A Stein variational Newton method

TL;DR

This paper enhances the Stein variational gradient descent (SVGD) algorithm by incorporating second-order information, leading to faster convergence and improved kernel selection, demonstrated through multiple test cases.

Contribution

It introduces a Newton-like method for SVGD that accelerates convergence and improves kernel choices by leveraging second-order information.

Findings

Significant computational gains over original SVGD.

Effective kernel selection through second-order information.

Accelerated convergence demonstrated in multiple tests.

Abstract

Stein variational gradient descent (SVGD) was recently proposed as a general purpose nonparametric variational inference algorithm [Liu & Wang, NIPS 2016]: it minimizes the Kullback-Leibler divergence between the target distribution and its approximation by implementing a form of functional gradient descent on a reproducing kernel Hilbert space. In this paper, we accelerate and generalize the SVGD algorithm by including second-order information, thereby approximating a Newton-like iteration in function space. We also show how second-order information can lead to more effective choices of kernel. We observe significant computational gains over the original SVGD algorithm in multiple test cases.