Learning Parametric-Output HMMs with Two Aliased States

2015/02/07 by Roi Weiss, Weiss, Roi, Boaz Nadler +1
Computer Science · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning and Algorithms #Speech Recognition and Synthesis

paper · pdf · doi:10.48550/arxiv.1502.02158

openalex publication_date 2015/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Probabilistic Functions of Finite State Markov Chains
• A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains
• On aggregated Markov processes

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