Oracle inequalities for ranking and U-processes with Lasso penalty

We investigate properties of estimators obtained by minimization of U-processes with the Lasso penalty in the high-dimensional setting. Our attention is focused on the ranking problem that is popular in machine learning. It is related to guessing the ordering between objects on the basis of their observed predictors. We prove the oracle inequality for the excess risk of the considered estimator as well as the bound for the l1 distance |θ^−θ*|1 between the estimator and the oracle. Besides, we study properties of estimators on simulated data sets.