Jointly interventional and observational data: estimation of interventional Markov equivalence classes of directed acyclic graphs

TL;DR

This paper introduces a Gaussian likelihood framework for jointly modeling observational and interventional data to improve causal graph estimation, with proven consistency and empirical validation.

Contribution

It proposes a novel joint modeling approach for observational and interventional data, enhancing identifiability of causal DAGs and providing theoretical and empirical validation.

Findings

Consistent BIC-based estimation of interventional Markov equivalence classes.

Improved identifiability reduces ambiguity in causal graph inference.

Empirical results demonstrate effectiveness on real and simulated data.

Abstract

In many applications we have both observational and (randomized) interventional data. We propose a Gaussian likelihood framework for joint modeling of such different data-types, based on global parameters consisting of a directed acyclic graph (DAG) and correponding edge weights and error variances. Thanks to the global nature of the parameters, maximum likelihood estimation is reasonable with only one or few data points per intervention. We prove consistency of the BIC criterion for estimating the interventional Markov equivalence class of DAGs which is smaller than the observational analogue due to increased partial identifiability from interventional data. Such an improvement in identifiability has immediate implications for tighter bounds for inferring causal effects. Besides methodology and theoretical derivations, we present empirical results from real and simulated data.