The paper Learning Optimal Cyclic Causal Graphs from Interventional Data by Kari Rantanen, Antti Hyttinen, and Matti Järvisalo has been accepted for publications in the proceedings of the 10th International Conference on Probabilistic Graphical Models (PGM 2020).
The work considers causal discovery in a very general setting involving non-linearities, cycles and several experimental datasets in which only a subset of variables are recorded. Recent approaches combining constraint-based causal discovery, weighted independence constraints and exact optimization have shown improved accuracy. However, they have mainly focused on the d-separation criterion, which is theoretically correct only under strong assumptions such as linearity or acyclicity. The more recently introduced sigma-separation criterion for statistical independence enables constraint-based causal discovery for both non-linear relations and cyclic structures. The paper makes several contributions in this setting. (i) Generalizes bcause, a recent exact branch-and- bound causal discovery approach, to this setting, integrating support for the sigma-separation criterion and several interventional datasets. (ii) Empirically analyzes different schemes for weighting independence constraints in terms of accuracy and runtimes of bcause. (iii) Provides improvements to a previous answer set programming (ASP) based approach for causal discovery employing the sigma-separation criterion, and empirically evaluates bcause and the refined ASP-approach.