Accelerated dimension-independent adaptive Metropolis

TL;DR

This paper introduces the dimension-independent adaptive Metropolis (DIAM) algorithm, which scales efficiently with high-dimensional parameters in Bayesian inference, leveraging GPU acceleration and concurrent chains for improved performance.

Contribution

The paper extends adaptive Metropolis to achieve dimension-independent scaling for Gaussian targets and enhances it with GPU acceleration and concurrent chains.

Findings

Achieves asymptotic dimension-independence for Gaussian targets.

GPU implementation yields fourfold speedup over CPU-based methods.

Demonstrates effective scaling on high-dimensional (over 1000 dimensions) targets.

Abstract

This work considers black-box Bayesian inference over high-dimensional parameter spaces. The well-known adaptive Metropolis (AM) algorithm of (Haario etal. 2001) is extended herein to scale asymptotically uniformly with respect to the underlying parameter dimension for Gaussian targets, by respecting the variance of the target. The resulting algorithm, referred to as the dimension-independent adaptive Metropolis (DIAM) algorithm, also shows improved performance with respect to adaptive Metropolis on non-Gaussian targets. This algorithm is further improved, and the possibility of probing high-dimensional targets is enabled, via GPU-accelerated numerical libraries and periodically synchronized concurrent chains (justified a posteriori). Asymptotically in dimension, this GPU implementation exhibits a factor of four improvement versus a competitive CPU-based Intel MKL parallel version alone. Strong scaling to concurrent chains is exhibited, through a combination of longer time per sample batch (weak scaling) and yet fewer necessary samples to convergence. The algorithm performance is illustrated on several Gaussian and non-Gaussian target examples, in which the dimension may be in excess of one thousand.