Tensor Kernel Recovery for Spatio-Temporal Hawkes Processes

TL;DR

This paper introduces a tensor recovery method for estimating influence functions in spatio-temporal Hawkes processes, leveraging low-rank tensor kernels and convex optimization to improve modeling accuracy and efficiency.

Contribution

It proposes a novel tensor kernel estimation framework with theoretical guarantees and an efficient algorithm, advancing the modeling of complex spatio-temporal dependencies.

Findings

Effective tensor kernel estimation demonstrated through simulations

Theoretical performance guarantees established for the method

Algorithm achieves efficient and accurate influence function recovery

Abstract

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.