Mean-field inference of Hawkes point processes - Département de mathématiques appliquées Accéder directement au contenu
Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2016

Mean-field inference of Hawkes point processes

Résumé

We propose a fast and efficient estimation method that is able to accurately recover the parameters of a d -dimensional Hawkes point-process from a set of observations. We exploit a mean-field approximation that is valid when the fluctuations of the stochastic intensity are small. We show that this is notably the case in situations when interactions are sufficiently weak, when the dimension of the system is high or when the fluctuations are self-averaging due to the large number of past events they involve. In such a regime the estimation of a Hawkes process can be mapped on a least-squares problem for which we provide an analytic solution. Though this estimator is biased, we show that its precision can be comparable to the one of the maximum likelihood estimator while its computation speed is shown to be improved considerably. We give a theoretical control on the accuracy of our new approach and illustrate its efficiency using synthetic datasets, in order to assess the statistical estimation error of the parameters.

Dates et versions

hal-01313837 , version 1 (10-05-2016)

Identifiants

Citer

Emmanuel Bacry, Stéphane Gaïffas, Iacopo Mastromatteo, Jean-François Muzy. Mean-field inference of Hawkes point processes. Journal of Physics A: Mathematical and Theoretical, 2016, 49 (17), pp.174006. ⟨10.1088/1751-8113/49/17/174006⟩. ⟨hal-01313837⟩
103 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More