Reference : Measuring the influence of the kth largest variable on functions over the unit hypercube
Scientific congresses, symposiums and conference proceedings : Paper published in a book
Physical, chemical, mathematical & earth Sciences : Mathematics
Business & economic sciences : Quantitative methods in economics & management
http://hdl.handle.net/10993/7259
Measuring the influence of the kth largest variable on functions over the unit hypercube
English
Marichal, Jean-Luc mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Mathonet, Pierre mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit]
19-Oct-2010
Modeling Decisions for Artificial Intelligence: Proceedings 7th International Conference, MDAI 2010, Perpignan, France, October 27-29, 2010
Torra, Vicenc
Narukawa, Yasuo
Daumas, Marc
Springer-Verlag
Lecture Notes in Artificial Intelligence Vol. 6408
7-18
Yes
No
International
978-3-642-16291-6
Berlin
Germany
7th Int. Conf. on Modeling Decisions for Artificial Intelligence (MDAI 2010)
from 27-10-2010 to 29-10-2010
Vicenc Torra (IIIA-CSIC, South Catalonia, Spain)
Yasuo Narukawa (Toho Gakuen, Japan)
Perpignan
France
[en] By considering a least squares approximation of a given square integrable function $f\colon [0,1]^n\to\R$ by a shifted $L$-statistic function (a shifted linear combination of order statistics), we define an index which measures the global influence of the $k$th largest variable on $f$. We show that this influence index has appealing properties and we interpret it as an average value of the difference quotient of $f$ in the direction of the $k$th largest variable or, under certain natural conditions on $f$, as an average value of the derivative of $f$ in the direction of the $k$th largest variable. We also discuss a few applications of this index in statistics and aggregation theory.
University of Luxembourg - UL
Researchers ; Professionals ; Students
http://hdl.handle.net/10993/7259
http://www.mdai.cat/mdai2010/
http://www.springer.com/computer/ai/book/978-3-642-16291-6

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