Faster Stochastic Variational Inference using Proximal-Gradient Methods with General Divergence Functions
Abstract
Several recent works have explored stochastic gradient methods for variational inference that exploit the geometry of the variational-parameter space. However, the theoretical properties of these methods are not well-understood and these methods typically only apply to conditionally-conjugate models. We present a new stochastic method for variational inference which exploits the geometry of the variational-parameter space and also yields simple closed-form updates even for non-conjugate models. We also give a convergence-rate analysis of our method and many other previous methods which exploit the geometry of the space. Our analysis generalizes existing convergence results for stochastic mirror-descent on non-convex objectives by using a more general class of divergence functions. Beyond giving a theoretical justification for a variety of recent methods, our experiments show that new algorithms derived in this framework lead to state of the art results on a variety of problems. Further, due to its generality, we expect that our theoretical analysis could also apply to other applications.
Cite
@article{arxiv.1511.00146,
title = {Faster Stochastic Variational Inference using Proximal-Gradient Methods with General Divergence Functions},
author = {Mohammad Emtiyaz Khan and Reza Babanezhad and Wu Lin and Mark Schmidt and Masashi Sugiyama},
journal= {arXiv preprint arXiv:1511.00146},
year = {2016}
}
Comments
Published in UAI 2016. We have made the following change in this revision: instead of expressing convergence rate results in terms of the iterate difference, we state them in terms of the iterate distance divided by the step-size (a measure of first-order optimality). We also removed some claims about the performance with a fixed step size