Neural Variational Gradient Descent

TL;DR

Neural Variational Gradient Descent (NVGD) introduces a neural network-based approach to particle inference that eliminates the need for kernel selection, improving flexibility and applicability in Bayesian inference tasks.

Contribution

NVGD replaces kernel-dependent Stein variational methods with a neural network parameterization of the Stein discrepancy, enabling adaptive and kernel-free Bayesian inference.

Findings

NVGD performs well on synthetic inference problems.

NVGD is effective for Bayesian linear regression.

NVGD successfully applies to Bayesian neural network inference.

Abstract

Particle-based approximate Bayesian inference approaches such as Stein Variational Gradient Descent (SVGD) combine the flexibility and convergence guarantees of sampling methods with the computational benefits of variational inference. In practice, SVGD relies on the choice of an appropriate kernel function, which impacts its ability to model the target distribution -- a challenging problem with only heuristic solutions. We propose Neural Variational Gradient Descent (NVGD), which is based on parameterizing the witness function of the Stein discrepancy by a deep neural network whose parameters are learned in parallel to the inference, mitigating the necessity to make any kernel choices whatsoever. We empirically evaluate our method on popular synthetic inference problems, real-world Bayesian linear regression, and Bayesian neural network inference.