Detecting Mutual Excitations in Non-Stationary Hawkes Processes

TL;DR

This paper presents an efficient algorithm for accurately learning the dependency network in non-stationary multivariate Hawkes processes, even with partial or imprecise data, under sparsity conditions.

Contribution

It introduces a novel method for reconstructing sparse dependency graphs in non-stationary Hawkes processes with theoretical guarantees and efficiency.

Findings

Accurately reconstructs dependency graphs from polylogarithmic observation time.

Works with partial observations and imprecise event times.

Provides theoretical guarantees for high-probability success.

Abstract

We consider the problem of learning the network of mutual excitations (i.e., the dependency graph) in a non-stationary, multivariate Hawkes process. We consider a general setting where baseline rates at each node are time-varying and delay kernels are not shift-invariant. Our main results show that if the dependency graph of an $n$-variate Hawkes process is sparse (i.e., it has a maximum degree that is bounded with respect to $n$), our algorithm accurately reconstructs it from data after observing the Hawkes process for $T = \mathrm{polylog}(n)$ time, with high probability. Our algorithm is computationally efficient, and provably succeeds in learning dependencies even if only a subset of time series are observed and event times are not precisely known.