High-dimensional generalized linear models and the lasso
van de Geer, Sara A.
Ann. Statist., Tome 36 (2008) no. 1, p. 614-645 / Harvested from Project Euclid
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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.
Publié le : 2008-04-15
Classification:  Lasso,  oracle inequality,  sparsity,  62G08 
@article{1205420513,
     author = {van de Geer, Sara A.},
     title = {High-dimensional generalized linear models and the lasso},
     journal = {Ann. Statist.},
     volume = {36},
     number = {1},
     year = {2008},
     pages = { 614-645},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1205420513}
}

van de Geer, Sara A. High-dimensional generalized linear models and the lasso. Ann. Statist., Tome 36 (2008) no. 1, pp.  614-645. http://gdmltest.u-ga.fr/item/1205420513/