Learning Optimal Cyclic Causal Graphs from Interventional Data

We consider 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 non-linear relations over cyclic structures. In this work we make several contributions in this setting. (i) We generalize 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) We empirically analyze different schemes for weighting independence constraints in terms of accuracy and runtimes of bcause. (iii) We provide improvements to a previous declarative answer set programming (ASP) based approach for causal discovery employing the sigma-separation criterion, and empirically evaluate bcause and the refined ASP-approach.