Learning causal structure among event types from discrete-time event sequences is a particularly important but challenging task. Existing methods, such as the multivariate Hawkes processes based methods, mostly boil down to learning the so-called Granger causality which assumes that the cause event happens strictly prior to its effect event. Such an assumption is often untenable beyond applications, especially when dealing with discrete-time event sequences in low-resolution; and typical discrete Hawkes processes mainly suffer from identifiability issues raised by the instantaneous effect, i.e., the causal relationship that occurred simultaneously due to the low-resolution data will not be captured by Granger causality. In this work, we propose Structure Hawkes Processes (SHPs) that leverage the instantaneous effect for learning the causal structure among events type in discrete-time event sequence. The proposed method is featured with the minorization-maximization of the likelihood function and a sparse optimization scheme. Theoretical results show that the instantaneous effect is a blessing rather than a curse, and the causal structure is identifiable under the existence of the instantaneous effect. Experiments on synthetic and real-world data verify the effectiveness of the proposed method.

翻译：从离散时间事件序列中学习事件类型间的因果结构是一项重要但具有挑战性的任务。现有方法（如基于多元霍克斯过程的方法）大多归结为学习所谓的格兰杰因果关系，其假设原因事件严格先于结果事件发生。这种假设在诸多应用场景中往往难以成立，尤其是在处理低分辨率的离散时间事件序列时；而典型的离散霍克斯过程主要面临瞬时效应（即由低分辨率数据导致的同步因果关系）所引发的可辨识性问题——这类因果关联无法被格兰杰因果关系所捕捉。本文提出结构型霍克斯过程（SHPs），利用瞬时效应从离散时间事件序列中学习事件类型间的因果结构。所提方法以似然函数的极小化-极大化算法和稀疏优化方案为特征。理论结果表明，瞬时效应实为“福音”而非“诅咒”，在瞬时效应存在的情况下因果结构具有可辨识性。合成数据与真实数据的实验验证了该方法的有效性。