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

TL;DR

This paper extends the concept of Markov equivalence classes of DAGs to interventional data, providing new criteria and algorithms for causal structure learning that improve identifiability over observational methods.

Contribution

It introduces a graph-theoretic criterion for interventional Markov equivalence and develops a generalized greedy algorithm for structure learning from interventional data.

Findings

Interventional Markov equivalence classes are finer than observational ones.

The interventional essential graph uniquely represents each equivalence class.

The new algorithm outperforms existing methods in simulation studies.

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.