  Dynamic Bayesian networks have been well explored in the literature as
discrete-time models: however, their continuous-time extensions have seen
comparatively little attention. In this paper, we propose the first
constraint-based algorithm for learning the structure of continuous-time
Bayesian networks. We discuss the different statistical tests and the
underlying hypotheses used by our proposal to establish conditional
independence. Furthermore, we analyze and discuss the computational complexity
of the best and worst cases for the proposed algorithm. Finally, we validate
its performance using synthetic data, and we discuss its strengths and
limitations comparing it with the score-based structure learning algorithm from
Nodelman et al. (2003). We find the latter to be more accurate in learning
networks with binary variables, while our constraint-based approach is more
accurate with variables assuming more than two values. Numerical experiments
confirm that score-based and constraint-based algorithms are comparable in
terms of computation time.
