Stein Variational Gradient Descent with Variance Reduction

Probabilistic inference is a common and important task in statistical machine learning. The recently proposed Stein variational gradient descent (SVGD) is a generic Bayesian inference method that has been shown to be successfully applied in a wide range of contexts, especially in dealing with large datasets, where existing probabilistic inference methods have been known to be ineffective. In a large-scale data setting, SVGD employs the mini-batch strategy but its mini-batch estimator has large variance, hence compromising its estimation quality in practice. To this end, we propose in this paper a generic SVGD-based inference method that can significantly reduce the variance of mini-batch estimator when working with large datasets. Our experiments on 14 datasets show that the proposed method enjoys substantial and consistent improvements compared with baseline methods in binary classification task and its pseudo-online learning setting, and regression task. Furthermore, our framework is generic and applicable to a wide range of probabilistic inference problems such as in Bayesian neural networks and Markov random fields.