Hyperedge-Triggered Hawkes Processes for Diagnosing Higher-Order Temporal Dependence in Event Streams
用于诊断事件流高阶时间依赖的超边触发 Hawkes 过程AI 解读 ↓
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用于诊断事件流高阶时间依赖的超边触发 Hawkes 过程
- 研究问题
- 如何区分多元事件流中的密集成对激励与真正的群组触发依赖，并评估两类机制在统计上能否被可靠区分？
- 方法与思路
- 作者提出成员须在触发窗口内全部发生事件的超边机制，以最近锚点避免累积，并用潜在分支 EM 算法估计各类来源。
- 材料陈述的贡献
- 摘要称该方法在信息充分的情形下可恢复高阶激励；神经放电应用中的留出拟合可改善，但成对与超边混淆仍是主要限制。
- 阅读关注点
- 应核对触发窗口、补偿项和正则化设置，检查参数匹配基准、留出评价及敏感性分析如何支持高阶依赖的诊断。
- 阅读边界
- 依据 arXiv v3 预印本摘要，不能声称已同行评审或获期刊接收。摘要未给出具体数值；拟合超边不能解释为经校准的生物学发现。
原文摘要
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.