A Unifying Frame for Neighbourhood and Distortion Models

Enrique Miranda, Ignacio Montes, Sébastien Destercke
Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 103:304-313, 2019.

Abstract

Neighbourhoods of precise probabilities are instrumental to perform robustness analysis, as they rely on very few parameters. Many such models, sometimes referred to as distortion models, have been proposed in the literature, such as the pari-mutuel model, linear vacuous mixtures or the constant odds ratio model. In this paper, we show that all of them can be represented as probability sets that are neighbourhoods defined over different (pre)-metrics, providing a unified view of such models. We also compare them in terms of a number of properties: precision, number of extreme points, n-monotonicity, … thus providing possible guidelines to pick a neighbourhood rather than another.

Cite this Paper

BibTeX
@InProceedings{pmlr-v103-miranda19a, title = {A Unifying Frame for Neighbourhood and Distortion Models}, author = {Miranda, Enrique and Montes, Ignacio and Destercke, S\'{e}bastien}, booktitle = {Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {304--313}, year = {2019}, editor = {De Bock, Jasper and de Campos, Cassio P. and de Cooman, Gert and Quaeghebeur, Erik and Wheeler, Gregory}, volume = {103}, series = {Proceedings of Machine Learning Research}, month = {03--06 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v103/miranda19a/miranda19a.pdf}, url = {https://proceedings.mlr.press/v103/miranda19a.html}, abstract = {Neighbourhoods of precise probabilities are instrumental to perform robustness analysis, as they rely on very few parameters. Many such models, sometimes referred to as distortion models, have been proposed in the literature, such as the pari-mutuel model, linear vacuous mixtures or the constant odds ratio model. In this paper, we show that all of them can be represented as probability sets that are neighbourhoods defined over different (pre)-metrics, providing a unified view of such models. We also compare them in terms of a number of properties: precision, number of extreme points, n-monotonicity, … thus providing possible guidelines to pick a neighbourhood rather than another.} }
Endnote
%0 Conference Paper %T A Unifying Frame for Neighbourhood and Distortion Models %A Enrique Miranda %A Ignacio Montes %A Sébastien Destercke %B Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications %C Proceedings of Machine Learning Research %D 2019 %E Jasper De Bock %E Cassio P. de Campos %E Gert de Cooman %E Erik Quaeghebeur %E Gregory Wheeler %F pmlr-v103-miranda19a %I PMLR %P 304--313 %U https://proceedings.mlr.press/v103/miranda19a.html %V 103 %X Neighbourhoods of precise probabilities are instrumental to perform robustness analysis, as they rely on very few parameters. Many such models, sometimes referred to as distortion models, have been proposed in the literature, such as the pari-mutuel model, linear vacuous mixtures or the constant odds ratio model. In this paper, we show that all of them can be represented as probability sets that are neighbourhoods defined over different (pre)-metrics, providing a unified view of such models. We also compare them in terms of a number of properties: precision, number of extreme points, n-monotonicity, … thus providing possible guidelines to pick a neighbourhood rather than another.
APA
Miranda, E., Montes, I. & Destercke, S.. (2019). A Unifying Frame for Neighbourhood and Distortion Models. Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 103:304-313 Available from https://proceedings.mlr.press/v103/miranda19a.html.

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