High-dimensional generalized linear models and the lasso
High-dimensional generalized linear models and the lasso
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DOI：
10.1214/009053607000000929
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发表时间：
2008-04-01
影响因子：
4.5
通讯作者：
van de Geer, Sara A.
中科院分区：
文献类型：
--
作者：
van de Geer, Sara A.
我们考虑具有 Lipschitz 损失函数的高维广义线性模型，并证明具有 Lasso 惩罚的经验风险最小化器的非渐近预言不等式。惩罚基于线性预测器中的系数，并使用经验范数进行归一化。这些例子包括逻辑回归、密度估计和铰链损失分类。还讨论了最小二乘回归。
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.