A hidden Markov random field is a generalization of a hidden Markov model. Instead of having an underlying Markov chain, hidden Markov random fields have an underlying Markov random field. Suppose that we observe a random variable <math> Y_i </math>, where <math> i \in S </math>.

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dbpprop:abstract
  • A hidden Markov random field is a generalization of a hidden Markov model. Instead of having an underlying Markov chain, hidden Markov random fields have an underlying Markov random field. Suppose that we observe a random variable <math> Y_i </math>, where <math> i \in S </math>. Hidden Markov random fields assume that the probabilistic nature of <math> Y_i </math> is determined by the unobservable Markov random field <math> X_i </math>, <math> i \in S </math>. That is, given the neighbors <math> N_i </math> of <math> X_i </math>, <math> X_i </math> is independent of all other <math> X_j </math> (Markov property). The main difference with a hidden Markov model is that neighborhood is not defined in 1 dimension but within a network, i.e. <math> X_i </math> is allowed to have more than the two neighbors that it would have in a Markov chain. The model is formulated in such a way that given <math> X_i </math>, <math> Y_i </math> are independent (conditional independence of the observable variables given the Markov random field).
rdfs:comment
  • A hidden Markov random field is a generalization of a hidden Markov model. Instead of having an underlying Markov chain, hidden Markov random fields have an underlying Markov random field. Suppose that we observe a random variable <math> Y_i </math>, where <math> i \in S </math>.
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  • Hidden Markov random field
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