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Causal statistical inference in high dimensions

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  • Peter Bühlmann

Abstract

We present a short selective review of causal inference from observational data, with a particular emphasis on the high-dimensional scenario where the number of measured variables may be much larger than sample size. Despite major identifiability problems, making causal inference from observational data very ill-posed, we outline a methodology providing useful bounds for causal effects. Furthermore, we discuss open problems in optimization, non-linear estimation and for assigning statistical measures of uncertainty, and we illustrate the benefits and limitations of high-dimensional causal inference for biological applications. Copyright Springer-Verlag 2013

Suggested Citation

  • Peter Bühlmann, 2013. "Causal statistical inference in high dimensions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 357-370, June.
    • Handle: RePEc:spr:mathme:v:77:y:2013:i:3:p:357-370
    DOI: 10.1007/s00186-012-0404-7
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    References listed on IDEAS

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    1. Kalisch, Markus & Mächler, Martin & Colombo, Diego & Maathuis, Marloes H. & Bühlmann, Peter, 2012. "Causal Inference Using Graphical Models with the R Package pcalg," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 47(i11).
    2. P. Bühlmann & M. Kalisch & M. H. Maathuis, 2010. "Variable selection in high-dimensional linear models: partially faithful distributions and the pc -simple algorithm," Biometrika, Biometrika Trust, vol. 97(2), pages 261-278.
    3. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    4. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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