异步事件流中多细胞相互作用超图的统计推断与稳定性边界
Hyperedge-Triggered Hawkes Processes for Diagnosing Higher-Order Temporal Dependence in Event Streams
AI总结：
提出超边触发霍克斯过程（HTH）用于从异步事件数据推断多细胞系统中的高阶交互结构，通过闭合形式的EM算法和CP张量分解实现高效推断，在合成实验中成对恢复误差低于5%，并在视网膜神经节细胞数据上获得+20.6 nats的似然增益。
摘要：
我们引入了超边触发霍克斯（HTH）过程，用于从异步事件时间数据推断多细胞系统中的高阶交互结构。除了标准的成对激发外，HTH强度还包括一个由时间窗口内细胞组同时共发激活的项。我们推导了一个闭合形式的期望最大化算法，其关键成分是一个分段补偿器，消除了朴素积分公式中存在的系统性偏差。CP张量分解将超边参数计数从O(N^K)减少到O(NR)。在十一个合成实验中，该框架实现了低于5%的成对恢复误差，同时揭示了超边权重上系统性的-22%偏差，该偏差在核衰减率上非单调，排除了简单的时间重叠解释，并激发了自适应核方法。在小鼠视网膜神经节细胞的多电极记录中，该模型相对于成对基线获得了+20.6 nats的似然增益，为高阶交互提供了提示性但非决定性的证据。代码和所有实验公开于https://github.com/Hanii0210/hypergraph-hawkes。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
