Detection of Short-Term Temporal Dependencies in Hawkes Processes with Heterogeneous Background Dynamics

Yu Chen, Fengpei Li, Anderson Schneider, Yuriy Nevmyvaka, Asohan Amarasingham, Henry Lam
Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, PMLR 216:369-380, 2023.

Abstract

Many kinds of simultaneously-observed event sequences exhibit mutually exciting or inhibiting patterns. Reliable detection of such temporal dependencies is crucial for scientific investigation. A common model is the Multivariate Hawkes Process (MHP), whose impact function naturally encodes a causal structure in Granger causality. However, the vast majority of existing methods use a transformed standard MHP intensity with a constant baseline, which may be inconsistent with real-world data. On the other hand, modeling irregular and unknown background dynamics directly is a challenge, as one struggles to distinguish the effect of mutual interaction from that of fluctuations in background dynamics. In this paper, we address the short-term temporal dependency detection issue. We show that maximum likelihood estimation (MLE) for cross-impact from MHP has an error that can not be eliminated, but may be reduced by an order of magnitude using a heterogeneous intensity not for the target HP but for the interacting HP. Then we propose a robust and computationally-efficient modification of MLE that does not rely on the prior estimation of the heterogeneous intensity and is thus applicable in a data-limited regime (e.g., few-shot, unrepeated observations). Extensive experiments on various datasets show that our method outperforms existing ones by notable margins, with highlighted novel applications in neuroscience.

Cite this Paper

BibTeX
@InProceedings{pmlr-v216-chen23g, title = {Detection of Short-Term Temporal Dependencies in {H}awkes Processes with Heterogeneous Background Dynamics}, author = {Chen, Yu and Li, Fengpei and Schneider, Anderson and Nevmyvaka, Yuriy and Amarasingham, Asohan and Lam, Henry}, booktitle = {Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence}, pages = {369--380}, year = {2023}, editor = {Evans, Robin J. and Shpitser, Ilya}, volume = {216}, series = {Proceedings of Machine Learning Research}, month = {31 Jul--04 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v216/chen23g/chen23g.pdf}, url = {https://proceedings.mlr.press/v216/chen23g.html}, abstract = {Many kinds of simultaneously-observed event sequences exhibit mutually exciting or inhibiting patterns. Reliable detection of such temporal dependencies is crucial for scientific investigation. A common model is the Multivariate Hawkes Process (MHP), whose impact function naturally encodes a causal structure in Granger causality. However, the vast majority of existing methods use a transformed standard MHP intensity with a constant baseline, which may be inconsistent with real-world data. On the other hand, modeling irregular and unknown background dynamics directly is a challenge, as one struggles to distinguish the effect of mutual interaction from that of fluctuations in background dynamics. In this paper, we address the short-term temporal dependency detection issue. We show that maximum likelihood estimation (MLE) for cross-impact from MHP has an error that can not be eliminated, but may be reduced by an order of magnitude using a heterogeneous intensity not for the target HP but for the interacting HP. Then we propose a robust and computationally-efficient modification of MLE that does not rely on the prior estimation of the heterogeneous intensity and is thus applicable in a data-limited regime (e.g., few-shot, unrepeated observations). Extensive experiments on various datasets show that our method outperforms existing ones by notable margins, with highlighted novel applications in neuroscience.} }
Endnote
%0 Conference Paper %T Detection of Short-Term Temporal Dependencies in Hawkes Processes with Heterogeneous Background Dynamics %A Yu Chen %A Fengpei Li %A Anderson Schneider %A Yuriy Nevmyvaka %A Asohan Amarasingham %A Henry Lam %B Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2023 %E Robin J. Evans %E Ilya Shpitser %F pmlr-v216-chen23g %I PMLR %P 369--380 %U https://proceedings.mlr.press/v216/chen23g.html %V 216 %X Many kinds of simultaneously-observed event sequences exhibit mutually exciting or inhibiting patterns. Reliable detection of such temporal dependencies is crucial for scientific investigation. A common model is the Multivariate Hawkes Process (MHP), whose impact function naturally encodes a causal structure in Granger causality. However, the vast majority of existing methods use a transformed standard MHP intensity with a constant baseline, which may be inconsistent with real-world data. On the other hand, modeling irregular and unknown background dynamics directly is a challenge, as one struggles to distinguish the effect of mutual interaction from that of fluctuations in background dynamics. In this paper, we address the short-term temporal dependency detection issue. We show that maximum likelihood estimation (MLE) for cross-impact from MHP has an error that can not be eliminated, but may be reduced by an order of magnitude using a heterogeneous intensity not for the target HP but for the interacting HP. Then we propose a robust and computationally-efficient modification of MLE that does not rely on the prior estimation of the heterogeneous intensity and is thus applicable in a data-limited regime (e.g., few-shot, unrepeated observations). Extensive experiments on various datasets show that our method outperforms existing ones by notable margins, with highlighted novel applications in neuroscience.
APA
Chen, Y., Li, F., Schneider, A., Nevmyvaka, Y., Amarasingham, A. & Lam, H.. (2023). Detection of Short-Term Temporal Dependencies in Hawkes Processes with Heterogeneous Background Dynamics. Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 216:369-380 Available from https://proceedings.mlr.press/v216/chen23g.html.

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