Stein Variational Gradient Descent With Matrix-Valued Kernels
This work addresses the need for more efficient approximate inference in Bayesian statistics, though it is incremental as it builds upon existing SVGD with matrix-valued kernels.
The authors tackled the problem of improving Stein variational gradient descent (SVGD) by incorporating geometric information through preconditioning matrices, resulting in a method that outperforms vanilla SVGD and other baselines on real-world Bayesian inference tasks.
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.