The Annals of Statistics

High-dimensional additive modeling

Lukas Meier, Sara van de Geer, and Peter Bühlmann

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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.

Article information

Ann. Statist. Volume 37, Number 6B (2009), 3779-3821.

First available in Project Euclid: 23 October 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G08: Nonparametric regression 62F12: Asymptotic properties of estimators
Secondary: 62J07: Ridge regression; shrinkage estimators

Group lasso model selection nonparametric regression oracle inequality penalized likelihood sparsity


Meier, Lukas; van de Geer, Sara; Bühlmann, Peter. High-dimensional additive modeling. Ann. Statist. 37 (2009), no. 6B, 3779--3821. doi:10.1214/09-AOS692.

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