Reference : Influence and interaction indexes for pseudo-Boolean functions: a unified least squar...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Business & economic sciences : Quantitative methods in economics & management
http://hdl.handle.net/10993/16791
Influence and interaction indexes for pseudo-Boolean functions: a unified least squares approach
English
Marichal, Jean-Luc mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Mathonet, Pierre mailto [University of Liège, Belgium > Department of Mathematics]
31-Dec-2014
Discrete Applied Mathematics
Elsevier Science
179
13–27
Yes
International
0166-218X
Amsterdam
The Netherlands
[en] Cooperative game ; pseudo-Boolean function ; power index ; influence index ; interaction index ; least squares approximation
[en] The Banzhaf power and interaction indexes for a pseudo-Boolean function (or a cooperative game) appear naturally as leading coefficients in the standard least squares approximation of the function by a pseudo-Boolean function of a specified degree. We first observe that this property still holds if we consider approximations by pseudo-Boolean functions depending only on specified variables. We then show that the Banzhaf influence index can also be obtained from the latter approximation problem. Considering certain weighted versions of this approximation problem, we introduce a class of weighted Banzhaf influence indexes, analyze their most important properties, and point out similarities between the weighted Banzhaf influence index and the corresponding weighted Banzhaf interaction index. We also discuss the issue of reconstructing a pseudo-Boolean function from prescribed influences and point out very different behaviors in the weighted and non-weighted cases.
University of Luxembourg - UL
F1R-MTH-PUL-12RDO2 > MRDO2 > 01/02/2012 - 31/01/2015 > MARICHAL Jean-Luc
Researchers ; Professionals ; Students
http://hdl.handle.net/10993/16791
10.1016/j.dam.2014.05.039
http://arxiv.org/abs/1201.3543

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