# Sparse and low-rank multivariate Hawkes processes

arXiv: https://arxiv.org/abs/1501.00725 · HTML: https://mlsanity.com/paper/1501.00725/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jan 2015.

## Built on by (most cited first, 19 of 19)

- [Cardinality-Regularized Hawkes-Granger Model](https://mlsanity.com/paper/2208.10671/) (2022)
- [FaDIn: Fast Discretized Inference for Hawkes Processes with General Parametric Kernels](https://mlsanity.com/paper/2210.04635/) (2022)
- [Granger Causal Inference in Multivariate Hawkes Processes by Minimum Message Length](https://mlsanity.com/paper/2309.02027/) (2023)
- [Flexible Parametric Inference for Space-Time Hawkes Processes](https://mlsanity.com/paper/2406.06849/) (2024)
- [A Graphical Point Process Framework for Understanding Removal Effects in Multi-Touch Attribution](https://mlsanity.com/paper/2302.06075/) (2023)
- [PCA for Point Processes](https://mlsanity.com/paper/2404.19661/) (2024)
- [Nonparametric estimation of Hawkes processes with RKHSs](https://mlsanity.com/paper/2411.00621/) (2024)
- [Your Autoregressive Model Already Reveals the Causal Graph](https://mlsanity.com/paper/2602.01135/) (2026)
- [Differentially Private Estimation of Hawkes Process](https://mlsanity.com/paper/2209.07303/) (2022)
- [Massively Parallel Exact Inference for Hawkes Processes](https://mlsanity.com/paper/2604.01342/) (2026)
- [Relaxed Clustered Hawkes Process for Procrastination Modeling in MOOCs](https://mlsanity.com/paper/2102.00093/) (2021)
- [Scalable and adaptive variational Bayes methods for Hawkes processes](https://mlsanity.com/paper/2212.00293/) (2022)
- [Sparklen: A Statistical Learning Toolkit for High-Dimensional Hawkes Processes in Python](https://mlsanity.com/paper/2502.18979/) (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)
- [From Hawkes Processes to Attention: Time-Modulated Mechanisms for Event Sequences](https://mlsanity.com/paper/2601.09220/) (2026)
- [On Observation Time for Recovering Latent Hawkes Networks](https://mlsanity.com/paper/2605.08400/) (2026)
- [seq2cause: One Autoregressive Backbone, Four Causal Discovery Tasks in Event Sequences](https://mlsanity.com/paper/2609.31801/) (2026)

## Abstract (arXiv)

We consider the problem of unveiling the implicit network structure of node interactions (such as user interactions in a social network), based only on high-frequency timestamps. Our inference is based on the minimization of the least-squares loss associated with a multivariate Hawkes model, penalized by ℓ1 and trace norm of the interaction tensor. We provide a first theoretical analysis for this problem, that includes sparsity and low-rank inducing penalizations. This result involves a new data-driven concentration inequality for matrix martingales in continuous time with observable variance, which is a result of independent interest and a broad range of possible applications since it extends to matrix martingales former results restricted to the scalar case. A consequence of our analysis is the construction of sharply tuned ℓ1 and trace-norm penalizations, that leads to a data-driven scaling of the variability of information available for each users. Numerical experiments illustrate the significant improvements achieved by the use of such data-driven penalizations.