On the median in imprecise ordinal problems - Archive ouverte HAL Access content directly
Journal Articles Annals of Operations Research Year : 2017

On the median in imprecise ordinal problems



When having to make a prediction under probabilistic uncertainty in ordinal problems , the median offers a number of interesting properties compared to other statistics such as the expected value. In particular, it does not depend on a particular metric defined over the elements, but still takes account of the ordinal nature of the data. It can also be shown to be the minimizer of the L 1 loss function. In this paper, we show that similar results can be obtained when the uncertainty is described not by a single probability distribution, but by a convex set of those. In particular, we relate the lower and upper medians to the L 1 loss function via the notion of lower and upper expectations (and extend these results to general quantiles). We also show that, using a different decision rule, the lower and upper median can be retrieved when assuming the cost to be strictly monotonic and symmetric, and nothing more. Finally, we run some tests to show the interest of using Median based predictions with convex sets of probabilities in ordinal regression problems.
Fichier principal
Vignette du fichier
Median_ordinal_paper.pdf (179 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-01618325 , version 1 (17-10-2017)



Sébastien Destercke. On the median in imprecise ordinal problems. Annals of Operations Research, 2017, 256 (2), pp.375-392. ⟨10.1007/s10479-016-2253-x⟩. ⟨hal-01618325⟩
65 View
185 Download



Gmail Facebook Twitter LinkedIn More