# Multivariate Hawkes Processes for Large-scale Inference

arXiv: https://arxiv.org/abs/1602.08418 · HTML: https://mlsanity.com/paper/1602.08418/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2016.

## Built on by (most cited first, 6 of 6)

- [Linking Across Data Granularity: Fitting Multivariate Hawkes Processes to Partially Interval-Censored Data](https://mlsanity.com/paper/2111.02062/) (2021)
- [A neural network based model for multi-dimensional nonlinear Hawkes processes](https://mlsanity.com/paper/2303.03073/) (2023)
- [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)
- [MDHP-Net: Detecting an Emerging Time-exciting Threat in IVN](https://mlsanity.com/paper/2411.10258/) (2024)
- [Uncovering Social Network Activity Using Joint User and Topic Interaction](https://mlsanity.com/paper/2506.12842/) (2025)

## Abstract (arXiv)

In this paper, we present a framework for fitting multivariate Hawkes processes for large-scale problems both in the number of events in the observed history n and the number of event types d (i.e. dimensions). The proposed Low-Rank Hawkes Process (LRHP) framework introduces a low-rank approximation of the kernel matrix that allows to perform the nonparametric learning of the d2 triggering kernels using at most O(ndr2) operations, where r is the rank of the approximation (r ll d,n). This comes as a major improvement to the existing state-of-the-art inference algorithms that are in O(nd2). Furthermore, the low-rank approximation allows LRHP to learn representative patterns of interaction between event types, which may be valuable for the analysis of such complex processes in real world datasets. The efficiency and scalability of our approach is illustrated with numerical experiments on simulated as well as real datasets.