Learning Choice Functions with Gaussian Processes

Alessio Benavoli, Dario Azzimonti, Dario Piga
Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, PMLR 216:141-151, 2023.

Abstract

In consumer theory, ranking available objects by means of preference relations yields the most common description of individual choices. However, preference-based models assume that individuals: (1) give their preferences only between pairs of objects; (2) are always able to pick the best preferred object. In many situations, they may be instead choosing out of a set with more than two elements and, because of lack of information and/or incomparability (objects with contradictory characteristics), they may not be able to select a single most preferred object. To address these situations, we need a choice model which allows an individual to express a set-valued choice. Choice functions provide such a mathematical framework. We propose a Gaussian Process model to learn choice functions from choice data. The model assumes a multiple utility representation of a choice function based on the concept of Pareto rationalization, and derives a strategy to learn both the number and the values of these latent multiple utilities. Simulation experiments demonstrate that the proposed model outperforms the state-of-the-art methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v216-benavoli23a, title = {Learning Choice Functions with {G}aussian Processes}, author = {Benavoli, Alessio and Azzimonti, Dario and Piga, Dario}, booktitle = {Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence}, pages = {141--151}, year = {2023}, editor = {Evans, Robin J. and Shpitser, Ilya}, volume = {216}, series = {Proceedings of Machine Learning Research}, month = {31 Jul--04 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v216/benavoli23a/benavoli23a.pdf}, url = {https://proceedings.mlr.press/v216/benavoli23a.html}, abstract = {In consumer theory, ranking available objects by means of preference relations yields the most common description of individual choices. However, preference-based models assume that individuals: (1) give their preferences only between pairs of objects; (2) are always able to pick the best preferred object. In many situations, they may be instead choosing out of a set with more than two elements and, because of lack of information and/or incomparability (objects with contradictory characteristics), they may not be able to select a single most preferred object. To address these situations, we need a choice model which allows an individual to express a set-valued choice. Choice functions provide such a mathematical framework. We propose a Gaussian Process model to learn choice functions from choice data. The model assumes a multiple utility representation of a choice function based on the concept of Pareto rationalization, and derives a strategy to learn both the number and the values of these latent multiple utilities. Simulation experiments demonstrate that the proposed model outperforms the state-of-the-art methods.} }
Endnote
%0 Conference Paper %T Learning Choice Functions with Gaussian Processes %A Alessio Benavoli %A Dario Azzimonti %A Dario Piga %B Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2023 %E Robin J. Evans %E Ilya Shpitser %F pmlr-v216-benavoli23a %I PMLR %P 141--151 %U https://proceedings.mlr.press/v216/benavoli23a.html %V 216 %X In consumer theory, ranking available objects by means of preference relations yields the most common description of individual choices. However, preference-based models assume that individuals: (1) give their preferences only between pairs of objects; (2) are always able to pick the best preferred object. In many situations, they may be instead choosing out of a set with more than two elements and, because of lack of information and/or incomparability (objects with contradictory characteristics), they may not be able to select a single most preferred object. To address these situations, we need a choice model which allows an individual to express a set-valued choice. Choice functions provide such a mathematical framework. We propose a Gaussian Process model to learn choice functions from choice data. The model assumes a multiple utility representation of a choice function based on the concept of Pareto rationalization, and derives a strategy to learn both the number and the values of these latent multiple utilities. Simulation experiments demonstrate that the proposed model outperforms the state-of-the-art methods.
APA
Benavoli, A., Azzimonti, D. & Piga, D.. (2023). Learning Choice Functions with Gaussian Processes. Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 216:141-151 Available from https://proceedings.mlr.press/v216/benavoli23a.html.

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