Reference : Measuring the interactions among variables of 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/10993/7260 | |||

Measuring the interactions among variables of functions over the unit hypercube | |

English | |

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] | |

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 | |

19-30 | |

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 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. | |

University of Luxembourg - UL | |

Researchers ; Professionals ; Students | |

http://hdl.handle.net/10993/7260 | |

10.1007/978-3-642-16292-3_5 | |

http://www.mdai.cat/mdai2010/ | |

http://www.springer.com/computer/ai/book/978-3-642-16291-6 |

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