Hidden Markov models with discrete infinite logistic normal distribution priors

In this article, we propose a discrete infinite logistic normal distribution (DILN) to estimate the number of states in a hidden Markov model (HMM). The HMM with the DILN priors (DILN-HMM) allows for infinite state support and model correlations between state transition probabilities. A variational Bayesian (VB) framework is proposed to infer the posterior distribution of the parameters of DILN-HMM. Experiments based on synthetic and real data show that the DILN-HMM is effective in handling situations where state transition matrix is correlated.