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# Rao-Blackwellized Stochastic Gradients for Discrete Distributions

*Proceedings of the 36th International Conference on Machine Learning*, PMLR 97:4023-4031, 2019.

#### 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.