Learning Acyclic Directed Mixed Graphs from Observations and Interventions

We introduce a new family of mixed graphical models that consists of graphs with possibly directed, undirected and bidirected edges but without directed cycles. Moreover, there can be up to three edges between any pair of nodes. The new family includes Richardson’s acyclic directed mixed graphs, as well as Andersson-Madigan-Perlman chain graphs. These features imply that no family of mixed graphical models that we know of subsumes the new models. We also provide a causal interpretation of the new models as systems of structural equations with correlated errors. Finally, we describe an exact algorithm for learning the new models from observational and interventional data via answer set programming.