Cumulants of Hawkes Processes are Robust to Observation Noise

William Trouleau, Jalal Etesami, Matthias Grossglauser, Negar Kiyavash, Patrick Thiran
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:10444-10454, 2021.

Abstract

Multivariate Hawkes processes (MHPs) are widely used in a variety of fields to model the occurrence of causally related discrete events in continuous time. Most state-of-the-art approaches address the problem of learning MHPs from perfect traces without noise. In practice, the process through which events are collected might introduce noise in the timestamps. In this work, we address the problem of learning the causal structure of MHPs when the observed timestamps of events are subject to random and unknown shifts, also known as random translations. We prove that the cumulants of MHPs are invariant to random translations, and therefore can be used to learn their underlying causal structure. Furthermore, we empirically characterize the effect of random translations on state-of-the-art learning methods. We show that maximum likelihood-based estimators are brittle, while cumulant-based estimators remain stable even in the presence of significant time shifts.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-trouleau21a, title = {Cumulants of Hawkes Processes are Robust to Observation Noise}, author = {Trouleau, William and Etesami, Jalal and Grossglauser, Matthias and Kiyavash, Negar and Thiran, Patrick}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {10444--10454}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/trouleau21a/trouleau21a.pdf}, url = {https://proceedings.mlr.press/v139/trouleau21a.html}, abstract = {Multivariate Hawkes processes (MHPs) are widely used in a variety of fields to model the occurrence of causally related discrete events in continuous time. Most state-of-the-art approaches address the problem of learning MHPs from perfect traces without noise. In practice, the process through which events are collected might introduce noise in the timestamps. In this work, we address the problem of learning the causal structure of MHPs when the observed timestamps of events are subject to random and unknown shifts, also known as random translations. We prove that the cumulants of MHPs are invariant to random translations, and therefore can be used to learn their underlying causal structure. Furthermore, we empirically characterize the effect of random translations on state-of-the-art learning methods. We show that maximum likelihood-based estimators are brittle, while cumulant-based estimators remain stable even in the presence of significant time shifts.} }
Endnote
%0 Conference Paper %T Cumulants of Hawkes Processes are Robust to Observation Noise %A William Trouleau %A Jalal Etesami %A Matthias Grossglauser %A Negar Kiyavash %A Patrick Thiran %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-trouleau21a %I PMLR %P 10444--10454 %U https://proceedings.mlr.press/v139/trouleau21a.html %V 139 %X Multivariate Hawkes processes (MHPs) are widely used in a variety of fields to model the occurrence of causally related discrete events in continuous time. Most state-of-the-art approaches address the problem of learning MHPs from perfect traces without noise. In practice, the process through which events are collected might introduce noise in the timestamps. In this work, we address the problem of learning the causal structure of MHPs when the observed timestamps of events are subject to random and unknown shifts, also known as random translations. We prove that the cumulants of MHPs are invariant to random translations, and therefore can be used to learn their underlying causal structure. Furthermore, we empirically characterize the effect of random translations on state-of-the-art learning methods. We show that maximum likelihood-based estimators are brittle, while cumulant-based estimators remain stable even in the presence of significant time shifts.
APA
Trouleau, W., Etesami, J., Grossglauser, M., Kiyavash, N. & Thiran, P.. (2021). Cumulants of Hawkes Processes are Robust to Observation Noise. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:10444-10454 Available from https://proceedings.mlr.press/v139/trouleau21a.html.

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