Reference : Measuring the interactions among variables of functions over the unit hypercube
 Document type : Scientific congresses, symposiums and conference proceedings : Paper published in a book Discipline(s) : Physical, chemical, mathematical & earth Sciences : MathematicsBusiness & economic sciences : Quantitative methods in economics & management To cite this reference: http://hdl.handle.net/10993/7260
 Title : Measuring the interactions among variables of functions over the unit hypercube Language : English Author, co-author : Marichal, Jean-Luc [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] Mathonet, Pierre [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit] Publication date : 19-Oct-2010 Main document title : Modeling Decisions for Artificial Intelligence: Proceedings 7th International Conference, MDAI 2010, Perpignan, France, October 27-29, 2010 Editor : Torra, Vicenc Narukawa, Yasuo Daumas, Marc Publisher : Springer-Verlag Collection and collection volume : Lecture Notes in Artificial Intelligence Vol. 6408 Pages : 19-30 Peer reviewed : Yes On invitation : No Audience : International ISBN : 978-3-642-16291-6 City : Berlin Country : Germany Event name : 7th Int. Conf. on Modeling Decisions for Artificial Intelligence (MDAI 2010) Event date : from 27-10-2010 to 29-10-2010 Event organizer : Vicenc Torra (IIIA-CSIC, South Catalonia, Spain) Yasuo Narukawa (Toho Gakuen, Japan) Event place (city) : Perpignan Event country : France Abstract : [en] By considering a least squares approximation of a given square integrable function $f\colon[0,1]^n\to\R$ by a multilinear polynomial of a specified degree, we define an index which measures the overall interaction among variables of $f$. This definition extends the concept of Banzhaf interaction index introduced in cooperative game theory. Our approach is partly inspired from multilinear regression analysis, where interactions among the independent variables are taken into consideration. We show that this interaction index has appealing properties which naturally generalize the properties of the Banzhaf interaction index. In particular, we interpret this index as an expected value of the difference quotients of $f$ or, under certain natural conditions on $f$, as an expected value of the derivatives of $f$. These interpretations show a strong analogy between the introduced interaction index and the overall importance index defined by Grabisch and Labreuche [7]. Finally, we discuss a few applications of the interaction index. Funders : University of Luxembourg - UL Target : Researchers ; Professionals ; Students Permalink : http://hdl.handle.net/10993/7260 DOI : 10.1007/978-3-642-16292-3_5 Other URL : http://www.mdai.cat/mdai2010/ http://www.springer.com/computer/ai/book/978-3-642-16291-6

File(s) associated to this reference

Fulltext file(s):

FileCommentaryVersionSizeAccess
Open access
InteractionVariablesMDAI.pdfAuthor postprint193.05 kBView/Open
Limited access
PV-InteractionVariablesMDAI.pdfPublisher postprint201.06 kBRequest a copy