Multiclass classification for Hawkes processes

Christophe Denis, Charlotte Dion-Blanc, Laure Sansonnet
Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, PMLR 180:539-547, 2022.

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.

Cite this Paper

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.} }
Endnote
%0 Conference Paper %T Multiclass classification for Hawkes processes %A Christophe Denis %A Charlotte Dion-Blanc %A Laure Sansonnet %B Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2022 %E James Cussens %E Kun Zhang %F pmlr-v180-denis22a %I PMLR %P 539--547 %U https://proceedings.mlr.press/v180/denis22a.html %V 180 %X 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.
APA
Denis, C., Dion-Blanc, C. & Sansonnet, L.. (2022). Multiclass classification for Hawkes processes. Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 180:539-547 Available from https://proceedings.mlr.press/v180/denis22a.html.

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