Scalable Inference for Hybrid Bayesian Hidden Markov Model Using Gaussian Process Emission

The hidden Markov model (HMM), used with Gaussian Process (GP) as an emission model, has been widely to sequential data in complex form. This study introduces the hybrid Bayesian HMM GP using SM kernel (HMM-GPSM) estimate state of each time-series observation, that is, sequentially observed from a single channel. We then propose scalable inference method train HMM-GPSM large-scale sequences dataset (1) large number for transitions and (2) points observation state. For sequences, we employ stochastic variational (SVI) update parameters efficiently. Also, points, approximate Random Fourier Feature (RFF), which is constructed by spectral are sampled density kernel. efficient hyperparameters corresponding HMM-GPSM. Specifically, derive training loss, evidence lower bound can be scalably computed observations employing regularized likelihood KL divergence. proposed methods together contains both (2). validate on synthetic real datasets clustering accuracy, marginal likelihood, time performance metrics.