A Midpoint--Radius approach to regression with interval data

Authors:
Reda Boukezzoula;Sylvie Galichet;Amory Bisserier
Affiliations:
Laboratoire d'Informatique, Systèmes, Traitement de l'Information et de la Connaissance -- LISTIC, Université de Savoie, BP. 80439, 74944 Annecy-le-vieux Cedex, France;Laboratoire d'Informatique, Systèmes, Traitement de l'Information et de la Connaissance -- LISTIC, Université de Savoie, BP. 80439, 74944 Annecy-le-vieux Cedex, France;Laboratoire d'Informatique, Systèmes, Traitement de l'Information et de la Connaissance -- LISTIC, Université de Savoie, BP. 80439, 74944 Annecy-le-vieux Cedex, France
Venue:
International Journal of Approximate Reasoning
Year:
2011

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Abstract

In this paper, a revisited interval approach for linear regression is proposed. In this context, according to the Midpoint-Radius (MR) representation, the uncertainty attached to the set-valued model can be decoupled from its trend. The estimated interval model is built from interval input-output data with the objective of covering all available data. The constrained optimization problem is addressed using a linear programming approach in which a new criterion is proposed for representing the global uncertainty of the interval model. The potential of the proposed method is illustrated by simulation examples.