Many event sequence data exhibit mutually exciting or inhibiting patterns. Reliable detection of such temporal dependency is crucial for scientific investigation. The de facto 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 direct or nonlinear transform of standard MHP intensity with constant baseline, inconsistent with real-world data. Under irregular and unknown heterogeneous intensity, capturing temporal dependency is hard as one struggles to distinguish the effect of mutual interaction from that of intensity fluctuation. In this paper, we address the short-term temporal dependency detection issue. We show the maximum likelihood estimation (MLE) for cross-impact from MHP has an error that can not be eliminated but may be reduced by order of magnitude, using heterogeneous intensity not of the target HP but of the interacting HP. Then we proposed a robust and computationally-efficient method modified from 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, no repeated observations). Extensive experiments on various datasets show that our method outperforms existing ones by notable margins, with highlighted novel applications in neuroscience.

翻译：许多事件序列数据表现出相互激发或抑制的模式。可靠检测此类时间依赖关系对于科学研究至关重要。事实上的模型是多变量霍克斯过程（MHP），其影响函数自然编码了格兰杰因果关系中的因果结构。然而，现有绝大多数方法使用具有恒定基线的标准MHP强度的直接或非线性变换，这与现实世界数据不一致。在不规则且未知的异构强度下，捕捉时间依赖关系变得困难，因为人们难以区分相互影响效应与强度波动效应。本文针对短期时间依赖检测问题展开研究。我们证明，MHP交叉影响的最大似然估计（MLE）存在无法消除的误差，但若使用交互HP（而非目标HP）的异构强度，该误差可降低一个数量级。随后，我们提出一种鲁棒且计算高效的MLE改进方法，该方法不依赖异构强度的先验估计，因此适用于数据受限场景（例如少样本、无重复观测）。在多种数据集上的大量实验表明，我们的方法显著优于现有方法，并在神经科学领域展现出新颖的应用价值。