Partially Markov models and unsupervised segmentation of semi-Markov chains hidden with long dependence noise

The hidden Markov chain (HMC) model is a couple of random sequences (X,Y), in which X is an unobservable Markov chain, and Y is its observable noisy version. Classically, the distribution p(ylx) is simple enough to ensure the Markovianity of p(xly), that enables one to use different Bayesian restoration techniques. HMC model has recently been extended to "triplet Markov chain" (TMC) model, which is obtained by adding a third chain U and considering the Markovianity of the triplet T = (X,U,Y). When U is not too complex, X can still be recovered from Y. In particular, a semi-Markov hidden chain is a particular TMC. Otherwise, the recent triplet partially Markov chain (TPMC) is a triplet T = (X,U,Y) such that p(x,u(y) is a Markov distribution, which still allows one to recover X from Y. The aim of this paper is to introduce, using a particular TPMC, semi-Markov chains hidden with long dependence noise. The general iterative conditional estimation (ICE) method is then used to estimate the model parameters, and the interest of the new model in unsupervised data segmentation is validated through experiments.