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We investigate properties of estimators obtained by minimization ofU-processes with the Lasso penalty in high-dimensional settings. Our attentionis focused on the ranking problem that is popular in machine learning. It isrelated to guessing the ordering between objects on the basis of their observedpredictors. We prove the oracle inequality for the excess risk of theconsidered estimator as well as the bound for the l1 distance between theestimator and the oracle.

Oracle inequalities for ranking and U-processes with Lasso penalty