Approximation Based Variance Reduction for Reparameterization Gradients

TL;DR

This paper introduces a quadratic approximation control variate for reparameterization gradients, significantly reducing variance and improving optimization in variational inference with complex distributions.

Contribution

It proposes a novel control variate applicable to any reparameterizable distribution with known mean and covariance, enhancing gradient estimation efficiency.

Findings

Large variance reduction in gradient estimates

Improved convergence in variational inference

Effective for non-factorized variational distributions

Abstract

Flexible variational distributions improve variational inference but are harder to optimize. In this work we present a control variate that is applicable for any reparameterizable distribution with known mean and covariance matrix, e.g. Gaussians with any covariance structure. The control variate is based on a quadratic approximation of the model, and its parameters are set using a double-descent scheme by minimizing the gradient estimator's variance. We empirically show that this control variate leads to large improvements in gradient variance and optimization convergence for inference with non-factorized variational distributions.