Tensor Kernel Recovery for Spatio-Temporal Hawkes Processes
This work provides a method for more accurately estimating influence functions in spatio-temporal Hawkes processes, which is significant for researchers and practitioners working with event data in fields like seismology, social media, or finance.
This paper addresses the estimation of general influence functions for spatio-temporal Hawkes processes by modeling the location-dependent influence as a tensor kernel. It assumes a low-rank structure for this tensor and formulates the estimation as a convex optimization problem using the Fourier transformed nuclear norm, demonstrating efficiency through numerical simulations.
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.