Neighbourhood models induced by the Euclidean distance and the Kullback-Leibler divergence

Ignacio Montes
Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 215:367-378, 2023.

Abstract

Neighbourhood or distortion models are particular imprecise probability models that appear by creating a neighbourhood around a probability measure given a distorting function and a distortion parameter. This paper investigates the distortion models obtained when considering the Euclidean distance or the Kullback-Leibler divergence as distorting function. We analyse the main properties of the credal sets induced by these two distorting functions as well as the main properties of the associated coherent lower previsions. To conclude the paper, we compare these two models with other well-known distortion models: the pari-mutuel, linear vacuous, constant odds ratio and total variation models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v215-montes23a, title = {Neighbourhood models induced by the {E}uclidean distance and the {K}ullback-{L}eibler divergence}, author = {Montes, Ignacio}, booktitle = {Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {367--378}, year = {2023}, editor = {Miranda, Enrique and Montes, Ignacio and Quaeghebeur, Erik and Vantaggi, Barbara}, volume = {215}, series = {Proceedings of Machine Learning Research}, month = {11--14 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v215/montes23a/montes23a.pdf}, url = {https://proceedings.mlr.press/v215/montes23a.html}, abstract = {Neighbourhood or distortion models are particular imprecise probability models that appear by creating a neighbourhood around a probability measure given a distorting function and a distortion parameter. This paper investigates the distortion models obtained when considering the Euclidean distance or the Kullback-Leibler divergence as distorting function. We analyse the main properties of the credal sets induced by these two distorting functions as well as the main properties of the associated coherent lower previsions. To conclude the paper, we compare these two models with other well-known distortion models: the pari-mutuel, linear vacuous, constant odds ratio and total variation models.} }
Endnote
%0 Conference Paper %T Neighbourhood models induced by the Euclidean distance and the Kullback-Leibler divergence %A Ignacio Montes %B Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2023 %E Enrique Miranda %E Ignacio Montes %E Erik Quaeghebeur %E Barbara Vantaggi %F pmlr-v215-montes23a %I PMLR %P 367--378 %U https://proceedings.mlr.press/v215/montes23a.html %V 215 %X Neighbourhood or distortion models are particular imprecise probability models that appear by creating a neighbourhood around a probability measure given a distorting function and a distortion parameter. This paper investigates the distortion models obtained when considering the Euclidean distance or the Kullback-Leibler divergence as distorting function. We analyse the main properties of the credal sets induced by these two distorting functions as well as the main properties of the associated coherent lower previsions. To conclude the paper, we compare these two models with other well-known distortion models: the pari-mutuel, linear vacuous, constant odds ratio and total variation models.
APA
Montes, I.. (2023). Neighbourhood models induced by the Euclidean distance and the Kullback-Leibler divergence. Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 215:367-378 Available from https://proceedings.mlr.press/v215/montes23a.html.

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