A Capacity-Based Semantics for Inconsistency-Tolerant Inferences

Dubois, Didier; Prade, Henri

doi:10.1007/978-3-031-18843-5_8

Cited by 1 publication

(2 citation statements)

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“…Enumerating all the MCS of a set of polytopes is a difficult problem in the general case. However, polynomial algorithms (Dubois et al (2000)) exist in the case of intervals. We will show in this section that such results can also be used in the case where we consider a set H of axis-aligned hyperrectangles, in order to efficiently determine the set of MCS C H .…”

Section: Enumerating the Mcss Of Axis-aligned Hyperrectanglesmentioning

confidence: 99%

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Multi-dimensional Maximal Coherent Subsets Made Easy: Illustration on an Estimation Problem

Loïc

Destercke

2022

Building Bridges Between Soft and Statistical Methodologies for Data Science

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Fusing uncertain pieces of information to obtain a synthetic estimation when those are inconsistent is a difficult task. A particularly appealing solution to solve such conflict or inconsistency is to look at maximal coherent subsets of sources (MCS), and to concentrate on those. Yet, enumerating MCS is a difficult combinatorial task in general, making the use of MCS limited in practice. In this paper, we are interested in the case where the pieces of information are multi-dimensional sets or polytopes. While the problem remains difficult for general polytopes, we show that it can be solved more efficiently for hyperrectangles. We then illustrate how such an approach could be used to estimate linear models in the presence of outliers or in the presence of misspecified model.

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Section: Enumerating the Mcss Of Axis-aligned Hyperrectanglesmentioning

confidence: 99%

“…Detecting and enumerating MCS are NP-hard problems, with intervals being a well-known exception (Dubois et al (2000)). In this paper, we show that we can extend this exception to hyperrectangles, which can in turn be used as approximations of polytopes.…”

Section: Introductionmentioning

confidence: 99%

Multi-dimensional Maximal Coherent Subsets Made Easy: Illustration on an Estimation Problem

Loïc

Destercke

2022

Building Bridges Between Soft and Statistical Methodologies for Data Science

View full text Add to dashboard Cite

show abstract

A Capacity-Based Semantics for Inconsistency-Tolerant Inferences

Cited by 1 publication

References 20 publications

Multi-dimensional Maximal Coherent Subsets Made Easy: Illustration on an Estimation Problem

Multi-dimensional Maximal Coherent Subsets Made Easy: Illustration on an Estimation Problem

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