Stein Variational Gradient Descent With Matrix-Valued Kernels

TL;DR

This paper extends Stein Variational Gradient Descent by introducing matrix-valued kernels and preconditioning matrices, enhancing geometric adaptation and accelerating convergence in Bayesian inference tasks.

Contribution

It generalizes SVGD with matrix-valued kernels, enabling the incorporation of preconditioning matrices like Hessian and Fisher information for improved performance.

Findings

Outperforms vanilla SVGD on real-world tasks

Accelerates exploration in probability landscapes

Effectively incorporates geometric information

Abstract

Stein variational gradient descent (SVGD) is a particle-based inference algorithm that leverages gradient information for efficient approximate inference. In this work, we enhance SVGD by leveraging preconditioning matrices, such as the Hessian and Fisher information matrix, to incorporate geometric information into SVGD updates. We achieve this by presenting a generalization of SVGD that replaces the scalar-valued kernels in vanilla SVGD with more general matrix-valued kernels. This yields a significant extension of SVGD, and more importantly, allows us to flexibly incorporate various preconditioning matrices to accelerate the exploration in the probability landscape. Empirical results show that our method outperforms vanilla SVGD and a variety of baseline approaches over a range of real-world Bayesian inference tasks.