Non-asymptotic Oracle Inequalities for the Lasso and Group Lasso in high dimensional logistic model

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We consider the problem of estimating a function f_0 in logistic regression model. We propose to estimate this function f_0 by a sparse approximation build as a linear combination of elements of a given dictionary of p functions. This sparse approximation is selected by the Lasso or Group Lasso procedure. In this context, we state non asymptotic oracle inequalities for Lasso and Group Lasso under restricted eigenvalues assumption as introduced in BRT.