Identification and Model Testing in Linear Structural Equation Models using Auxiliary Variables

Bryant Chen, Daniel Kumor, Elias Bareinboim
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:757-766, 2017.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-chen17f, title = {Identification and Model Testing in Linear Structural Equation Models using Auxiliary Variables}, author = {Bryant Chen and Daniel Kumor and Elias Bareinboim}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {757--766}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/chen17f/chen17f.pdf}, url = {https://proceedings.mlr.press/v70/chen17f.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Identification and Model Testing in Linear Structural Equation Models using Auxiliary Variables %A Bryant Chen %A Daniel Kumor %A Elias Bareinboim %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-chen17f %I PMLR %P 757--766 %U https://proceedings.mlr.press/v70/chen17f.html %V 70 %X 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.
APA
Chen, B., Kumor, D. & Bareinboim, E.. (2017). Identification and Model Testing in Linear Structural Equation Models using Auxiliary Variables. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:757-766 Available from https://proceedings.mlr.press/v70/chen17f.html.

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