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arXiv · 1810.04777

Rao-Blackwellized Stochastic Gradients for Discrete Distributions

Runjing Liu·Jeffrey Regier·Nilesh Tripuraneni·Michael I. Jordan·Jon McAuliffe
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Abstract

We wish to compute the gradient of an expectation over a finite or countably infinite sample space having $K \leq \infty$ categories. When $K$ is indeed infinite, or finite but very large, the relevant summation is intractable. Accordingly, various stochastic gradient estimators have been proposed. In this paper, we describe a technique that can be applied to reduce the variance of any such estimator, without changing its bias---in particular, unbiasedness is retained. We show that our technique is an instance of Rao-Blackwellization, and we demonstrate the improvement it yields on a semi-supervised classification problem and a pixel attention task.

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Runjing Liu, Jeffrey Regier, Nilesh Tripuraneni, Michael I. Jordan, Jon McAuliffe. 2018-10-10. Rao-Blackwellized Stochastic Gradients for Discrete Distributions. https://arxiv.org/abs/1810.04777

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