Learning Hawkes Processes Under Synchronization Noise

William Trouleau, Jalal Etesami, Matthias Grossglauser, Negar Kiyavash, Patrick Thiran
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:6325-6334, 2019.

Abstract

Multivariate Hawkes processes (MHP) are widely used in a variety of fields to model the occurrence of discrete events. Prior work on learning MHPs has only focused on inference in the presence of perfect traces without noise. We address the problem of learning the causal structure of MHPs when observations are subject to an unknown delay. In particular, we introduce the so-called synchronization noise, where the stream of events generated by each dimension is subject to a random and unknown time shift. We characterize the robustness of the classic maximum likelihood estimator to synchronization noise, and we introduce a new approach for learning the causal structure in the presence of noise. Our experimental results show that our approach accurately recovers the causal structure of MHPs for a wide range of noise levels, and significantly outperforms classic estimation methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-trouleau19a, title = {Learning {H}awkes Processes Under Synchronization Noise}, author = {Trouleau, William and Etesami, Jalal and Grossglauser, Matthias and Kiyavash, Negar and Thiran, Patrick}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {6325--6334}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/trouleau19a/trouleau19a.pdf}, url = {https://proceedings.mlr.press/v97/trouleau19a.html}, abstract = {Multivariate Hawkes processes (MHP) are widely used in a variety of fields to model the occurrence of discrete events. Prior work on learning MHPs has only focused on inference in the presence of perfect traces without noise. We address the problem of learning the causal structure of MHPs when observations are subject to an unknown delay. In particular, we introduce the so-called synchronization noise, where the stream of events generated by each dimension is subject to a random and unknown time shift. We characterize the robustness of the classic maximum likelihood estimator to synchronization noise, and we introduce a new approach for learning the causal structure in the presence of noise. Our experimental results show that our approach accurately recovers the causal structure of MHPs for a wide range of noise levels, and significantly outperforms classic estimation methods.} }
Endnote
%0 Conference Paper %T Learning Hawkes Processes Under Synchronization Noise %A William Trouleau %A Jalal Etesami %A Matthias Grossglauser %A Negar Kiyavash %A Patrick Thiran %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-trouleau19a %I PMLR %P 6325--6334 %U https://proceedings.mlr.press/v97/trouleau19a.html %V 97 %X Multivariate Hawkes processes (MHP) are widely used in a variety of fields to model the occurrence of discrete events. Prior work on learning MHPs has only focused on inference in the presence of perfect traces without noise. We address the problem of learning the causal structure of MHPs when observations are subject to an unknown delay. In particular, we introduce the so-called synchronization noise, where the stream of events generated by each dimension is subject to a random and unknown time shift. We characterize the robustness of the classic maximum likelihood estimator to synchronization noise, and we introduce a new approach for learning the causal structure in the presence of noise. Our experimental results show that our approach accurately recovers the causal structure of MHPs for a wide range of noise levels, and significantly outperforms classic estimation methods.
APA
Trouleau, W., Etesami, J., Grossglauser, M., Kiyavash, N. & Thiran, P.. (2019). Learning Hawkes Processes Under Synchronization Noise. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:6325-6334 Available from https://proceedings.mlr.press/v97/trouleau19a.html.

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