Stochastic Gradient MCMC Methods for Hidden Markov Models
This work addresses the challenge of efficient parameter learning for HMMs in time-series data, which is incremental as it adapts existing SG-MCMC methods to a non-i.i.d. setting.
The authors tackled the problem of scaling Bayesian inference for hidden Markov models (HMMs) with time-dependent data by developing a stochastic gradient MCMC algorithm, resulting in significantly faster runtimes compared to batch MCMC in synthetic and ion channel recording experiments.
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.