Diversity depends on different dimensions, hence its measures is usually parameterised. We seek to determine whether one distribution is absolutely, for all parameter values, more diverse than another.
The diversity of many phenomena is worth measuring because diversity is often related to fairness and sometimes to resilience. It is also good to measure how our actions increase or decrease diversity. We are interested in knowledge diversity: the fact that different people may held different knowledge and beliefs [1].
Measuring diversity amounts to associate a relative quantity to the knowledge diversity of a population of agents. We only consider agent populations of the same size whose individuals are distributed in different categories. Diversity may be considered from three different dimensions:
We defined an entropy-based measure [1] inspired from the work of Tom Leinster [2] which is parametrised by a similarity measure between the categories. It puts the emphasis of the equal dispersion of observations in these types weighted by the similarity between such types. In our case, the categories are ontologies and the similarity measure will account for the semantic similarity between them. It is parametrised by another parameter $q$, ranging in $[0,+\infty[$, which puts more or less emphasis on variety and balance. One population can be said to be more diverse than another if the measure of the former is higher than that of the latter for all values of $q$.
The question is, given two populations whose distribution within categories are $d$ and $d′$, how to determine which one is more diverse than the other independently from $q$? I.e. for all $q\in [0, +\infty[$, the diversity of $d$ is higher than that of $d'$.
The question may be answered analytically by finding necessary conditions for this to be the case or computationally by designing an algorithm comparing the curves of the diversity of the two measures with respect to $q$.
The task of the student would be:
References:
[1] Yasser Bourahla, Jérôme David, Jérôme Euzenat, Meryem Naciri, Measuring and controlling knowledge diversity, Proc. 1st JOWO workshop on formal models of knowledge diversity (FMKD), Jönköping (SE), 2022 https://moex.inria.fr/files/papers/bourahla2022c.pdf
[2] Tom Leinster, Entropy and diversity: the axiomatic approach, Cambridge university press, Cambridge (UK), 2021
https://arxiv.org/pdf/2012.02113.pdf
Links:
Advisor: Jérôme David (Jerome:David#inria:fr), Koji Hasebe (hasebe#cs:tsukuba:ac:jp), Jérôme Euzenat (Jerome:Euzenat#inria:fr).
Team: The work will be carried out in the mOeX team common to INRIA & Université Grenoble Alpes. mOeX is dedicated to study knowledge evolution through adaptation. It can be used as a joint M1 project with the University of Tsukuba. .
Laboratory: LIG.
Place of work: The position is located at INRIA Grenoble Rhône-Alpes, Montbonnot (near Grenoble, France) a main computer science research lab, in a stimulating research environment.
Procedure: Contact us and provide vitæ and possibly motivation letter and references.