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arXiv · 2010.10436

VarGrad: A Low-Variance Gradient Estimator for Variational Inference

Lorenz Richter·Ayman Boustati·Nikolas Nüsken·Francisco J. R. Ruiz·Ömer Deniz Akyildiz
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Abstract

We analyse the properties of an unbiased gradient estimator of the ELBO for variational inference, based on the score function method with leave-one-out control variates. We show that this gradient estimator can be obtained using a new loss, defined as the variance of the log-ratio between the exact posterior and the variational approximation, which we call the $\textit{log-variance loss}$. Under certain conditions, the gradient of the log-variance loss equals the gradient of the (negative) ELBO. We show theoretically that this gradient estimator, which we call $\textit{VarGrad}$ due to its connection to the log-variance loss, exhibits lower variance than the score function method in certain settings, and that the leave-one-out control variate coefficients are close to the optimal ones. We empirically demonstrate that VarGrad offers a favourable variance versus computation trade-off compared to other state-of-the-art estimators on a discrete VAE.

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BibTeXRIS

Lorenz Richter, Ayman Boustati, Nikolas Nüsken, Francisco J. R. Ruiz, Ömer Deniz Akyildiz. 2020-10-20. VarGrad: A Low-Variance Gradient Estimator for Variational Inference. https://arxiv.org/abs/2010.10436

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