### 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}

}

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

### 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}

}

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.