# On Observation Time for Recovering Latent Hawkes Networks

arXiv: https://arxiv.org/abs/2605.08400 · HTML: https://mlsanity.com/paper/2605.08400/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 67 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 14 of 14)

- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [Fully Neural Network based Model for General Temporal Point Processes](https://mlsanity.com/paper/1905.09690/) (2019)
- [Learning Granger Causality for Hawkes Processes](https://mlsanity.com/paper/1602.04511/) (2016)
- [Uncovering Causality from Multivariate Hawkes Integrated Cumulants](https://mlsanity.com/paper/1607.06333/) (2016)
- [Discovering Latent Network Structure in Point Process Data](https://mlsanity.com/paper/1402.0914/) (2014)
- [Expecting to be HIP: Hawkes Intensity Processes for Social Media Popularity](https://mlsanity.com/paper/1602.06033/) (2016)
- [Add and Thin: Diffusion for Temporal Point Processes](https://mlsanity.com/paper/2311.01139/) (2023)
- [Sparse and low-rank multivariate Hawkes processes](https://mlsanity.com/paper/1501.00725/) (2015)
- [Latent Network Structure Learning from High Dimensional Multivariate Point Processes](https://mlsanity.com/paper/2004.03569/) (2020)
- [A space-time conditional intensity model for invasive meningococcal disease occurrence](https://mlsanity.com/paper/1508.05740/) (2015)
- [Learning Granger Causality from Instance-wise Self-attentive Hawkes Processes](https://mlsanity.com/paper/2402.03726/) (2024)
- [Hawkes graphs](https://mlsanity.com/paper/1601.01879/) (2016)
- [A Graph Dynamics Prior for Relational Inference](https://mlsanity.com/paper/2306.06041/) (2023)

## Abstract (arXiv)

Dynamics of interacting systems in engineering, society, and nature often evolve over latent networks that govern which entities can interact. We study the problem of inferring these networks from event-based observations, which arise naturally in finance, seismology, and neuroscience. While there is substantial algorithmic work addressing this important problem, theoretical results are scarce. In this paper we ask the following fundamental question: what is the minimum time that one must observe the dynamics in order to exactly recover the underlying network, as a function of the number d of interacting entities? For a class of stationary Hawkes processes with sparse, weak interactions, we prove that an observation time of order log d is sufficient and necessary. For the upper bound we construct a two-stage estimator that uses clipped and binned event data for screening, followed by a least-squares refinement, and apply concentration bounds derived from the Poisson cluster representation. For the lower bound we combine Fano's inequality with Jacod's Girsanov formula for point processes on a suitable subclass of networks.