Bi-level path following for cross validated solution of kernel quantile regression

Saharon Rosset*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations

Abstract

Modeling of conditional quantiles requires specification of the quantile being estimated and can thus be viewed as a parameterized predictive modeling problem. Quantile loss is typically used, and it is indeed parameterized by a quantile parameter. In this paper we show how to follow the path of cross validated solutions to regularized kernel quantile regression. Even though the bi-level optimization problem we encounter for every quantile is non-convex, the manner in which the optimal cross-validated solution evolves with the parameter of the loss function allows tracking of this solution. We prove this property, construct the resulting algorithm, and demonstrate it on data. This algorithm allows us to efficiently solve the whole family of bi-level problems.

Original languageEnglish
Title of host publicationProceedings of the 25th International Conference on Machine Learning
PublisherAssociation for Computing Machinery (ACM)
Pages840-847
Number of pages8
ISBN (Print)9781605582054
DOIs
StatePublished - 2008
Event25th International Conference on Machine Learning - Helsinki, Finland
Duration: 5 Jul 20089 Jul 2008

Publication series

NameProceedings of the 25th International Conference on Machine Learning

Conference

Conference25th International Conference on Machine Learning
Country/TerritoryFinland
CityHelsinki
Period5/07/089/07/08

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