Learning Input Driven Dynamic Bayesian Networks with Measurement Noise

Dynamic Bayesian Networks (DBNs) are useful tools for modelling complex systems whose network representations can be elicited a priori or learnt from data. In this paper, a maximum likelihood Doubly-Iterative Expectation Maximization (DI-EM) Algorithm is developed for the identification of grey-box ARMAX state-space model representations of DBNs involving known, noisy measurement processes. The grey-box model incorporates network dependencies among time series variables and exploits time series data of low longitudinal and high cross-sectional dimensions. A network learning procedure is developed using a score-based structure-selection method to find the underlying network of an input-driven dynamical system. By computing a finite data version of the Bayesian Information Criterion (BIC) for small sample sizes, the proposed method's performance is investigated on simulated and real-world data. The algorithm recovers the underlying ground-truth networks of simulated systems under finite data criteria with Jaccard Coefficient values of up to 0.84, and selects structures with improved weighted mean-squared error loss over a baseline black-box model fit on real-world data.