用于推断时间点过程中事件分支的即插即用 Bregman ADMM 模块
A Plug-and-Play Bregman ADMM Module for Inferring Event Branches in Temporal Point Processes
AI总结：
本文提出一种即插即用的 BADMM 模块，将事件分支推断转化为稀疏低秩事件转移矩阵优化，可嵌入经典与神经 TPP，提升性能并给出可解释事件分支。
摘要：
由时间点过程生成的事件序列通常与一个隐藏且结构化的事件分支过程相关联，该过程捕捉其历史事件与当前事件之间的触发关系。在本研究中，我们设计了一种基于 Bregman ADMM（BADMM）算法的新型即插即用模块，用于在时间点过程（TPP）的最大似然估计框架中推断与事件序列相关联的事件分支。具体而言，我们将事件分支推断表述为在稀疏和低秩约束下对事件转移矩阵的优化问题，并将其嵌入到现有 TPP 模型或其学习范式中。我们可以分别基于子空间聚类和稀疏组 lasso 实现该优化问题，并使用 Bregman ADMM 算法求解；将该算法展开即得到所提出的 BADMM 模块。当通过期望最大化算法学习经典 TPP（例如 Hawkes 过程）时，BADMM 模块有助于在 E 步中导出结构化责任矩阵。类似地，对于具有自注意力层的神经 TPP，BADMM 模块有助于导出低秩且稀疏的注意力图。结构化责任矩阵和注意力图充当学习到的事件转移矩阵，可指示事件分支，例如推断孤立事件以及那些触发许多后续事件的关键事件。在合成数据和真实世界数据上的实验均表明，将我们的 BADMM 模块插入现有 TPP 模型和学习范式中，可以提升模型性能，并为我们提供可解释的结构化事件分支。代码可在 https://github.com/qingmeiwangdaily/BADMM_TPP 获取。
英文摘要：
An event sequence generated by a temporal point process is often associated with a hidden and structured event branching process that captures the triggering relations between its historical and current events. In this study, we design a new plug-and-play module based on the Bregman ADMM (BADMM) algorithm, which infers event branches associated with event sequences in the maximum likelihood estimation framework of temporal point processes (TPPs). Specifically, we formulate the inference of event branches as an optimization problem for the event transition matrix under sparse and low-rank constraints, which is embedded in existing TPP models or their learning paradigms. We can implement this optimization problem based on subspace clustering and sparse group-lasso, respectively, and solve it using the Bregman ADMM algorithm, whose unrolling leads to the proposed BADMM module. When learning a classic TPP (e.g., Hawkes process) by the expectation-maximization algorithm, the BADMM module helps derive structured responsibility matrices in the E-step. Similarly, the BADMM module helps derive low-rank and sparse attention maps for the neural TPPs with self-attention layers. The structured responsibility matrices and attention maps, which work as learned event transition matrices, indicate event branches, e.g., inferring isolated events and those key events triggering many subsequent events. Experiments on both synthetic and real-world data show that plugging our BADMM module into existing TPP models and learning paradigms can improve model performance and provide us with interpretable structured event branches. The code is available at \url{https://github.com/qingmeiwangdaily/BADMM_TPP}.
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。
