Semi-Implicit Variational Inference via Score Matching

Longlin Yu, Cheng Zhang

Keywords: Semi-implicit variational inference, denoising score matching, minimax optimization

Abstract: Semi-implicit variational inference (SIVI) greatly enriches the expressiveness of variational families by considering implicit variational distributions defined in a hierarchical manner. However, due to the intractable densities of variational distributions, current SIVI approaches often use surrogate evidence lower bounds (ELBOs) or employ expensive inner-loop MCMC runs for unbiased ELBOs for training. In this paper, we propose SIVI-SM, a new method for SIVI based on an alternative training objective via score matching. Leveraging the hierarchical structure of semi-implicit variational families, the score matching objective allows a minimax formulation where the intractable variational densities can be naturally handled with denoising score matching. We show that SIVI-SM closely matches the accuracy of MCMC and outperforms ELBO-based SIVI methods in a variety of Bayesian inference tasks.

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TL;DR: A new semi-implict variational inference method using a score matching training objective

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2308.10014/code)