Hyperedge-Triggered Hawkes Processes for Diagnosing Higher-Order Temporal Dependence in Event Streams
Abstract
Monte Carlo simulation is used to assess a likelihood-based EM procedure for diagnosing higher-order temporal dependence in multivariate event streams. Multivariate Hawkes processes provide a likelihood-based framework for modelling self- and cross-excitation in continuous-time event streams, but their standard pairwise formulation can confound dense dyadic excitation with genuinely group-triggered temporal dependence. We introduce a hyperedge-triggered Hawkes model in which a candidate group contributes additional intensity only after all of its member nodes fire within a prescribed trigger window. A most-recent-anchor convention makes this higher-order component non-accumulating and leads to a corresponding piecewise compensator in the likelihood. The model is estimated by a latent-branching EM algorithm that assigns event-level responsibilities to background, pairwise, and hyperedge-triggered sources. Controlled simulations evaluate recovery, regularisation, convergence, separation from pairwise baselines, trigger-window and kernel-timescale sensitivity, computational scaling, and comparison with a parameter-matched third-order surrogate. The results show that higher-order excitation can be recovered in informative regimes, while pairwise--hyperedge confounding remains the main statistical limitation. Applications to retinal and visual-cortex spike trains are presented as exploratory predictive analyses: the hyperedge-triggered component can improve candidate-penalised held-out fit, but the fitted effects should be interpreted as diagnostics of higher-order temporal dependence rather than calibrated discoveries of individual biological hyperedges.
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BibTeX
@misc{xu2026hyperedgetriggered,
title = {{Hyperedge-Triggered Hawkes Processes for Diagnosing Higher-Order Temporal Dependence in Event Streams}},
author = {Zihan Xu},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2605.26608},
eprint = {2605.26608},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.26608},
}
RIS
TY - UNPB
TI - Hyperedge-Triggered Hawkes Processes for Diagnosing Higher-Order Temporal Dependence in Event Streams
AU - Zihan Xu
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2605.26608
UR - https://arxiv.org/abs/2605.26608
AB - Monte Carlo simulation is used to assess a likelihood-based EM procedure for diagnosing higher-order temporal dependence in multivariate event streams. Multivariate Hawkes processes provide a likelihood-based framework for modelling self- and cross-excitation in continuous-time event streams, but their standard pairwise formulation can confound dense dyadic excitation with genuinely group-triggered temporal dependence. We introduce a hyperedge-triggered Hawkes model in which a candidate group contributes additional intensity only after all of its member nodes fire within a prescribed trigger window. A most-recent-anchor convention makes this higher-order component non-accumulating and leads to a corresponding piecewise compensator in the likelihood. The model is estimated by a latent-branching EM algorithm that assigns event-level responsibilities to background, pairwise, and hyperedge-triggered sources. Controlled simulations evaluate recovery, regularisation, convergence, separation from pairwise baselines, trigger-window and kernel-timescale sensitivity, computational scaling, and comparison with a parameter-matched third-order surrogate. The results show that higher-order excitation can be recovered in informative regimes, while pairwise--hyperedge confounding remains the main statistical limitation. Applications to retinal and visual-cortex spike trains are presented as exploratory predictive analyses: the hyperedge-triggered component can improve candidate-penalised held-out fit, but the fitted effects should be interpreted as diagnostics of higher-order temporal dependence rather than calibrated discoveries of individual biological hyperedges.
ER -