Nonlinear Desirability as a Linear Classification Problem

Arianna Casanova, Alessio Benavoli, Marco Zaffalon
Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, PMLR 147:61-71, 2021.

Abstract

The present paper proposes a generalization of linearity axioms of coherence through a geometrical approach, which leads to an alternative interpretation of desirability as a classification problem. In particular, we analyze different sets of rationality axioms and, for each one of them, we show that proving that a subject, who provides finite accept and reject statements, respects these axioms, corresponds to solving a binary classification task using, each time, a different (usually nonlinear) family of classifiers. Moreover, by borrowing ideas from machine learning, we show the possibility to define a feature mapping allowing us to reformulate the above nonlinear classification problems as linear ones in a higher-dimensional space. This allows us to interpret gambles directly as payoffs vectors of monetary lotteries, as well as to reduce the task of proving the rationality of a subject to a linear classification task.

Cite this Paper

BibTeX
@InProceedings{pmlr-v147-casanova21a, title = {Nonlinear Desirability as a Linear Classification Problem}, author = {Casanova, Arianna and Benavoli, Alessio and Zaffalon, Marco}, booktitle = {Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications}, pages = {61--71}, 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/casanova21a/casanova21a.pdf}, url = {https://proceedings.mlr.press/v147/casanova21a.html}, abstract = {The present paper proposes a generalization of linearity axioms of coherence through a geometrical approach, which leads to an alternative interpretation of desirability as a classification problem. In particular, we analyze different sets of rationality axioms and, for each one of them, we show that proving that a subject, who provides finite accept and reject statements, respects these axioms, corresponds to solving a binary classification task using, each time, a different (usually nonlinear) family of classifiers. Moreover, by borrowing ideas from machine learning, we show the possibility to define a feature mapping allowing us to reformulate the above nonlinear classification problems as linear ones in a higher-dimensional space. This allows us to interpret gambles directly as payoffs vectors of monetary lotteries, as well as to reduce the task of proving the rationality of a subject to a linear classification task.} }
Endnote
%0 Conference Paper %T Nonlinear Desirability as a Linear Classification Problem %A Arianna Casanova %A Alessio Benavoli %A Marco Zaffalon %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-casanova21a %I PMLR %P 61--71 %U https://proceedings.mlr.press/v147/casanova21a.html %V 147 %X The present paper proposes a generalization of linearity axioms of coherence through a geometrical approach, which leads to an alternative interpretation of desirability as a classification problem. In particular, we analyze different sets of rationality axioms and, for each one of them, we show that proving that a subject, who provides finite accept and reject statements, respects these axioms, corresponds to solving a binary classification task using, each time, a different (usually nonlinear) family of classifiers. Moreover, by borrowing ideas from machine learning, we show the possibility to define a feature mapping allowing us to reformulate the above nonlinear classification problems as linear ones in a higher-dimensional space. This allows us to interpret gambles directly as payoffs vectors of monetary lotteries, as well as to reduce the task of proving the rationality of a subject to a linear classification task.
APA
Casanova, A., Benavoli, A. & Zaffalon, M.. (2021). Nonlinear Desirability as a Linear Classification Problem. Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 147:61-71 Available from https://proceedings.mlr.press/v147/casanova21a.html.

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