High-dimensional generalized linear models and the lasso

Details High-dimensional generalized linear models and the lasso High-dimensional generalized linear models and the lasso

2008-04-04

arxiv.org/abs/0804.0703v1

Annals of Statistics 2008, Vol. 36, No. 2, 614-645

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/009053607000000929 the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053607000000929

We consider high-dimensional generalized linear models with Lipschitz loss functions, and prove a nonasymptotic oracle inequality for the empirical risk minimizer with Lasso penalty. The penalty is based on the coefficients in the linear predictor, after normalization with the empirical norm. The examples include logistic regression, density estimation and classification with hinge loss. Least squares regression is also discussed.

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