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Dynamic Bayesian networks have been well explored in the literature asdiscrete-time models: however, their continuous-time extensions have seencomparatively little attention. In this paper, we propose the firstconstraint-based algorithm for learning the structure of continuous-timeBayesian networks. We discuss the different statistical tests and theunderlying hypotheses used by our proposal to establish conditionalindependence. Furthermore, we analyze and discuss the computational complexityof the best and worst cases for the proposed algorithm. Finally, we validateits performance using synthetic data, and we discuss its strengths andlimitations comparing it with the score-based structure learning algorithm fromNodelman et al. (2003). We find the latter to be more accurate in learningnetworks with binary variables, while our constraint-based approach is moreaccurate with variables assuming more than two values. Numerical experimentsconfirm that score-based and constraint-based algorithms are comparable interms of computation time.

A Constraint-Based Algorithm for the Structural Learning of Continuous-Time Bayesian Networks