Learning Parametric-Output HMMs with Two Aliased States
This solves a long-standing theoretical problem in HMMs for applications where state aliasing occurs, offering incremental algorithmic improvements for specific parametric families.
The paper tackled the problem of learning hidden Markov models (HMMs) with two aliased states, which have identical output distributions, by providing a complete characterization of minimality and identifiability for parametric-output HMMs and developing efficient, consistent algorithms for detection and parameter learning.
In various applications involving hidden Markov models (HMMs), some of the hidden states are aliased, having identical output distributions. The minimality, identifiability and learnability of such aliased HMMs have been long standing problems, with only partial solutions provided thus far. In this paper we focus on parametric-output HMMs, whose output distributions come from a parametric family, and that have exactly two aliased states. For this class, we present a complete characterization of their minimality and identifiability. Furthermore, for a large family of parametric output distributions, we derive computationally efficient and statistically consistent algorithms to detect the presence of aliasing and learn the aliased HMM transition and emission parameters. We illustrate our theoretical analysis by several simulations.