bayesian models. Naive or `brute force' CV approaches are often too computationally costly for interactive modeling workflows, especially when inference relies on Markov chain Monte Carlo (MCMC). We propose overcoming this limitation using massively parallel MCMC. Using accelerator hardware such as graphics processor units (GPUs), our approach can be about as fast (in wall clock time) as a single full-data model fit. Parallel CV is flexible because it can easily exploit a wide range data partitioning schemes, such as those designed for non-exchangeable data. It can also accommodate a range of scoring rules. We propose MCMC diagnostics, including a summary of MCMC mixing based on the popular potential scale reduction factor ($\widehat{R}$) and MCMC effective sample size ($\widehat{ESS}$) measures. We also describe a method for determining whether an $\widehat{R}$ diagnostic indicates approximate stationarity of the chains, that may be of more general interest for applications beyond parallel CV. Finally, we show that parallel CV and its diagnostics can be implemented with online algorithms, allowing parallel CV to scale up to very large blocking designs on memory-constrained computing accelerators.