Integrating expert's knowledge constraint of time dependent exposures in structure learning for Bayesian networks

Learning a Bayesian network is a difficult and well known task that has been largely investigated. To reduce the number of candidate graphs to test, some authors proposed to incorporate a priori expert knowledge. Most of the time, this a priori information between variables influences the learning but never contradicts the data. In addition, the development of Bayesian networks integrating time such as dynamic Bayesian networks allows identifying causal graphs in the context of longitudinal data. Moreover, in the context where the number of strongly correlated variables is large (i.e. oncology) and the number of patients low; if a biomarker has a mediated effect on another, the learning algorithm would associate them wrongly and vice versa. In this article we propose a method to use the a priori expert knowledge as hard constraints in a structure learning method for Bayesian networks with a time dependant exposure. Based on a simulation study and an application, where we compared our method to the state of the art PC-algorithm, the results showed a better recovery of the true graphs when integrating hard constraints a priori expert knowledge even for small level of information.