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

Imhoi Koo; Rhee Man Kil

doi:10.1007/978-3-540-72383-7_131

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

Imhoi Koo, Rhee Man Kil

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	Advances in Neural Networks - ISNN 2007 - 4th International Symposium on Neural Networks, ISNN 2007, Proceedings
Publisher	Springer Verlag
Pages	1117-1126
Number of pages	10
Edition	PART 1
ISBN (Print)	9783540723820
DOIs	https://doi.org/10.1007/978-3-540-72383-7_131
State	Published - Jan 1 2007
Event	4th International Symposium on Neural Networks, ISNN 2007 - Nanjing, China Duration: Jun 3 2007 → Jun 7 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Number	PART 1
Volume	4491 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	4th International Symposium on Neural Networks, ISNN 2007
Country/Territory	China
City	Nanjing
Period	6/3/07 → 6/7/07

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-540-72383-7_131

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). Springer Verlag. https://doi.org/10.1007/978-3-540-72383-7_131

Koo, Imhoi ; Kil, Rhee Man. / Regularization for regression models based on the k-functional with Besov norm. Advances in Neural Networks - ISNN 2007 - 4th International Symposium on Neural Networks, ISNN 2007, Proceedings. PART 1. ed. Springer Verlag, 2007. pp. 1117-1126 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1).

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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.",

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Koo, I & Kil, RM 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 edn, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 1, vol. 4491 LNCS, Springer Verlag, pp. 1117-1126, 4th International Symposium on Neural Networks, ISNN 2007, Nanjing, China, 6/3/07. https://doi.org/10.1007/978-3-540-72383-7_131

Regularization for regression models based on the k-functional with Besov norm. / Koo, Imhoi; Kil, Rhee Man.
Advances in Neural Networks - ISNN 2007 - 4th International Symposium on Neural Networks, ISNN 2007, Proceedings. PART 1. ed. Springer Verlag, 2007. p. 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).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AB - 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.

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Koo I, Kil RM. 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. Springer Verlag. 2007. p. 1117-1126. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1). doi: 10.1007/978-3-540-72383-7_131

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

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