Article (Scientific journals)
Influence and interaction indexes for pseudo-Boolean functions: a unified least squares approach
Marichal, Jean-Luc; Mathonet, Pierre
2014In Discrete Applied Mathematics, 179, p. 13–27
Peer reviewed
 

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Keywords :
Cooperative game; pseudo-Boolean function; power index; influence index; interaction index; least squares approximation
Abstract :
[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.
Disciplines :
Quantitative methods in economics & management
Mathematics
Author, co-author :
Marichal, Jean-Luc ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Mathonet, Pierre ;  University of Liège, Belgium > Department of Mathematics
Language :
English
Title :
Influence and interaction indexes for pseudo-Boolean functions: a unified least squares approach
Publication date :
31 December 2014
Journal title :
Discrete Applied Mathematics
ISSN :
0166-218X
Publisher :
Elsevier Science, Amsterdam, Netherlands
Volume :
179
Pages :
13–27
Peer reviewed :
Peer reviewed
Name of the research project :
F1R-MTH-PUL-12RDO2 > MRDO2 > 01/02/2012 - 31/01/2015 > MARICHAL Jean-Luc
Funders :
University of Luxembourg - UL
Available on ORBilu :
since 19 May 2014

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