Local Independence Testing for Point Processes

TL;DR

This paper introduces a new method for testing local independence in point processes that overcomes limitations of existing tests by using Volterra-like expansions to better handle latent confounders.

Contribution

It develops a novel expansion-based approach to approximate marginalized intensities, enabling more accurate local independence testing in complex point process models.

Findings

The proposed test can accurately detect local independence in simulated data.

The method performs well on real-world datasets, demonstrating practical applicability.

Theoretical results show the expansion can approximate marginalized intensities arbitrarily well.

Abstract

Constraint based causal structure learning for point processes require empirical tests of local independence. Existing tests require strong model assumptions, e.g. that the true data generating model is a Hawkes process with no latent confounders. Even when restricting attention to Hawkes processes, latent confounders are a major technical difficulty because a marginalized process will generally not be a Hawkes process itself. We introduce an expansion similar to Volterra expansions as a tool to represent marginalized intensities. Our main theoretical result is that such expansions can approximate the true marginalized intensity arbitrarily well. Based on this we propose a test of local independence and investigate its properties in real and simulated data.