We estimate the general influence functions for spatio-temporal Hawkes processes using a tensor recovery approach by formulating the location dependent influence function that captures the influence of historical events as a tensor kernel. We assume a low-rank structure for the tensor kernel and cast the estimation problem as a convex optimization problem using the Fourier transformed nuclear norm (TNN). We provide theoretical performance guarantees for our approach and present an algorithm to solve the optimization problem. Moreover, we demonstrate the efficiency of our estimation with numerical simulations.

翻译：我们用“高压回收法”来评估时空鹰工艺的总体影响功能。 我们用“高压回收法”来估算时空鹰工艺的总体影响功能,方法是制定基于位置的影响力功能,将历史事件的影响作为“高压内核”来捕捉。 我们对“高压内核”采取低级别结构,并将估算问题作为使用Fourier变换的核规范(TNN)的“软化优化”问题。我们为我们的方法提供了理论性能保障,并提出了解决优化问题的算法。此外,我们用数字模拟来展示了我们估算的效率。