Closure operators, classifiers and desirability

Alessio Benavoli, Alessandro Facchini, Marco Zaffalon
Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 215:25-36, 2023.

Abstract

At the core of Bayesian probability theory, or dually desirability theory, lies an assumption of linearity of the scale in which rewards are measured. We revisit two recent papers that extend desirability theory to the nonlinear case by letting the utility scale be represented either by a general closure operator or by a binary general (nonlinear) classifier. By using standard results in logic, we highlight the connection between these two approaches and show that this connection allows us to extend the separating hyper plane theorem (which is at the core of the duality between Bayesian decision theory and desirability theory) to the nonlinear case.

Cite this Paper

BibTeX
@InProceedings{pmlr-v215-benavoli23a, title = {Closure operators, classifiers and desirability}, author = {Benavoli, Alessio and Facchini, Alessandro and Zaffalon, Marco}, booktitle = {Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {25--36}, 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/benavoli23a/benavoli23a.pdf}, url = {https://proceedings.mlr.press/v215/benavoli23a.html}, abstract = {At the core of Bayesian probability theory, or dually desirability theory, lies an assumption of linearity of the scale in which rewards are measured. We revisit two recent papers that extend desirability theory to the nonlinear case by letting the utility scale be represented either by a general closure operator or by a binary general (nonlinear) classifier. By using standard results in logic, we highlight the connection between these two approaches and show that this connection allows us to extend the separating hyper plane theorem (which is at the core of the duality between Bayesian decision theory and desirability theory) to the nonlinear case.} }
Endnote
%0 Conference Paper %T Closure operators, classifiers and desirability %A Alessio Benavoli %A Alessandro Facchini %A Marco Zaffalon %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-benavoli23a %I PMLR %P 25--36 %U https://proceedings.mlr.press/v215/benavoli23a.html %V 215 %X At the core of Bayesian probability theory, or dually desirability theory, lies an assumption of linearity of the scale in which rewards are measured. We revisit two recent papers that extend desirability theory to the nonlinear case by letting the utility scale be represented either by a general closure operator or by a binary general (nonlinear) classifier. By using standard results in logic, we highlight the connection between these two approaches and show that this connection allows us to extend the separating hyper plane theorem (which is at the core of the duality between Bayesian decision theory and desirability theory) to the nonlinear case.
APA
Benavoli, A., Facchini, A. & Zaffalon, M.. (2023). Closure operators, classifiers and desirability. Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 215:25-36 Available from https://proceedings.mlr.press/v215/benavoli23a.html.

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