Statistical learning of collections of networks with applications in ecology and sociology

Abstract

This thesis deals with the development of statistical methods for the analysis of collections of interaction networks through three original contributions. Interaction networks are a natural way to represent in graph form the exchanges or relationships existing between a set of nodes representing species or individuals. Considering collections of networks allows to study heterogeneous systems, composed of several kinds of interactions involving different types of nodes. When the different networks of the collection are linked by a hierarchical relationship, we speak of multilevel networks. The stochastic block model has proven its relevance to model the heterogeneity of the behavior of nodes in a single network. Extensions to collections of networks and to multilevel networks are proposed. They allow to obtain a clustering of the nodes of the networks according to their role in the ecosystem or social system, and to summarize the structure of the system at the mesoscopic scale through a small number of parameters. The inference of these models is complex and variational methods are adapted for this purpose. Model selection methods are also used to determine the dependence between levels for multilevel networks and the similarity between structures for collections of networks.A last part of this thesis proposes a new method to study the robustness of ecological interaction networks. Each network is modeled by a probabilistic model whose parameters represent the network structure. This allows to make the link between the structure of the ecosystem and its robustness, but also to compare the robustness of a collection of networks and to correct the robustness of a network whose sampling would be incomplete.The developed methods are implemented in R packages and applied on data from social sciences and ecology.