Statistics – Methodology
Scientific paper
2009-06-17
Biometrika 2010, Vol. 97, No. 2, 261-278
Statistics
Methodology
20 pages, 3 figures
Scientific paper
10.1093/biomet/asq008
We consider variable selection in high-dimensional linear models where the number of covariates greatly exceeds the sample size. We introduce the new concept of partial faithfulness and use it to infer associations between the covariates and the response. Under partial faithfulness, we develop a simplified version of the PC algorithm (Spirtes et al., 2000), the PC-simple algorithm, which is computationally feasible even with thousands of covariates and provides consistent variable selection under conditions on the random design matrix that are of a different nature than coherence conditions for penalty-based approaches like the Lasso. Simulations and application to real data show that our method is competitive compared to penalty-based approaches. We provide an efficient implementation of the algorithm in the R-package pcalg.
Bühlmann Peter
Kalisch Markus
Maathuis Marloes H.
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