# Learning Network of Multivariate Hawkes Processes: A Time Series Approach

arXiv: https://arxiv.org/abs/1603.04319 · HTML: https://mlsanity.com/paper/1603.04319/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Mar 2016.

## Built on by (most cited first, 15 of 15)

- [Transformer Embeddings of Irregularly Spaced Events and Their Participants](https://mlsanity.com/paper/2201.00044/) (2021)
- [Language Models Can Improve Event Prediction by Few-Shot Abductive Reasoning](https://mlsanity.com/paper/2305.16646/) (2023)
- [THP: Topological Hawkes Processes for Learning Causal Structure on Event Sequences](https://mlsanity.com/paper/2105.10884/) (2021)
- [Mutually exciting point process graphs for modelling dynamic networks](https://mlsanity.com/paper/2102.06527/) (2021)
- [Surfacing Estimation Uncertainty in the Decay Parameters of Hawkes Processes with Exponential Kernels](https://mlsanity.com/paper/2104.01029/) (2021)
- [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)
- [Differentially Private Learning of Hawkes Processes](https://mlsanity.com/paper/2207.13741/) (2022)
- [Causal Graph Discovery from Self and Mutually Exciting Time Series](https://mlsanity.com/paper/2301.11197/) (2023)
- [Massively Parallel Exact Inference for Hawkes Processes](https://mlsanity.com/paper/2604.01342/) (2026)
- [Fine-Grained ε-Margin Closed-Form Stabilization of Parametric Hawkes Processes](https://mlsanity.com/paper/2105.03800/) (2021)
- [Causal Graph Discovery from Self and Mutually Exciting Time Series](https://mlsanity.com/paper/2106.02600/) (2021)
- [Local Independence Testing for Point Processes](https://mlsanity.com/paper/2110.12709/) (2021)
- [Causal Structural Learning from Time Series: A Convex Optimization Approach](https://mlsanity.com/paper/2301.11336/) (2023)
- [Detecting Structural Shifts in Multivariate Hawkes Processes with Fr'echet Statistics](https://mlsanity.com/paper/2308.06769/) (2023)

## Abstract (arXiv)

Learning the influence structure of multiple time series data is of great interest to many disciplines. This paper studies the problem of recovering the causal structure in network of multivariate linear Hawkes processes. In such processes, the occurrence of an event in one process affects the probability of occurrence of new events in some other processes. Thus, a natural notion of causality exists between such processes captured by the support of the excitation matrix. We show that the resulting causal influence network is equivalent to the Directed Information graph (DIG) of the processes, which encodes the causal factorization of the joint distribution of the processes. Furthermore, we present an algorithm for learning the support of excitation matrix (or equivalently the DIG). The performance of the algorithm is evaluated on synthesized multivariate Hawkes networks as well as a stock market and MemeTracker real-world dataset.