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 ob...

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Bibliographic Details
Published inNeurocomputing (Amsterdam) Vol. 239; pp. 214 - 222
Main Author Rejchel, Wojciech
Format Journal Article
LanguageEnglish
Published Elsevier B.V 24.05.2017
Subjects
High-dimensional problem
Machine learning
Oracle inequality
Penalized risk minimization
Sparse model
U-process
Penalized risk minimization
Oracle inequality
High-dimensional problem
U-process
Sparse model
Machine learning
Online AccessGet full text
ISSN0925-2312
1872-8286
DOI10.1016/j.neucom.2017.02.018

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Summary: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.
ISSN:0925-2312
1872-8286
DOI:10.1016/j.neucom.2017.02.018