Exact active subspace Metropolis-Hastings, with applications to the Lorenz-96 system

TL;DR

This paper introduces an unbiased active subspace Metropolis-Hastings algorithm that reduces computational complexity in sampling problems, demonstrated on synthetic and Lorenz-96 system applications.

Contribution

It develops an asymptotically unbiased variant of the active subspace MCMC method, addressing bias issues in the original formulation.

Findings

The new algorithm reduces computational cost in high-dimensional sampling.

It successfully applies to multimodal distributions and Lorenz-96 system inference.

The method achieves unbiased sampling asymptotically.

Abstract

We consider the application of active subspaces to inform a Metropolis-Hastings algorithm, thereby aggressively reducing the computational dimension of the sampling problem. We show that the original formulation, as proposed by Constantine, Kent, and Bui-Thanh (SIAM J. Sci. Comput., 38(5):A2779-A2805, 2016), possesses asymptotic bias. Using pseudo-marginal arguments, we develop an asymptotically unbiased variant. Our algorithm is applied to a synthetic multimodal target distribution as well as a Bayesian formulation of a parameter inference problem for a Lorenz-96 system.