On the median in imprecise ordinal problems

Abstract : 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.
Document type :
Journal articles
Complete list of metadatas

Cited literature [28 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01618325
Contributor : Sébastien Destercke <>
Submitted on : Tuesday, October 17, 2017 - 4:48:55 PM
Last modification on : Tuesday, May 28, 2019 - 4:07:59 PM
Long-term archiving on : Thursday, January 18, 2018 - 3:26:12 PM

File

Median_ordinal_paper.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

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

Share

Metrics

Record views

120

Files downloads

131