# Latent Network Structure Learning from High Dimensional Multivariate Point Processes

arXiv: https://arxiv.org/abs/2004.03569 · HTML: https://mlsanity.com/paper/2004.03569/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Apr 2020.

## Built on by (most cited first, 12 of 12)

- [A Graphical Point Process Framework for Understanding Removal Effects in Multi-Touch Attribution](https://mlsanity.com/paper/2302.06075/) (2023)
- [On Non-asymptotic Theory of Recurrent Neural Networks in Temporal Point Processes](https://mlsanity.com/paper/2406.00630/) (2024)
- [Causal Discovery in High-Dimensional Point Process Networks with Hidden Nodes](https://mlsanity.com/paper/2109.10947/) (2021)
- [Joint Estimation and Inference for Multi-Experiment Networks of High-Dimensional Point Processes](https://mlsanity.com/paper/2109.11634/) (2021)
- [Cox-Hawkes: doubly stochastic spatiotemporal Poisson processes](https://mlsanity.com/paper/2210.11844/) (2022)
- [Scalable and adaptive variational Bayes methods for Hawkes processes](https://mlsanity.com/paper/2212.00293/) (2022)
- [Amortized Network Intervention to Steer the Excitatory Point Processes](https://mlsanity.com/paper/2310.04159/) (2023)
- [Learning under Commission and Omission Event Outliers](https://mlsanity.com/paper/2501.13599/) (2025)
- [K2IE: Kernel Method-based Kernel Intensity Estimators for Inhomogeneous Poisson Processes](https://mlsanity.com/paper/2505.24704/) (2025)
- [Latent Factor Point Processes for Patient Representation in Electronic Health Records](https://mlsanity.com/paper/2508.20327/) (2025)
- [A Representer Theorem for Hawkes Processes via Penalized Least Squares Minimization](https://mlsanity.com/paper/2510.08916/) (2025)
- [On Observation Time for Recovering Latent Hawkes Networks](https://mlsanity.com/paper/2605.08400/) (2026)

## Abstract (arXiv)

Learning the latent network structure from large scale multivariate point process data is an important task in a wide range of scientific and business applications. For instance, we might wish to estimate the neuronal functional connectivity network based on spiking times recorded from a collection of neurons. To characterize the complex processes underlying the observed data, we propose a new and flexible class of nonstationary Hawkes processes that allow both excitatory and inhibitory effects. We estimate the latent network structure using an efficient sparse least squares estimation approach. Using a thinning representation, we establish concentration inequalities for the first and second order statistics of the proposed Hawkes process. Such theoretical results enable us to establish the non-asymptotic error bound and the selection consistency of the estimated parameters. Furthermore, we describe a least squares loss based statistic for testing if the background intensity is constant in time. We demonstrate the efficacy of our proposed method through simulation studies and an application to a neuron spike train data set.