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

Abstract

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.