Inducing Hidden Markov Models to model long-term dependencies

We propose in this paper a novel approach to the induction of the structure of Hidden Markov Models. The induced model is seen as a lumped process of a Markov chain. It is constructed to fit the dynamics of the target machine, that is to best approximate the stationary distribution and the mean first passage times observed in the sample. The induction relies on non-linear optimization and iterative state splitting from an initial order one Markov chain