Measuring the diversity of classifications obtained by transmission chains

Short topic / Sujet de TER

Knowledge diversity is a key ingredient of knowledge evolution. We aim at measuring the diversity of classifications obtained through transmission chain experiments with an original entropy-based diversity measure.

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. Diversity may be considered from three different dimensions:

Variety: how many categories of individuals are represented? (insects, molluscs, vertebrate vs. insects, molluscs)
Balance: how many representatives of each category are there? (1 vertebrates, 99 insects vs. 50 vertebrate, 50 insects)
Disparity: how different are these categories? (33 ants, 33 bugs, 33 grasshoppers vs. 33 rabbits, 33 ants, 33 snakes)

We defined an entropy-based measure [5] inspired from the work of Tom Leinster [1] 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 +∞], 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.

We are interested in knowledge diversity: the fact that different people may held different knowledge and beliefs [2]. The categories thus correspond to equivalent knowledge and their distance is computed semantically. Measuring diversity amounts to associate a relative quantity to the knowledge diversity of a population of agents.

In cultural evolution, transmission chain experiments have highlighted how diversity can occur during knowledge transmission [3]. We have proposed a way to simulate transmission chain experiments on computers that also generate variation in the transmitted knowledge. In this case, the knowledge to be transmitted is a classification of the Class? game that we developed [4,6] and the message to transmit it are class samples.

The goal of this topic is to investigate the influence of various parameters (number of cards, completion strategy, length of the chain) on the fidelity and the diversity of the knowledge of a population obtained through transmission chains.

The work should unfold in the following way:

Read literature
Adapt entropic diversity measures to the Class? game structure
Design experiments for testing parameters
Run experiments
Write report and presentation

References:

[1] Tom Leinster, Entropy and diversity: the axiomatic approach, Cambridge university press, Cambridge (UK), 2021 https://arxiv.org/pdf/2012.02113.pdf
[2] 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
[3] Alex Mesoudi, Andrew Whiten, The multiple roles of cultural transmission experiments in understanding human cultural evolution, Philosophical transactions of the royal society B 363:3489–3501, 2008 http://dx.doi.org/10.1098/rstb.2008.0129
[4] Line van den Berg, Jérôme Euzenat, Class? en classe: jouer avec des classifications pour combiner mathématiques et informatique, Recherches et recherches-actions en didactique de l'informatique 1(1), 2024 https://moex.inria.fr/files/papers/vandenberg2024a.pdf

Links:
[5] Knowledge diversity notebook: https://moex.inria.fr/software/kdiv/index.html
[6] Class? game site: https://moex.inria.fr/mediation/class/
[7] mOeX web site: https://moex.inria.fr

Advisor: 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. .

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.