Structure learning algorithms for multidimensional continuous-time Bayesian network classifiers

Learning the structure of continuous-time Bayesian networks directly from data has traditionally been performed using score-based structure learning algorithms. Only recently has a constraint-based method been proposed, proving to be more suitable under specific settings, as in modelling systems with variables having more than two states. As a result, studying diverse structure learning algorithms is essential to learn the most appropriate models according to data characteristics and task-related priorities, such as learning speed or accuracy. This article proposes several alternatives of such algorithms for learning multidimensional continuous-time Bayesian network classifiers, introducing for the first time constraint-based and hybrid algorithms for these models. Nevertheless, these contributions also apply to the simpler one-dimensional classification problem for which only score-based solutions exist in the literature. More specifically, the aforementioned constraint-based structure learning algorithm is first adapted to the supervised classification setting. Then, a novel algorithm of this kind, specifically tailored for the multidimensional classification problem, is presented to improve the learning times for the induction of multidimensional classifiers. Finally, a hybrid algorithm is introduced, attempting to combine the strengths of the score- and constraint-based approaches. Experiments with synthetic data are performed not only to validate the capabilities of the proposed algorithms but also to conduct a comparative study of the available structure learning algorithms.