Semi-Implicit Variational Inference via Kernelized Path Gradient Descent

TL;DR

This paper introduces a stabilized kernelized KL divergence estimator with importance sampling correction for semi-implicit variational inference, improving training stability and efficiency in high-dimensional posterior approximation.

Contribution

It proposes a novel kernelized KL estimator with importance sampling, connecting to Stein variational gradient descent, reducing variance and bias in semi-implicit variational inference.

Findings

Outperforms existing SIVI methods in accuracy

Achieves more stable and efficient training

Demonstrates effectiveness in high-dimensional settings

Abstract

Semi-implicit variational inference (SIVI) is a powerful framework for approximating complex posterior distributions, but training with the Kullback-Leibler (KL) divergence can be challenging due to high variance and bias in high-dimensional settings. While current state-of-the-art semi-implicit variational inference methods, particularly Kernel Semi-Implicit Variational Inference (KSIVI), have been shown to work in high dimensions, training remains moderately expensive. In this work, we propose a kernelized KL divergence estimator that stabilizes training through nonparametric smoothing. To further reduce the bias, we introduce an importance sampling correction. We provide a theoretical connection to the amortized version of the Stein variational gradient descent, which estimates the score gradient via Stein's identity, showing that both methods minimize the same objective, but our semi-implicit approach achieves lower gradient variance. In addition, our method's bias in function space is benign, leading to more stable and efficient optimization. Empirical results demonstrate that our method outperforms or matches state-of-the-art SIVI methods in both performance and training efficiency.