Characterizing and Learning Equivalence Classes of Causal DAGs under Interventions

TL;DR

This paper extends the understanding of causal DAG identifiability under general interventions, characterizes equivalence classes, and proposes a consistent algorithm for learning DAGs from combined observational and interventional data.

Contribution

It generalizes previous results to non-perfect interventions, defines interventional Markov equivalence classes, and introduces the first provably consistent learning algorithm for this setting.

Findings

The proposed algorithm accurately recovers causal structures in simulations.

The method effectively analyzes biological gene regulatory networks.

Interventional data improves causal discovery over observational data alone.

Abstract

We consider the problem of learning causal DAGs in the setting where both observational and interventional data is available. This setting is common in biology, where gene regulatory networks can be intervened on using chemical reagents or gene deletions. Hauser and B\"uhlmann (2012) previously characterized the identifiability of causal DAGs under perfect interventions, which eliminate dependencies between targeted variables and their direct causes. In this paper, we extend these identifiability results to general interventions, which may modify the dependencies between targeted variables and their causes without eliminating them. We define and characterize the interventional Markov equivalence class that can be identified from general (not necessarily perfect) intervention experiments. We also propose the first provably consistent algorithm for learning DAGs in this setting and evaluate our algorithm on simulated and biological datasets.