Hidden Markov random field

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 Y_i, where $i \in S$. Hidden Markov random fields assume that the probabilistic nature of Y_i is determined by the unobservable Markov random field X_i, $i \in S$. That is, given the neighbors N_i of X_i, X_i is independent of all other X_j (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. X_i 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 X_i, Y_i are independent (conditional independence of the observable variables given the Markov random field).

See also

• Hidden Markov model
• Markov network
• Bayesian network

References

• [1] (by Yongyue Zhang)