Rao-Blackwellised Reparameterisation Gradients
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.
Cite
@article{arxiv.2506.07687,
title = {Rao-Blackwellised Reparameterisation Gradients},
author = {Kevin H. Lam and Thang D. Bui and George Deligiannidis and Yee Whye Teh},
journal= {arXiv preprint arXiv:2506.07687},
year = {2025}
}
Comments
Accepted at the 39th Conference on Neural Information Processing Systems (NeurIPS 2025)