Uncovering Causality from Multivariate Hawkes Integrated Cumulants - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Machine Learning Research Année : 2018

Uncovering Causality from Multivariate Hawkes Integrated Cumulants

Résumé

We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each node of the process, but also disentangles the causality relationships between them. Our approach is the first that leads to an estimation of this matrix without any parametric modeling and estimation of the kernels themselves. As a consequence, it can give an estimation of causality relationships between nodes (or users), based on their activity timestamps (on a social network for instance), without knowing or estimating the shape of the activities lifetime. For that purpose, we introduce a moment matching method that fits the second-order and the third-order integrated cumulants of the process. A theoretical analysis allows us to prove that this new estimation technique is consistent. Moreover, we show, on numerical experiments, that our approach is indeed very robust with respect to the shape of the kernels and gives appealing results on the MemeTracker database and on financial order book data.
Fichier principal
Vignette du fichier
17-284.pdf (1.51 Mo) Télécharger le fichier
Origine : Fichiers éditeurs autorisés sur une archive ouverte
Loading...

Dates et versions

hal-02393136 , version 1 (04-12-2019)

Identifiants

  • HAL Id : hal-02393136 , version 1

Citer

Massil Achab, Emmanuel Bacry, Stéphane Gaïffas, Iacopo Mastromatteo, Jean-François Muzy. Uncovering Causality from Multivariate Hawkes Integrated Cumulants. Journal of Machine Learning Research, 2018, 18, pp.192. ⟨hal-02393136⟩
72 Consultations
22 Téléchargements

Partager

Gmail Facebook X LinkedIn More