Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm

TL;DR

This paper introduces Stein Variational Gradient Descent, a versatile Bayesian inference algorithm that transports particles to approximate target distributions by minimizing KL divergence, combining theoretical insights with empirical validation.

Contribution

It presents a novel variational inference method using functional gradient descent, connecting KL divergence derivatives with Stein's identity and kernelized Stein discrepancy.

Findings

Competitive performance on real-world datasets

Theoretical connection between KL derivatives and Stein's identity

Applicable to various Bayesian models

Abstract

We propose a general purpose variational inference algorithm that forms a natural counterpart of gradient descent for optimization. Our method iteratively transports a set of particles to match the target distribution, by applying a form of functional gradient descent that minimizes the KL divergence. Empirical studies are performed on various real world models and datasets, on which our method is competitive with existing state-of-the-art methods. The derivation of our method is based on a new theoretical result that connects the derivative of KL divergence under smooth transforms with Stein's identity and a recently proposed kernelized Stein discrepancy, which is of independent interest.