Niodeling non stationary hidden semi-Markov chains with triplet Markov chains and theory of evidence

Hidden Markov chains, enabling one to recover the hidden process even for very large size. are widely used in various problems. On the one hand, it has been recently established that when the hidden chain is not stationary, the use of the theory, of evidence is equivalent to consider a triplet Markov chain and can improve the efficiency of unsupervised segmentation. On the other hand, hidden semi-Markov chains can also be considered as particular triplet Markov chains. The aim of this paper is to use these two points simultaneously. Considering a non stationary hidden semi-Markov chain, we show that it is possible to consider two auxiliary random chains in such a way that unsupervised segmentation of non stationary hidden semi-Markov chains is workable.