Self- and mutually-exciting point processes are popular models in machine learning and statistics for dependent discrete event data. To date, most existing models assume stationary kernels (including the classical Hawkes processes) and simple parametric models. Modern applications with complex event data require more general point process models that can incorporate contextual information of the events, called marks, besides the temporal and location information. Moreover, such applications often require non-stationary models to capture more complex spatio-temporal dependence. To tackle these challenges, a key question is to devise a versatile influence kernel in the point process model. In this paper, we introduce a novel and general neural network-based non-stationary influence kernel with high expressiveness for handling complex discrete events data while providing theoretical performance guarantees. We demonstrate the superior performance of our proposed method compared with the state-of-the-art on synthetic and real data.

翻译：自我和相互启发的点点进程是机器学习和统计中流行的模式,用于独立的离散事件数据。迄今为止,大多数现有模式都假定固定内核(包括古典霍克斯进程)和简单的参数模型。复杂的事件数据的现代应用需要更一般的点进程模型,除了时间和位置信息外,还可以包括事件的背景信息,称为标记。此外,这些应用往往需要非静止模型来捕捉更复杂的时空依赖性。为了应对这些挑战,关键的问题是在点处理模型中设计一个多功能的内核。在本文中,我们引入了一个新的和一般性的基于神经网络的非静止影响内核,在处理复杂的离散事件数据时具有高度的清晰度,同时提供理论性能保证。我们展示了我们所提议的方法与合成和真实数据最新技术相比的优异性。