摘要：While many efforts have been made to prove that the Lasso behaves like a variable selection procedure at the price of strong (though unavoidable) assumptions on the geometric structure of these variables, much less attention has been paid to the oracle inequalities for the Lasso involving the ℓ1-norm of the target vector. Such inequalities proved in the literature show that, provided that the regularization parameter is properly chosen, the Lasso approximately mimics the deterministic Lasso. Some of them do not require any assumption at all, neither on the structure of the variables nor on the regression function. Our first purpose here is to provide a conceptually very simple result in this direction in the framework of Gaussian models with non-random regressors.
关键词：Lasso;ℓ1-oracle inequalities;model selection by penalization;ℓ1-balls;generalized linear Gaussian model.
