Regularization for regression models based on the k-functional with Besov norm

Imhoi Koo, Rhee Man Kil

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper presents a new method of regularization in regression problems using a Besov norm (or semi-norm) acting as a regularization operator. This norm is more general smoothness measure to approximation spaces compared to other norms such as Sobolev and RKHS norms which are usually used in the conventional regularization methods. In our work, we also suggest a new candidate of the regularization parameter, that is, the trade-off between the data fit and the smoothness of the estimation function. Through the simulation for function approximation, we have shown that the suggested regularization method is effective and the estimated values of regularization parameters are close to the optimal values associated with the minimum expected risks.

Original languageEnglish (US)
Title of host publicationAdvances in Neural Networks - ISNN 2007 - 4th International Symposium on Neural Networks, ISNN 2007, Proceedings
Pages1117-1126
Number of pages10
EditionPART 1
StatePublished - Dec 24 2007
Event4th International Symposium on Neural Networks, ISNN 2007 - Nanjing, China
Duration: Jun 3 2007Jun 7 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume4491 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference4th International Symposium on Neural Networks, ISNN 2007
CountryChina
CityNanjing
Period6/3/076/7/07

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Koo, I., & Kil, R. M. (2007). Regularization for regression models based on the k-functional with Besov norm. In Advances in Neural Networks - ISNN 2007 - 4th International Symposium on Neural Networks, ISNN 2007, Proceedings (PART 1 ed., pp. 1117-1126). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4491 LNCS, No. PART 1).