Supervised classification of Hawkes processes for Ecology

Hawkes processes have recently gained significant attention for their strong modeling capabilities.
In this talk, I will address the supervised classification of multivariate Hawkes processes, assuming that the classes differ through the parameters governing their intensity functions.

This work is motivated by an ecological application: classifying commuting and foraging behaviors of bats from nocturnal activity recorded at various sites in France. We model the distribution of bat calls, detected by acoustic sensors, using Hawkes processes that capture two distinct behavioral patterns.
Our classification algorithm, based on the Empirical Risk Minimization (ERM) principle, provides accurate classifications and is validated on real data.

While the study initially focused on a single species, we aim to extend it to multiple species, which leads to the multivariate and potentially high-dimensional setting.
We propose a new methodology combining two steps: (1) an interaction recovery step per class using a Lasso-type estimator, and (2) a refitting step guided by a suitable classification criterion. We establish the consistency of the recovered interaction structures and derive convergence rates for the resulting classifier.