Title: Bouligand derivatives and robustness of support vector machines for regression
Authors: Christmann, Andreas ×
Van Messem, Arnout #
Issue Date: May-2008
Publisher: MIT Press
Series Title: Journal of Machine Learning Research vol:9 pages:915-936
Abstract: We investigate robustness properties for a broad class of support vector machines with non-smooth loss functions. These kernel methods are inspired by convex risk minimization in infinite dimensional Hilbert spaces. Leading examples are the support vector machine based on the e-insensitive loss function, and kernel based quantile regression based on the pinball loss function. Firstly, we propose with the Bouligand influence function (BIF) a modification of F. R. Hampel's influence function. The BIF has the advantage of being positive homogeneous which is in general not true for Hampel's influence function. Secondly, we show that many support vector machines based on a Lipschitz continuous loss function and a bounded kernel have a bounded BIF and are thus robust in the sense of robust statistics based on influence functions.
ISSN: 1532-4435
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Non-KU Leuven Association publications
× corresponding author
# (joint) last author

Files in This Item:

There are no files associated with this item.

Request a copy


All items in Lirias are protected by copyright, with all rights reserved.

© Web of science