Finite state space non parametric Hidden Markov Models are in general identifiable
نویسندگان
چکیده
Finite mixtures are widely used in applications to model data coming from different populations. Let X be the latent random variable whose value is the label of the population the observation comes from, and let Y be the observed random variable. With finitely many populations, X takes values in {1, . . . , k} for some fixed integer k, and conditionally to X = j, Y has distribution μj. Here, μ1, . . . , μk are probability distributions on the observation space Y endowed with its Borel sigma-field and are called emission distributions. Assume that we are given n observations Y1, . . . , Yn with the same distribution as Y , that is with distribution k ∑
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