Projected Stein Variational Gradient Descent

TL;DR

This paper introduces pSVGD, a method that leverages low-dimensional data-informed subspaces to improve Bayesian inference efficiency and accuracy in high-dimensional problems.

Contribution

The paper proposes a novel projected SVGD approach that adaptively constructs low-dimensional subspaces based on gradient information, enhancing scalability and performance.

Findings

pSVGD outperforms standard SVGD in accuracy and efficiency

The method scales well with increasing parameter dimensions

Experimental results show improved scalability with data points and cores

Abstract

The curse of dimensionality is a longstanding challenge in Bayesian inference in high dimensions. In this work, we propose a projected Stein variational gradient descent (pSVGD) method to overcome this challenge by exploiting the fundamental property of intrinsic low dimensionality of the data informed subspace stemming from ill-posedness of such problems. We adaptively construct the subspace using a gradient information matrix of the log-likelihood, and apply pSVGD to the much lower-dimensional coefficients of the parameter projection. The method is demonstrated to be more accurate and efficient than SVGD. It is also shown to be more scalable with respect to the number of parameters, samples, data points, and processor cores via experiments with parameters dimensions ranging from the hundreds to the tens of thousands.