The Hawkes process is used to model point process data where events occur in clusters and bursts. In a standard multivariate Hawkes process, every event that occurs in a dimension has an equal impact on the process intensity. However, this assumption is unrealistic in applications such as the modelling of message cascades where the effect of an event depends on whether it was the initiator or a member of a particular cluster. To alleviate this, we introduce a new Hawkes process model, the Ancestor Hawkes process, which allows the impact of each event to vary based on its origin. The relevance of the Ancestor Hawkes process is showcased on real data from a 9-person group chat, where our proposed approach reveals individual response preferences. Crucially, this is achieved in a privacy-conscious manner, as only the sender and the time at which a message was sent -- but not its content -- are utilised. These nuances of messaging cascades are missed by the standard Hawkes process, but are relevant for studying latent interaction structure and for personalised notification management.

翻译：霍克斯过程用于建模事件以簇和爆发形式发生的点过程数据。在标准多元霍克斯过程中，某个维度上发生的每个事件对过程强度产生相同的影响。然而，这一假设在消息级联建模等应用中并不现实，因为事件的影响取决于其是否为特定簇的发起者或成员。为缓解这一问题，我们引入了一种新的霍克斯过程模型——祖先霍克斯过程，该模型允许每个事件的影响力根据其起源而变化。通过一个9人群聊的真实数据，我们展示了祖先霍克斯过程的相关性——我们提出的方法揭示了个体响应偏好。关键在于，这是以保护隐私的方式实现的，因为仅利用了消息的发送者和发送时间（而非消息内容）。标准霍克斯过程无法捕捉这些消息级联的细微差别，但这些差别对于研究潜在交互结构以及个性化通知管理具有重要意义。