Equipping Graphical Models with Interventions and Interactions Simultaneously

In this work, we reinvestigate the classical Markov equivalence classes (MECs) and the interventional Markov equivalence classes ($\cal{I}$\-MECs) with a new lens using higher-order feature interactions. We find that this perspective is particularly insightful for understanding statistical aspects (finite sample complexity) of recovering the true DAG, highlighting the shortcomings which must be faced in practical settings with finite sample availability. We propose this research direction can help close the gap between theoretical results on $\cal{I}$\-MECs and practical approaches in Bayesian experiment design, serving as a possible theoretical support for results occurring in actual experiment data.