Supervised Ensemble-based Causal DAG Selection

Causal Discovery (CD) identifes cause-and-effect relationships from data using statistical learning. Several CD algorithms have been proposed relying on different assumptions, e.g. about the statistical relations among variables. However, which assumptions actually hold for a specifc case study is not known a priori. Given a dataset obtained by sampling the joint distribution of all variables of a generative causal model, in general each algorithm could reconstruct a different Direct Acyclic Graph (DAG): some will be closer to the ground truth (GT) DAG than others, depending also on the applicability of the respective assumptions to the case study. As a consequence, given a collection of heterogeneous case studies, a hypothetical GT-aware oracle, able to select the best DAG out of the set of reconstructed DAGs, will outclass the average performance of the individual algorithms of the ensemble. In this work, we propose a supervised approach, relying on multilabel classifcation, to select the DAGs closest to GT by only comparing the topologies of the reconstructed DAGs. We carried out the study on a wide synthetic data set of causal models, sampling DAG topologies up to ten vertices, and using a representative set of linear and non-linear statistical dependencies. Whereas the best individual CD algorithm yields, on average, a distance from GT three times larger than the oracle, our algorithm features an average distance from GT only about 10% larger than the oracle.