Learning Discretized Bayesian Networks with GOMEA
Damy M. F. Ha Tanja Alderliesten Peter A. N. Bosman
Bayesian networks model relationships between random variables under
uncertainty and can be used to predict the likelihood of events and outcomes
while incorporating observed evidence. From an eXplainable AI (XAI)
perspective, such models are interesting as they tend to be compact. Moreover,
captured relations can be directly inspected by domain experts. In practice,
data is often real-valued. Unless assumptions of normality can be made,
discretization is often required. The optimal discretization, however, depends
on the relations modelled between the variables. This complicates learning
Bayesian networks from data. For this reason, most literature focuses on
learning conditional dependencies between sets of variables, called structure
learning. In this work, we extend an existing state-of-the-art structure
learning approach based on the Gene-pool Optimal Mixing Evolutionary Algorithm
(GOMEA) to jointly learn variable discretizations. The proposed Discretized
Bayesian Network GOMEA (DBN-GOMEA) obtains similar or better results than the
current state-of-the-art when tasked to retrieve randomly generated
ground-truth networks. Moreover, leveraging a key strength of evolutionary
algorithms, we can straightforwardly perform DBN learning multi-objectively. We
show how this enables incorporating expert knowledge in a uniquely insightful
fashion, finding multiple DBNs that trade-off complexity, accuracy, and the
difference with a pre-determined expert network.