Partially-Hidden Markov Models

This paper addresses the problem of Hidden Markov Models (HMM) training and inference when the training data are composed of feature vectors plus uncertain and imprecise labels. The "soft" labels represent partial knowledge about the possible states at each time step and the "softness" is encoded by belief functions. For the obtained model, called a Partially-Hidden Markov Model (PHMM), the training algorithm is based on the Evidential Expectation-Maximisation (E2M) algorithm. The usual HMM model is recovered when the belief functions are vacuous and the obtained model includes supervised, unsupervised and semi-supervised learning as special cases.