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### Project: Implementing 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 decisions 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 are (i) to implement the inference
algorithms mentioned in the papers above, and (ii) to experimentally
compare both algorithms from a complexity point of view. These
implementations will be used in later algorithms about Bayesian networks
with choice functions as local models.

This project requires programming skills. It is a version that is more
focussed on programming and experiments of the related master project
'Local inference algorithms for choice functions'.

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?
- Get in contact