A solution for the learning problem in evidential (Partially) hidden markov models based on conditional belief functions and EM

Abstract

Evidential Hidden Markov Models (EvHMM) is a particular Evidential Temporal Graphical Model that aims at statistically representing the kynetics of a system by means of an Evidential Markov Chain and an observation model. Observation models are made of mixture of densities to represent the inherent variability of sensor measurements, whereas uncertainty on the latent structure, that is generally only partially known due to lack of knowledge, is managed by Dempster-Shafer’s theory of belief functions. This paper is dedicated to the presentation of an Expectation-Maximization procedure to learn parameters in EvHMM. Results demonstrate the high potential of this method illustrated on complex datasets originating from turbofan engines where the aim is to provide early warnings of malfunction and failure.