A Constraint-Based Algorithm for the Structural Learning of Continuous-Time Bayesian Networks
This work addresses a gap in machine learning for modeling dynamic systems in continuous time, but it is incremental as it adapts existing constraint-based techniques to a specific extension of Bayesian networks.
The authors tackled the problem of learning the structure of continuous-time Bayesian networks, which are less studied than discrete-time models, by proposing the first constraint-based algorithm. They validated it on synthetic data, finding it more accurate than a score-based method for variables with more than two values, while both algorithms had comparable computation times.
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.