Recovering the state sequence of hidden Markov models using mean-field approximations

Inferring the sequence of states from observations is one of the most fundamental problems in Hidden Markov Models. In statistical physics language, this problem is equivalent to computing the marginals of a one-dimensional model with a random external field. While this task can be accomplished through transfer matrix methods, it becomes quickly intractable when the underlying state space is large. This paper develops several low-complexity approximate algorithms to address this inference problem when the state space becomes large. The new algorithms are based on various mean-field approximations of the transfer matrix. Their performances are studied in detail on a simple realistic model for DNA pyrosequencing.