Modelling regimes with Bayesian network mixtures

Bayesian networks (BNs) are advantageous when representing single independence models, however they do not allow us to model changes among the relationships of the random variables over time. Due to such regime changes, it may be necessary to use di↵erent BNs at di↵erent times in order to have an appropriate model over the random variables. In this paper we propose two extensions to the traditional hidden Markov model, allowing us to represent both the di↵erent regimes using di↵erent BNs, and potential driving forces behind the regime changes, by modelling potential dependence between state transitions and some observable variables. We show how expectation maximisation can be used to learn the parameters of the proposed model, and run both synthetic and real-world experiments to show the model’s potential.