Séminaire MODAL'X : Romain Lacoste (INRIA)

Résumé : In this talk, I will present several statistical contributions to the analysis of Hawkes processes developed during my PhD, following a trajectory from application to theory, bridged by implementation. The application concerns bat behavior monitoring across France, using echolocation call data collected through the Vigie-Chiro citizen science project. To distinguish between foraging and commuting behaviors, we model call sequences with Hawkes processes, leveraging the temporal structure of the data. Taking advantage of this modelling, a classification procedure based on empirical risk minimization is proposed. The overall methodology is evaluated with a goodness-of-fit test and results on real data are presented. The results are convincing and show the relevance of our method, which could contribute to a better understanding of behavioural determinants. This application motivates a theoretical investigation into support recovery in high-dimensional multivariate Hawkes processes. Assuming repeated short-time observations and sparse structure of the interaction matrix, we develop a Lasso-penalized least-squares estimator. Under standard assumptions, we establish support recovery consistency as the number of repetitions increases. Leveraging this estimator, we derive a classification method within the framework of supervised learning for which we establish rates of convergence. An in-depth numerical study, using both synthetic and real-world datasets, corroborates our theoretical findings, both for support recovery and for supervised classification. To bridge theory and practice, an open-source Python package named Sparklen, was developed as part of this thesis. It provides a comprehensive suite for the analysis of exponential Hawkes processes, with a focus on high-dimensional settings. Powered by a C++ core code, Sparklen combines ease-of-use with computational efficiency. This dual-language approach makes Sparklen a powerful solution for computationally demanding real-world applications. We present its design and demonstrate its use through practical examples.