Rao-Blackwellized Stochastic Gradients for Discrete Distributions
Runjing Liu, Jeffrey Regier, Nilesh Tripuraneni, Michael I. Jordan, Jon McAuliffe · International Conference on Machine Learning · 2019
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.