# Local Independence Testing for Point Processes

arXiv: https://arxiv.org/abs/2110.12709 · HTML: https://mlsanity.com/paper/2110.12709/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 47 references that are in the map.
- First posted on arXiv 25 Oct 2021.

## Builds on (most cited first, 5 of 5)

- [Uncovering Causality from Multivariate Hawkes Integrated Cumulants](https://mlsanity.com/paper/1607.06333/) (2016)
- [THP: Topological Hawkes Processes for Learning Causal Structure on Event Sequences](https://mlsanity.com/paper/2105.10884/) (2021)
- [Learning Network of Multivariate Hawkes Processes: A Time Series Approach](https://mlsanity.com/paper/1603.04319/) (2016)
- [Tracking Dynamic Point Processes on Networks](https://mlsanity.com/paper/1409.0031/) (2014)
- [A Prospect of Earthquake Prediction Research](https://mlsanity.com/paper/1312.7712/) (2013)

## Abstract (arXiv)

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.