High-dimensional generalized linear models and the lasso

• 成果类型: Article
• 署名作者: van de Geer, Sara A.
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000929
• 发表日期: 2008
• 页码: 614-645
• 关键词: large underdetermined systems; selection; inequalities; aggregation; CLASSIFIERS; EQUATIONS; sparsity

摘要

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.