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### Project: Local inference algorithms for choice functions

##### Description

##### Details

In recent years, imprecise-probabilistic choice functions have gained growing interest, primarily from a theoretical point of view. These versatile and expressive uncertainty models have demonstrated their capacity to represent decision-making scenarios that extend beyond simple pairwise comparisons of options, accommodating situations of indecision as well. They generalise many other uncertainty models, such as probability measures, and even sets of them.

A choice function maps any (finite) set of possible decisions, called 'option set', to a subset of admissible (or non-rejected) decisions. The idea is that a choice function identifies the decisions that are not rejected from within every option set.

One of the topics that have been studied, is how to do inference. An expert tells you, for a finite number of option sets, which decisions he or she rejects. The question is: What are the options that should be rejected from a new option set? This question defines a general inference problem under uncertainty, and the idea is to use only well-established rationality axioms (called 'coherence') only.

This question has been studied from an algorithmic point of view to some extent: "Arne Decadt, Jasper De Bock & Gert de Cooman, Inference with choice Functions made practical" introduce a linear programming technique that solves this question, which they further specialise to the specific decision rule called 'E-admissibility' in "Arne Decadt, Alexander Erreygers, Jasper De Bock & Gert de Cooman, Decision-making with E-admissibility given a finite assessment of choices".

The aim of this master project is twofold: (i) to devise an efficient algorithm for inferring choices based on the decision rule called '(Walleyâ€“Sen) maximality', and (ii) to implement this algorithm, as well as existing algorithms for another decision. These implementations will be used in later algorithms about Bayesian networks with choice functions as local models.

This project requires mathematical interest and programming skills.

Literature

Introduction to choice functions: https://arxiv.org/pdf/1903.00336.pdf

Linear programming solution to inference: https://arxiv.org/pdf/2005.03098.pdf

Algorithm for E-admissibility: https://arxiv.org/pdf/1905.09301.pdf

- Supervisor
- Arthur van Camp
- Secondary supervisor
- Cassio de Campos
- Interested?
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