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Fitting aggregation functions to data: part I-linearization and regularization

Version 2 2024-06-04, 03:29
Version 1 2016-08-31, 11:38
conference contribution
posted on 2024-06-04, 03:29 authored by M Bartoszuk, Gleb BeliakovGleb Beliakov, M Gagolewski, Simon JamesSimon James
The use of supervised learning techniques for fitting weights and/or generator functions of weighted quasi-arithmetic means – a special class of idempotent and nondecreasing aggregation functions – to empirical data has already been considered in a number of papers. Nevertheless, there are still some important issues that have not been discussed in the literature yet. In the first part of this two-part contribution we deal with the concept of regularization, a quite standard technique from machine learning applied so as to increase the fit quality on test and validation data samples. Due to the constraints on the weighting vector, it turns out that quite different methods can be used in the current framework, as compared to regression models. Moreover, it is worth noting that so far fitting weighted quasi-arithmetic means to empirical data has only been performed approximately, via the so-called linearization technique. In this paper we consider exact solutions to such special optimization tasks and indicate cases where linearization leads to much worse solutions.

History

Volume

611

Pagination

767-779

Location

Eindhoven, The Netherlands

Start date

2016-06-20

End date

2016-06-24

ISSN

1865-0929

ISBN-13

9783319405803

Language

eng

Notes

This publication is part II of the 16th IPMU International Conference held on 20-24 June 2016, Eindhoven, The Netherlands.

Publication classification

E Conference publication, E1 Full written paper - refereed

Copyright notice

2016, Springer

Extent

67

Editor/Contributor(s)

Carvalho J, Lesot M, Kaymak U, Vieira S, Bouchon-Meunier B, Yager R

Title of proceedings

IPMU 2016 : Proceedings of the 16th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems

Publisher

Springer

Place of publication

Berlin, Germany

Series

Communications in computer and information science