Independent Natural Extension for Choice Functions

Arthur Van Camp, Kevin Blackwell, Jason Konek
Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, PMLR 147:320-330, 2021.

Abstract

We investigate epistemic independence for choice functions in a multivariate setting. This work is a continuation of earlier work of one of the authors [23], and our results build on the characterization of choice functions in terms of sets of binary preferences recently established by De Bock and De Cooman [7]. We obtain the independent natural extension in this framework. Given the generality of choice functions, our expression for the independent natural extension is the most general one we are aware of, and we show how it implies the independent natural extension for sets of desirable gambles, and therefore also for less informative imprecise-probabilistic models. Once this is in place, we compare this concept of epistemic independence to another independence concept for choice functions proposed by Seidenfeld [22], which De Bock and De Cooman [1]:S-independence have called S-independence. We show that neither is more general than the other.

Cite this Paper

BibTeX
@InProceedings{pmlr-v147-van-camp21a, title = {Independent Natural Extension for Choice Functions}, author = {Van Camp, Arthur and Blackwell, Kevin and Konek, Jason}, booktitle = {Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications}, pages = {320--330}, year = {2021}, editor = {Cano, Andrés and De Bock, Jasper and Miranda, Enrique and Moral, Serafı́n}, volume = {147}, series = {Proceedings of Machine Learning Research}, month = {06--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v147/van-camp21a/van-camp21a.pdf}, url = {https://proceedings.mlr.press/v147/van-camp21a.html}, abstract = {We investigate epistemic independence for choice functions in a multivariate setting. This work is a continuation of earlier work of one of the authors [23], and our results build on the characterization of choice functions in terms of sets of binary preferences recently established by De Bock and De Cooman [7]. We obtain the independent natural extension in this framework. Given the generality of choice functions, our expression for the independent natural extension is the most general one we are aware of, and we show how it implies the independent natural extension for sets of desirable gambles, and therefore also for less informative imprecise-probabilistic models. Once this is in place, we compare this concept of epistemic independence to another independence concept for choice functions proposed by Seidenfeld [22], which De Bock and De Cooman [1]:S-independence have called S-independence. We show that neither is more general than the other.} }
Endnote
%0 Conference Paper %T Independent Natural Extension for Choice Functions %A Arthur Van Camp %A Kevin Blackwell %A Jason Konek %B Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2021 %E Andrés Cano %E Jasper De Bock %E Enrique Miranda %E Serafı́n Moral %F pmlr-v147-van-camp21a %I PMLR %P 320--330 %U https://proceedings.mlr.press/v147/van-camp21a.html %V 147 %X We investigate epistemic independence for choice functions in a multivariate setting. This work is a continuation of earlier work of one of the authors [23], and our results build on the characterization of choice functions in terms of sets of binary preferences recently established by De Bock and De Cooman [7]. We obtain the independent natural extension in this framework. Given the generality of choice functions, our expression for the independent natural extension is the most general one we are aware of, and we show how it implies the independent natural extension for sets of desirable gambles, and therefore also for less informative imprecise-probabilistic models. Once this is in place, we compare this concept of epistemic independence to another independence concept for choice functions proposed by Seidenfeld [22], which De Bock and De Cooman [1]:S-independence have called S-independence. We show that neither is more general than the other.
APA
Van Camp, A., Blackwell, K. & Konek, J.. (2021). Independent Natural Extension for Choice Functions. Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 147:320-330 Available from https://proceedings.mlr.press/v147/van-camp21a.html.

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