Fast sampling from a Hidden Markov Model posterior for large data

Hidden Markov Models are of interest in a broad set of applications including modern data driven systems involving very large data sets. However, approximate inference methods based on Bayesian averaging are precluded in such applications as each sampling step requires a full sweep over the data. We show that Approximate Bayesian Computation offers an interesting alternative for approximate sampling from the posterior distribution. In particular we use recent advances in moment based methods for HMM estimation to generate summary statistics for Approximate Bayesian Computation for large data sets offering fast access to approximate posterior samples. In a specific example we see that the new scheme is a hundred times faster than conventional Markov Chain Monte Carlo sampling using the Forward-backward method.