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December 2014 CAM: Causal additive models, high-dimensional order search and penalized regression
Peter Bühlmann, Jonas Peters, Jan Ernest
Ann. Statist. 42(6): 2526-2556 (December 2014). DOI: 10.1214/14-AOS1260


We develop estimation for potentially high-dimensional additive structural equation models. A key component of our approach is to decouple order search among the variables from feature or edge selection in a directed acyclic graph encoding the causal structure. We show that the former can be done with nonregularized (restricted) maximum likelihood estimation while the latter can be efficiently addressed using sparse regression techniques. Thus, we substantially simplify the problem of structure search and estimation for an important class of causal models. We establish consistency of the (restricted) maximum likelihood estimator for low- and high-dimensional scenarios, and we also allow for misspecification of the error distribution. Furthermore, we develop an efficient computational algorithm which can deal with many variables, and the new method’s accuracy and performance is illustrated on simulated and real data.


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Peter Bühlmann. Jonas Peters. Jan Ernest. "CAM: Causal additive models, high-dimensional order search and penalized regression." Ann. Statist. 42 (6) 2526 - 2556, December 2014.


Published: December 2014
First available in Project Euclid: 12 November 2014

zbMATH: 1309.62063
MathSciNet: MR3277670
Digital Object Identifier: 10.1214/14-AOS1260

Primary: 62G99, 62H99
Secondary: 68T99

Rights: Copyright © 2014 Institute of Mathematical Statistics


Vol.42 • No. 6 • December 2014
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