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Fitting aggregation functions to data: part I-linearization and regularization
conference contribution
posted on 2016-06-11, 00:00 authored by M Bartoszuk, Gleb BeliakovGleb Beliakov, Marek Gagolewski, Simon JamesSimon JamesThe 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.
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Source
Information processing and management of uncertainty in knowledge-based systemsVolume
611Series
Communications in computer and information sciencePagination
767 - 779Publisher
SpringerLocation
Eindhoven, The NetherlandsPlace of publication
Berlin, GermanyPublisher DOI
Start date
2016-06-20End date
2016-06-24ISSN
1865-0929ISBN-13
9783319405803Language
engNotes
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 - refereedCopyright notice
2016, SpringerExtent
67Editor/Contributor(s)
J Carvalho, M Lesot, U Kaymak, S Vieira, B Bouchon-Meunier, R YagerTitle of proceedings
IPMU 2016 : Proceedings of the 16th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based SystemsUsage metrics
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