Open Access
December 2009 High-dimensional additive modeling
Lukas Meier, Sara van de Geer, Peter Bühlmann
Ann. Statist. 37(6B): 3779-3821 (December 2009). DOI: 10.1214/09-AOS692


We propose a new sparsity-smoothness penalty for high-dimensional generalized additive models. The combination of sparsity and smoothness is crucial for mathematical theory as well as performance for finite-sample data. We present a computationally efficient algorithm, with provable numerical convergence properties, for optimizing the penalized likelihood. Furthermore, we provide oracle results which yield asymptotic optimality of our estimator for high dimensional but sparse additive models. Finally, an adaptive version of our sparsity-smoothness penalized approach yields large additional performance gains.


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Lukas Meier. Sara van de Geer. Peter Bühlmann. "High-dimensional additive modeling." Ann. Statist. 37 (6B) 3779 - 3821, December 2009.


Published: December 2009
First available in Project Euclid: 23 October 2009

zbMATH: 1360.62186
MathSciNet: MR2572443
Digital Object Identifier: 10.1214/09-AOS692

Primary: 62F12 , 62G08
Secondary: 62J07

Keywords: group lasso , Model selection , Nonparametric regression , Oracle inequality , penalized likelihood , Sparsity

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 6B • December 2009
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