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Identification and Model Testing in Linear Structural Equation Models using Auxiliary Variables
Bryant Chen · Daniel Kumor · Elias Bareinboim

Tue Aug 08 09:24 PM -- 09:42 PM (PDT) @ C4.1

We developed a novel approach to identification and model testing in linear structural equation models (SEMs) based on auxiliary variables (AVs), which generalizes a widely-used family of methods known as instrumental variables. The identification problem is concerned with the conditions under which causal parameters can be uniquely estimated from an observational, non-causal covariance matrix. In this paper, we provide an algorithm for the identification of causal parameters in linear structural models that subsumes previous state-of-the-art methods. In other words, our algorithm identifies strictly more coefficients and models than methods previously known in the literature. Our algorithm builds on a graph-theoretic characterization of conditional independence relations between auxiliary and model variables, which is developed in this paper. Further, we leverage this new characterization for allowing identification when limited experimental data or new substantive knowledge about the domain is available. Lastly, we develop a new procedure for model testing using AVs.

Author Information

Bryant Chen (IBM Research)
Daniel Kumor (Purdue University)
Elias Bareinboim (Purdue)
Elias Bareinboim

Elias Bareinboim is an associate professor in the Department of Computer Science and the director of the Causal Artificial Intelligence (CausalAI) Laboratory at Columbia University. His research focuses on causal and counterfactual inference and their applications to artificial intelligence and machine learning as well as data-driven fields in the health and social sciences. His work was the first to propose a general solution to the problem of ``causal data-fusion,'' providing practical methods for combining datasets generated under different experimental conditions and plagued with various biases. In the last years, Bareinboim has been exploring the intersection of causal inference with decision-making (including reinforcement learning) and explainability (including fairness analysis). Before joining Columbia, he was an assistant professor at Purdue University and received his Ph.D. in Computer Science from the University of California, Los Angeles. Bareinboim was named one of ``AI's 10 to Watch'' by IEEE, and is a recipient of an NSF CAREER Award, the Dan David Prize Scholarship, the 2014 AAAI Outstanding Paper Award, and the 2019 UAI Best Paper Award.

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