Inférence d'interactions d'ordre supérieur et de complexes simpliciaux à partir de données de présence/absence

Authors: Roy-Pomerleau, Xavier
Advisor: Dubé, Louis J.; Desrosiers, Patrick
Abstract: Despite the effectiveness of networks to represent complex systems, recent work has shownthat their structure sometimes limits the explanatory power of the theoretical models, sinceit only encodes dyadic interactions. If a more complex interaction exists in the system, it isautomatically reduced to a group of pairwise interactions that are of the first order. We thusneed to use structures that can take higher-order interactions into account. However, whetherrelationships are of higher order or not is rarely explicit in real data sets. This is the case ofpresence/absence data, that only indicate which species (of animals, plants or others) can befound (or not) on a site without showing the interactions between them.The goal of this project is to develop an inference method to find higher-order interactionswithin presence/absence data. Here, two frameworks are examined. The first one is based onthe comparison of the topology of the data, obtained with a non-restrictive hypothesis, andthe topology of a random ensemble. The second one uses log-linear models and hypothesistesting to infer interactions one by one until the desired order. From this framework, we havedevelopped several inference methods to generate simplicial complexes (or hypergraphs) thatcan be studied with regular tools of network science as well as homology. In order to validatethese methods, we have developed a generative model of presence/absence data in which thetrue interactions are known. Results have also been obtained on real data sets. For instance,from presence/absence data of nesting birds in Québec, we were able to infer co-occurrencesof order two
Document Type: Mémoire de maîtrise
Issue Date: 2020
Open Access Date: 26 October 2020
Grantor: Université Laval
Collection:Thèses et mémoires

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