The equivalence between Stein variational gradient descent and black-box variational inference

TL;DR

This paper demonstrates the formal equivalence between Stein variational gradient descent (SVGD) and black-box variational inference (BBVI) under certain kernel conditions, unifying various inference and generative modeling techniques.

Contribution

It establishes a precise connection between SVGD and BBVI using the neural tangent kernel, and interprets both as kernel gradient flows, providing a unified theoretical framework.

Findings

BBVI corresponds exactly to SVGD with the neural tangent kernel

Both methods can be viewed as kernel gradient flows in probability space

Kernel gradient flow dynamics relate to GAN training processes

Abstract

We formalize an equivalence between two popular methods for Bayesian inference: Stein variational gradient descent (SVGD) and black-box variational inference (BBVI). In particular, we show that BBVI corresponds precisely to SVGD when the kernel is the neural tangent kernel. Furthermore, we interpret SVGD and BBVI as kernel gradient flows; we do this by leveraging the recent perspective that views SVGD as a gradient flow in the space of probability distributions and showing that BBVI naturally motivates a Riemannian structure on that space. We observe that kernel gradient flow also describes dynamics found in the training of generative adversarial networks (GANs). This work thereby unifies several existing techniques in variational inference and generative modeling and identifies the kernel as a fundamental object governing the behavior of these algorithms, motivating deeper analysis of its properties.