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Article Dans Une Revue Machine Learning Année : 2022

Partially Hidden Markov Chain Multivariate Linear Autoregressive model: inference and forecasting—application to machine health prognostics

Résumé

Time series subject to regime shifts have attracted much interest in domains such as econometry, finance or meteorology. For discrete-valued regimes, models such as the popular Hidden Markov Chain (HMC) describe time series whose state process is unknown at all time-steps. Sometimes, time series are annotated. Thus, another category of models handles the case with regimes observed at all time-steps. We present a novel model which addresses the intermediate case: (i) state processes associated to such time series are modelled by Partially Hidden Markov Chains (PHMCs); (ii) a multivariate linear autoregressive (MLAR) model drives the dynamics of the time series, within each regime. We describe a variant of the expectation maximization (EM) algorithm devoted to PHMC-MLAR model learning. We propose a hidden state inference procedure and a forecasting function adapted to the semi-supervised framework. We first assess inference and prediction performances, and analyze EM convergence times for PHMC-MLAR, using simulated data. We show the benefits of using partially observed states as well as a fully labelled scheme with unreliable labels, to decrease EM convergence times. We highlight the robustness of PHMC-MLAR to labelling errors in inference and prediction tasks. Finally, using turbofan engine data from a NASA repository, we show that PHMC-MLAR outperforms or largely outperforms other models: PHMC and MSAR (Markov Switching AutoRegressive model) for the feature prediction task, PHMC and five out of six recent state-of-the-art methods for the prediction of machine useful remaining life.
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hal-04586874 , version 1 (24-05-2024)

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Fatoumata Dama, Christine Sinoquet. Partially Hidden Markov Chain Multivariate Linear Autoregressive model: inference and forecasting—application to machine health prognostics. Machine Learning, 2022, 112 (1), pp.45-97. ⟨10.1007/s10994-022-06209-5⟩. ⟨hal-04586874⟩
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