Rao-Blackwellised Reparameterisation Gradients

Kevin H. Lam, Thang D Bui, George Deligiannidis, Yee Whye Teh

Keywords: reparameterisation trick, stochastic gradient estimation, Rao-Blackwellisation, variance reduction

TL;DR: We present the Rao-Blackwellised reparameterisation gradient estimator and show its performance gains on a suite of probabilistic models.

Abstract: Latent Gaussian variables have been popularised in probabilistic machine learning. In turn, gradient estimators are the machinery that facilitates gradient-based optimisation for models with latent Gaussian variables. The reparameterisation trick is often used as the default estimator as it is simple to implement and yields low-variance gradients for variational inference. In this work, we propose the R2-G2 estimator as the Rao-Blackwellisation of the reparameterisation gradient estimator. Interestingly, we show that the local reparameterisation gradient estimator for Bayesian MLPs is an instance of the R2-G2 estimator and Rao-Blackwellisation. This lets us extend benefits of Rao-Blackwellised gradients to a suite of probabilistic models. We show that initial training with R2-G2 consistently yields better performance in models with multiple applications of the reparameterisation trick.

Primary Area: Probabilistic methods (e.g., variational inference, causal inference, Gaussian processes)

Submission Number: 15177