We investigate spatio-temporal event analysis using point processes. Inferring the dynamics of event sequences spatio-temporally has many practical applications including crime prediction, social media analysis, and traffic forecasting. In particular, we focus on spatio-temporal Hawkes processes that are commonly used due to their capability to capture excitations between event occurrences. We introduce a novel inference framework based on randomized transformations and gradient descent to learn the process. We replace the spatial kernel calculations by randomized Fourier feature-based transformations. The introduced randomization by this representation provides flexibility while modeling the spatial excitation between events. Moreover, the system described by the process is expressed within closed-form in terms of scalable matrix operations. During the optimization, we use maximum likelihood estimation approach and gradient descent while properly handling positivity and orthonormality constraints. The experiment results show the improvements achieved by the introduced method in terms of fitting capability in synthetic and real-life datasets with respect to the conventional inference methods in the spatio-temporal Hawkes process literature. We also analyze the triggering interactions between event types and how their dynamics change in space and time through the interpretation of learned parameters.

中文翻译：

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使用随机核对时空霍克斯过程进行建模

我们使用点过程研究时空事件分析。时空推断事件序列的动态具有许多实际应用，包括犯罪预测、社交媒体分析和交通预测。特别是，我们关注时空霍克斯过程，这些过程由于能够捕获事件发生之间的激发而被广泛使用。我们引入了一种基于随机变换和梯度下降的新型推理框架来学习该过程。我们用基于随机傅立叶特征的变换代替空间核计算。这种表示引入的随机化在对事件之间的空间激励建模时提供了灵活性。此外，该过程描述的系统在可扩展矩阵运算方面以封闭形式表示。在优化过程中，我们使用最大似然估计方法和梯度下降，同时正确处理正性和正交性约束。实验结果表明，相对于时空霍克斯过程文献中的传统推理方法，引入的方法在合成和现实数据集的拟合能力方面取得了改进。我们还通过对学习参数的解释来分析事件类型之间的触发交互以及它们的动态如何在空间和时间上变化。实验结果表明，相对于时空霍克斯过程文献中的传统推理方法，引入的方法在合成和现实数据集的拟合能力方面取得了改进。我们还通过对学习参数的解释来分析事件类型之间的触发交互以及它们的动态如何在空间和时间上变化。实验结果表明，相对于时空霍克斯过程文献中的传统推理方法，引入的方法在合成和现实数据集的拟合能力方面取得了改进。我们还通过对学习参数的解释来分析事件类型之间的触发交互以及它们的动态如何在空间和时间上变化。