Reparameterized Variational Rejection Sampling

TL;DR

This paper introduces Reparameterized Variational Rejection Sampling (RVRS), a novel inference method that enhances variational approximation flexibility by combining rejection sampling with low-variance gradient estimators, improving black-box inference for models with continuous latent variables.

Contribution

The paper proposes RVRS, a new approach that reparameterizes Variational Rejection Sampling to enable efficient, flexible inference with continuous latent variables, addressing limitations of existing variational families.

Findings

RVRS achieves a good balance between computational cost and inference accuracy.

The method performs well empirically on models with local latent variables.

RVRS is particularly effective for black-box inference in complex models.

Abstract

Traditional approaches to variational inference rely on parametric families of variational distributions, with the choice of family playing a critical role in determining the accuracy of the resulting posterior approximation. Simple mean-field families often lead to poor approximations, while rich families of distributions like normalizing flows can be difficult to optimize and usually do not incorporate the known structure of the target distribution due to their black-box nature. To expand the space of flexible variational families, we revisit Variational Rejection Sampling (VRS) [Grover et al., 2018], which combines a parametric proposal distribution with rejection sampling to define a rich non-parametric family of distributions that explicitly utilizes the known target distribution. By introducing a low-variance reparameterized gradient estimator for the parameters of the proposal distribution, we make VRS an attractive inference strategy for models with continuous latent variables. We argue theoretically and demonstrate empirically that the resulting method--Reparameterized Variational Rejection Sampling (RVRS)--offers an attractive trade-off between computational cost and inference fidelity. In experiments we show that our method performs well in practice and that it is well-suited for black-box inference, especially for models with local latent variables.