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Comparing Interval-Valued Estimations with Point-Valued Estimations

Hugo Saulnier 1, 2 Olivier Strauss 1 Ines Couso 2 
1 ICAR - Image & Interaction
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : In the last decade, numerous proposals have been made to deal with imprecision in estimation problems. Those approaches, many of which involve dealing with interval-valued outputs, deal with the subtle difference between uncertainty and imprecision. One of the crucial points − which to our knowledge has never been addressed − is “how to compare an interval-valued method with a precise valued method?” The usual way to compare two estimation methods is to use benchmark data with ground truths and to compute a distance between the estimates of each method and the ground truth. However, most of the mathematical available extensions of distances are either biased in favor of a precise approach or in favor of an imprecise approach. This paper proposes a new tool, the weighted variation of the mid-point distance (WVD), that is more suitable to achieve this kind of comparison, dealing with imprecision with a particular semantic. After reviewing existing distances, we introduce the WVD, first from an intuitive perspective, then from a more mathematical point of view. Its very satisfactory properties are highlighted through an experiment.
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Submitted on : Tuesday, May 17, 2022 - 12:16:41 PM
Last modification on : Friday, August 5, 2022 - 3:02:19 PM


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Hugo Saulnier, Olivier Strauss, Ines Couso. Comparing Interval-Valued Estimations with Point-Valued Estimations. IPMU 2016 - 16th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Jun 2016, Eindhoven, Netherlands. pp.595-604, ⟨10.1007/978-3-319-40581-0_48⟩. ⟨lirmm-01488052⟩



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