  Stochastic gradient MCMC (SG-MCMC) algorithms have proven useful in scaling
Bayesian inference to large datasets under an assumption of i.i.d data. We
instead develop an SG-MCMC algorithm to learn the parameters of hidden Markov
models (HMMs) for time-dependent data. There are two challenges to applying
SG-MCMC in this setting: The latent discrete states, and needing to break
dependencies when considering minibatches. We consider a marginal likelihood
representation of the HMM and propose an algorithm that harnesses the inherent
memory decay of the process. We demonstrate the effectiveness of our algorithm
on synthetic experiments and an ion channel recording data, with runtimes
significantly outperforming batch MCMC.
