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Markov Boundary Discovery with Ridge Regularized Linear Models

Author

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  • Strobl Eric V.
  • Visweswaran Shyam

    (Center for Causal Discovery, Department of Biomedical Informatics, University of Pittsburgh School of Medicine, 5607 Baum Boulevard, Pittsburgh, PA 15206, USA)

Abstract

Ridge regularized linear models (RRLMs), such as ridge regression and the SVM, are a popular group of methods that are used in conjunction with coefficient hypothesis testing to discover explanatory variables with a significant multivariate association to a response. However, many investigators are reluctant to draw causal interpretations of the selected variables due to the incomplete knowledge of the capabilities of RRLMs in causal inference. Under reasonable assumptions, we show that a modified form of RRLMs can get “very close” to identifying a subset of the Markov boundary by providing a worst-case bound on the space of possible solutions. The results hold for any convex loss, even when the underlying functional relationship is nonlinear, and the solution is not unique. Our approach combines ideas in Markov boundary and sufficient dimension reduction theory. Experimental results show that the modified RRLMs are competitive against state-of-the-art algorithms in discovering part of the Markov boundary from gene expression data.

Suggested Citation

  • Strobl Eric V. & Visweswaran Shyam, 2016. "Markov Boundary Discovery with Ridge Regularized Linear Models," Journal of Causal Inference, De Gruyter, vol. 4(1), pages 31-48, March.
    • Handle: RePEc:bpj:causin:v:4:y:2016:i:1:p:31-48:n:2
    DOI: 10.1515/jci-2015-0011
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    References listed on IDEAS

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    2. Eaton, Morris L., 1986. "A characterization of spherical distributions," Journal of Multivariate Analysis, Elsevier, vol. 20(2), pages 272-276, December.
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