Least Median of Squares (LMS) and Least Trimmed Squares (LTS) Fitting for the Weighted Arithmetic Mean

Gleb Beliakov , Marek Gągolewski , Simon James

Abstract

We look at different approaches to learning the weights of the weighted arithmetic mean such that the median residual or sum of the smallest half of squared residuals is minimized. The more general problem of multivariate regression has been well studied in statistical literature, however in the case of aggregation functions we have the restriction on the weights and the domain is also usually restricted so that ‘outliers’ may not be arbitrarily large. A number of algorithms are compared in terms of accuracy and speed. Our results can be extended to other aggregation functions.
Author Gleb Beliakov - [Deakin University]
Gleb Beliakov,,
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, Marek Gągolewski (FMIS / DIE) - [Systems Research Institute (IBS PAN) [Polish Academy of Sciences (PAN)]]
Marek Gągolewski,,
- Department of Integral Equations
- Instytucie Badań Systemowych
, Simon James - [Deakin University]
Simon James,,
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Pages367-378
Publication size in sheets0.55
Book Medina Jesús, Ojeda-Aciego M, Verdegay José Luis, Pelta David A., Cabrera Inma P., Bouchon-Meunier Bernadette, Yager Ronald R. (eds.): IPMU 2018: Proceedings of the 17th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems : Theory and Foundations, Communications in Computer and Information Science, vol. 854, 2018, Springer International Publishing, ISBN 978-3-319-91475-6, [978-3-319-91476-3], DOI:10.1007/978-3-319-91476-3
ASJC Classification2600 General Mathematics; 1700 General Computer Science
DOIDOI:10.1007/978-3-319-91476-3_31
Languageen angielski
Score (nominal)15
Score sourceconferenceIndex
ScoreMinisterial score = 15.0, 26-01-2020, ChapterFromConference
Publication indicators WoS Citations = 1; Scopus Citations = 2; Scopus SNIP (Source Normalised Impact per Paper): 2018 = 0.385
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