Multiclass classification for Hawkes processes
Christophe Denis, Charlotte Dion-Blanc, Laure Sansonnet
Abstract
We investigate the multiclass classification prob- lem where the features are event sequences. More precisely, the data are assumed to be generated by a mixture of simple linear Hawkes processes. In this new setting, the classes are discriminated by various triggering kernels. A challenge is then to build an efficient classification procedure. We de- rive the optimal Bayes rule and provide a two-step estimation procedure of the Bayes classifier. In the first step, the weights of the mixture are estimated; in the second step, an empirical risk minimization procedure is performed to estimate the parameters of the Hawkes processes. We establish the consis- tency of the resulting procedure and derive rates of convergence. Finally, the numerical properties of the data-driven algorithm are illustrated through a simulation study where the triggering kernels are assumed to belong to the popular parametric expo- nential family. It highlights the accuracy and the robustness of the proposed algorithm. In particular, even if the underlying kernels are misspecified, the procedure exhibits good performance.
BibTeX
@InProceedings{pmlr-v180-denis22a,
title = {Multiclass classification for Hawkes processes},
author = {Denis, Christophe and Dion-Blanc, Charlotte and Sansonnet, Laure},
booktitle = {Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence},
pages = {539--547},
year = {2022},
editor = {Cussens, James and Zhang, Kun},
volume = {180},
series = {Proceedings of Machine Learning Research},
month = {01--05 Aug},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v180/denis22a/denis22a.pdf},
url = {https://proceedings.mlr.press/v180/denis22a.html},
abstract = {We investigate the multiclass classification prob- lem where the features are event sequences. More precisely, the data are assumed to be generated by a mixture of simple linear Hawkes processes. In this new setting, the classes are discriminated by various triggering kernels. A challenge is then to build an efficient classification procedure. We de- rive the optimal Bayes rule and provide a two-step estimation procedure of the Bayes classifier. In the first step, the weights of the mixture are estimated; in the second step, an empirical risk minimization procedure is performed to estimate the parameters of the Hawkes processes. We establish the consis- tency of the resulting procedure and derive rates of convergence. Finally, the numerical properties of the data-driven algorithm are illustrated through a simulation study where the triggering kernels are assumed to belong to the popular parametric expo- nential family. It highlights the accuracy and the robustness of the proposed algorithm. In particular, even if the underlying kernels are misspecified, the procedure exhibits good performance.}
}