### 2023

Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco

Closure operators, classifiers and desirability Proceeding

Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 215:25-36, 2023.

Abstract | Links | BibTeX | Tags: imprecise probability

@proceedings{Benavoli2023e,

title = {Closure operators, classifiers and desirability},

author = {Alessio Benavoli and Alessandro Facchini and Marco Zaffalon},

editor = {Enrique Miranda, Ignacio Montes, Erik Quaeghebeur, Barbara Vantaggi},

url = {https://proceedings.mlr.press/v215/benavoli23a/benavoli23a.pdf},

year = {2023},

date = {2023-07-15},

urldate = {2023-07-15},

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.},

howpublished = {Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 215:25-36},

keywords = {imprecise probability},

pubstate = {published},

tppubtype = {proceedings}

}

### 2021

Casanova, Arianna; Benavoli, Alessio; Zaffalon, Marco

Nonlinear Desirability as a Linear Classification Problem Inproceedings

In: ISIPTA'21 Int. Symposium on Imprecise Probability: Theories and Applications, PJMLR, 2021.

Abstract | Links | BibTeX | Tags: desirability, imprecise probability

@inproceedings{Casanova2021,

title = {Nonlinear Desirability as a Linear Classification Problem},

author = {Casanova, Arianna and Benavoli, Alessio and Zaffalon, Marco},

url = {http://alessiobenavoli.com/wp-content/uploads/2021/07/casanova21-1.pdf},

year = {2021},

date = {2021-07-07},

booktitle = {ISIPTA'21 Int. Symposium on Imprecise Probability: Theories and Applications, PJMLR},

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},

keywords = {desirability, imprecise probability},

pubstate = {published},

tppubtype = {inproceedings}

}

### 2020

Ristic, Branko; Gilliam, Christopher; Byrne, Marion; Benavoli, Alessio

A tutorial on uncertainty modeling for machine reasoning Journal Article

In: Information Fusion, vol. 55, pp. 30 - 44, 2020, ISSN: 1566-2535.

Abstract | Links | BibTeX | Tags: imprecise probability

@article{RISTIC2019,

title = {A tutorial on uncertainty modeling for machine reasoning},

author = {Branko Ristic and Christopher Gilliam and Marion Byrne and Alessio Benavoli},

url = {http://alessiobenavoli.com/wp-content/uploads/2019/08/Uncertainty_tutorial.pdf},

doi = {https://doi.org/10.1016/j.inffus.2019.08.001},

issn = {1566-2535},

year = {2020},

date = {2020-01-01},

journal = {Information Fusion},

volume = {55},

pages = {30 - 44},

abstract = {Increasingly we rely on machine intelligence for reasoning and decision making under uncertainty. This tutorial reviews the prevalent methods for model-based autonomous decision making based on observations and prior knowledge, primarily in the context of classification. Both observations and the knowledge-base available for reasoning are treated as being uncertain. Accordingly, the central themes of this tutorial are quantitative modeling of uncertainty, the rules required to combine such uncertain information, and the task of decision making under uncertainty. The paper covers the main approaches to uncertain knowledge representation and reasoning, in particular, Bayesian probability theory, possibility theory, reasoning based on belief functions and finally imprecise probability theory. The main feature of the tutorial is that it illustrates various approaches with several testing scenarios, and provides MATLAB solutions for them as a supplementary material for an interested reader.},

keywords = {imprecise probability},

pubstate = {published},

tppubtype = {article}

}