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

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.

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• Penalized Estimation of Directed Acyclic Graphs From Discrete Data
• ABCD-Strategy: Budgeted Experimental Design for Targeted Causal Structure Discovery
• Comparative Benchmarking of Causal Discovery Techniques
• High-Dimensional Joint Estimation of Multiple Directed Gaussian Graphical Models
• Model-based causal feature selection for general response types
• Algebraic Problems in Structural Equation Modeling
• Marginal integration for nonparametric causal inference
• Learning Linear Gaussian Polytree Models with Interventions
• Variance Minimization in the Wasserstein Space for Invariant Causal Prediction
• Distributional Invariances and Interventional Markov Equivalence for Mixed Graph Models
• Analysis of an interventional protein experiment using a vine copula based structural equation model