Oracle inequalities for ranking and U-processes with Lasso penalty

TL;DR

This paper establishes oracle inequalities for Lasso-penalized estimators in high-dimensional ranking problems using U-processes, providing theoretical guarantees on excess risk and estimator accuracy.

Contribution

It introduces novel oracle inequalities for Lasso-penalized U-process estimators specifically in high-dimensional ranking tasks, advancing theoretical understanding.

Findings

Proved oracle inequality for excess risk

Bounded L1 distance between estimator and oracle

Applicable to high-dimensional ranking problems

Abstract

We investigate properties of estimators obtained by minimization of U-processes with the Lasso penalty in high-dimensional settings. 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 between the estimator and the oracle.