Equivalence and Reduction of Hidden Markov Models

摘要: This report studies when and why two Hidden Markov Models (HMMs) may represent the same stochastic process. HMMs are characterized in terms of equivalence classes whose elements identical processes. characterization yields polynomial time algorithms to detect equivalent HMMs. We also find fast reduce essentially unique minimal canonical representations. The reduction a form leads definition "Generalized Models" which without positivity constraint on their parameters. discuss how this generalization can yield more parsimonious representations processes at cost probabilistic interpretation model