Natural Gradient Variational Inference with Gaussian Mixture Models

Abstract: Bayesian methods estimate a measure of uncertainty by using the posterior distribution. One source of difficulty in these methods is the computation of the normalizing constant. Calculating exact posterior is generally intractable and we usually approximate it. Variational Inference (VI) methods approximate the posterior with a distribution usually chosen from a simple family using optimization. The main contribution of this work is described is a set of update rules for natural gradient variational inference with mixture of Gaussians, which can be run independently for each of the mixture components, potentially in parallel.