Prediction and Inference in a Partially Hidden Markov-switching Framework with Autoregression. Application to Machinery Health Diagnosis - Dama, Fatoumata; Sinoquet, Christine (Proceedings - International Conference on Tools with Artificial Intelligence, TAI, 2021)
Time series subject to changes in regime are encountered in multiple applications. Models such as the renowned Hidden Markov Model (HMM) describe time series whose states are unknown at all time-steps. In some situations, partial knowledge on states is available. In this paper, we describe the Partially Hidden Markov Chain Linear AutoRegressive (PHMC-LAR) model. This model combines a HMM framework with local state-specific linear autoregressive dynamics. Namely, this hybrid model extends two published models, the Markov-Switching AutoRegressive (MSAR) model and the Partially Hidden Markov Chain (PHMC). Our contributions in this paper address: (i) Expectation-Maximization-based semi-supervised parameter learning, (ii) time series prediction, (iii) latent state inference via a variant of the Viterbi algorithm. We first validate our model on synthetic data. We show that integrating relatively limited knowledge on states considerably accelerates model training, while still preserving good prediction and state inference performances. Further, we compare the state inference performances of PHMC-LAR, PHMC and MSAR on realistic data with ground truth, in the context of a machine health diagnosis application. PHMC and PHMC-LAR show comparable performances, while PHMC-LAR is mainly subject to state degradation anticipation errors. This is a desirable property to ensure system safety through early maintenance operations. Thus PHMC-LAR illustrates a contribution to machine learning with potential beneficial impacts on safety in industrial, transportation and health applications.