Reference : Measuring the Interactions among Variables of Functions over the Unit hypercube
Scientific congresses and symposiums : Paper published in a book
Engineering, computing & technology : Computer science
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/92808
Measuring the Interactions among Variables of Functions over the Unit hypercube
English
Marichal, Jean-Luc mailto [University of Luxembourg > FSTC > Mathematics Research Unit > >]
Mathonet, Pierre mailto [University of Luxembourg > FSTC > Mathematics Research Unit > >]
2010
Modeling Decisions for Artificial Intelligence 7th International Conference, MDAI 2010
Springer
Lecture notes in artificial intelligence 6408
19-30
Yes
No
International
0302-9743
Berlin
Germany
Modeling Decisions for Artificial Intelligence, 7th International Conference, MDAI 2010
October 27-29, 2010
Perpignan
France
[en] Interaction index ; multilinear polynomial ; least squares approximation ; difference operator ; aggregation function ; cooperative game
[en] By considering a least squares approximation of a given square integrable function f:[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. Finally, we discuss a few applications of the interaction index.
Researchers
http://hdl.handle.net/2268/92808
10.1007/978-3-642-16292-3_5

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