Inference and learning in evidential discrete latent markov models

International audienceWe present the Evidential Hidden Markov Model (EvHMM), an extension of standard HMM for time-series modelling whereconditional belief functions are used in place of probabilities to manage uncertainty on discrete latent variables. Inference andlearning mechanisms are described and allow to solve the three problems initially defined for HMM, namely: the classificationproblem (find the most plausible model), the decoding problem (finding the best sequence of hidden states) and the learning problembased on incomplete and uncertain data (estimate the parameters). Exact inference mechanisms based on the Generalized BayesianTheorem are proposed which allows one to recover standard HMM when probabilities are considered. An EM-like procedure isdeveloped for parameter learning, relying on some approximations suggested to make the solutions tractable. Relationships arediscussed with both the learning criterion conjectured by Vannoorenberghe and Smets and the formulation of Evidential MarkovChains by Pieczynski et al. A comparison with standard HMM on simulated data confirms the interest of considering randomdisjuctive sets to represent data incompleteness in evidential temporal graphical models