A new ensemble estimator for nonlinear Hawkes processes

par Dr Félix Cheysson (Université Gustave Eiffel)

mardi 3 nov. 2026, 14:00 → 15:00 Europe/Paris

GI UTC

Hawkes processes are a family of 1d point processes for which the occurrence of an event temporarily increases the probability of occurrence of further events.
The nonlinear version of the Hawkes process allows the reproduction function (which in the linear case dictates the increase of probability of occurrence) to be negative, thereby allowing self-inhibition as well as self-excitation.
In this work, we propose a new nonparametric method for the inference of nonlinear Hawkes processes, based on an ensemble estimator inspired by the work of Reynaud-Bouret and Schbath (2010).
This ensemble estimator is constructed by aggregating many random histograms of the reproduction function, obtained via least squares estimation.
We prove an oracle inequality for this estimation method, and investigate numerical simulations which support the proven convergence rate.
This is a joint work with Xuejiao Wang (PhD student, Université Gustave Eiffel) and Mohamed Hebiri (UGE).