SoftCVI: Contrastive variational inference with self-generated soft labels

TL;DR

SoftCVI introduces a contrastive variational inference method that leverages self-generated soft labels from unnormalized posteriors, enabling stable, mass-covering Bayesian inference without requiring positive or negative samples.

Contribution

The paper proposes SoftCVI, a novel contrastive variational inference framework that learns from soft labels derived directly from unnormalized posteriors, improving stability and coverage.

Findings

SoftCVI outperforms traditional variational methods in stability and coverage.

The approach works with both simple and complex variational distributions.

Zero variance gradient when the variational approximation is exact.

Abstract

Estimating a distribution given access to its unnormalized density is pivotal in Bayesian inference, where the posterior is generally known only up to an unknown normalizing constant. Variational inference and Markov chain Monte Carlo methods are the predominant tools for this task; however, both are often challenging to apply reliably, particularly when the posterior has complex geometry. Here, we introduce Soft Contrastive Variational Inference (SoftCVI), which allows a family of variational objectives to be derived through a contrastive estimation framework. The approach parameterizes a classifier in terms of a variational distribution, reframing the inference task as a contrastive estimation problem aiming to identify a single true posterior sample among a set of samples. Despite this framing, we do not require positive or negative samples, but rather learn by sampling the variational distribution and computing ground truth soft classification labels from the unnormalized posterior itself. The objectives have zero variance gradient when the variational approximation is exact, without the need for specialized gradient estimators. We empirically investigate the performance on a variety of Bayesian inference tasks, using both simple (e.g. normal) and expressive (normalizing flow) variational distributions. We find that SoftCVI can be used to form objectives which are stable to train and mass-covering, frequently outperforming inference with other variational approaches.