Representing uncertainty on set-valued variables using belief functions

Authors:
Thierry Denœux;Zoulficar Younes;Fahed Abdallah
Affiliations:
HEUDIASYC, UTC, CNRS, Centre de Recherche de Royallieu, BP 20529, F-60205 Compiègne, France;HEUDIASYC, UTC, CNRS, Centre de Recherche de Royallieu, BP 20529, F-60205 Compiègne, France;HEUDIASYC, UTC, CNRS, Centre de Recherche de Royallieu, BP 20529, F-60205 Compiègne, France
Venue:
Artificial Intelligence
Year:
2010

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Abstract

A formalism is proposed for representing uncertain information on set-valued variables using the formalism of belief functions. A set-valued variable X on a domain @W is a variable taking zero, one or several values in @W. While defining mass functions on the frame 2^2^^^@W is usually not feasible because of the double-exponential complexity involved, we propose an approach based on a definition of a restricted family of subsets of 2^@W that is closed under intersection and has a lattice structure. Using recent results about belief functions on lattices, we show that most notions from Dempster-Shafer theory can be transposed to that particular lattice, making it possible to express rich knowledge about X with only limited additional complexity as compared to the single-valued case. An application to multi-label classification (in which each learning instance can belong to several classes simultaneously) is demonstrated.