## Characterization and Greedy Learning of Interventional Markov Equivalence Classes of Directed Acyclic Graphs

** Alain Hauser, Peter Bühlmann**; 13(Aug):2409−2464, 2012.

### Abstract

The investigation of directed acyclic graphs (DAGs) encoding the same Markov property, that is the same conditional independence relations of multivariate observational distributions, has a long tradition; many algorithms exist for model selection and structure learning in Markov equivalence classes. In this paper, we extend the notion of Markov equivalence of DAGs to the case of interventional distributions arising from*multiple*intervention experiments. We show that under reasonable assumptions on the intervention experiments, interventional Markov equivalence defines a finer partitioning of DAGs than observational Markov equivalence and hence improves the identifiability of causal models. We give a graph theoretic criterion for two DAGs being Markov equivalent under interventions and show that each interventional Markov equivalence class can, analogously to the observational case, be uniquely represented by a chain graph called

*interventional essential graph*(also known as

*CPDAG*in the observational case). These are key insights for deriving a generalization of the Greedy Equivalence Search algorithm aimed at structure learning from interventional data. This new algorithm is evaluated in a simulation study.

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