Clustering-Enhanced Stochastic Gradient MCMC for Hidden Markov Models

Abstract

MCMC algorithms for hidden Markov models, which often rely on the forward-backward sampler, suffer with large sample size due to the temporal dependence inherent in the data. Recently, a number of approaches have been developed for posterior inference which make use of the mixing of the hidden Markov process to approximate the full posterior by using small chunks of the data. However, in the presence of imbalanced data resulting from rare latent states, the proposed minibatch estimates will often exclude rare state data resulting in poor inference of the associated emission parameters and inaccurate prediction or detection of rare events. Here, we propose to use a preliminary clustering to over-sample the rare clusters and reduce variance in gradient estimation within Stochastic Gradient MCMC. We demonstrate very substantial gains in predictive and inferential accuracy on real and synthetic examples.