Non-asymptotic oracle inequalities for the Lasso and Group Lasso in high dimensional logistic model

Abstract : 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 eigenvalue assumption as introduced in [P.J. Bickel, Y. Ritov and A.B. Tsybakov, Ann. Statist. 37 (2009) 1705-1732].
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Marius Kwemou. Non-asymptotic oracle inequalities for the Lasso and Group Lasso in high dimensional logistic model. ESAIM: Probability and Statistics, EDP Sciences, 2016, 20, pp.309-331. ⟨10.1051/ps/2015020⟩. ⟨hal-01601407⟩

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