Oracle inequalities for ranking and U-processes with Lasso penalty
This provides theoretical guarantees for ranking methods, addressing a popular machine learning problem, but appears incremental as it extends existing Lasso-based analyses to U-processes.
The paper tackles the ranking problem in high-dimensional settings by analyzing estimators from U-processes with Lasso penalty, proving an oracle inequality for excess risk and a bound for the l1 distance to the oracle.
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.