Different phases and phase transition points in hidden Markov models.

We are looking for different phases in hidden Markov models (HMMs). By analyzing the stationary solution of the master equation, we discover different situations with localized or delocalized distributions for the stationary distributions of the master equation. We hypothesize that these phases are related to the relaxation dynamics of the HMM ensemble. We have derived precise phase transition points. We test whether the behavior of the HMMs and their associated numerical algorithms change near the transition points. We find that the accuracy of the Viterbi and Baum-Welch algorithms sometimes is worse near the phase transition, which contradicts the edge of chaos hypothesis.