# Uncovering Causality from Multivariate Hawkes Integrated Cumulants

arXiv: https://arxiv.org/abs/1607.06333 · HTML: https://mlsanity.com/paper/1607.06333/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2016.

## Built on by (most cited first, 30 of 39)

- [Neural Temporal Point Processes: A Review](https://mlsanity.com/paper/2104.03528/) (2021)
- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Counterfactual Temporal Point Processes](https://mlsanity.com/paper/2111.07603/) (2021)
- [THP: Topological Hawkes Processes for Learning Causal Structure on Event Sequences](https://mlsanity.com/paper/2105.10884/) (2021)
- [Cardinality-Regularized Hawkes-Granger Model](https://mlsanity.com/paper/2208.10671/) (2022)
- [Structural Hawkes Processes for Learning Causal Structure from Discrete-Time Event Sequences](https://mlsanity.com/paper/2305.05986/) (2023)
- [Mitigating Performance Saturation in Neural Marked Point Processes: Architectures and Loss Functions](https://mlsanity.com/paper/2107.03354/) (2021)
- [Causal Discovery in Hawkes Processes by Minimum Description Length](https://mlsanity.com/paper/2206.06124/) (2022)
- [Sequential change-point detection for mutually exciting point processes over networks](https://mlsanity.com/paper/2102.05724/) (2021)
- [Nonparametric Conditional Local Independence Testing](https://mlsanity.com/paper/2203.13559/) (2022)
- [Learning Granger Causality from Instance-wise Self-attentive Hawkes Processes](https://mlsanity.com/paper/2402.03726/) (2024)
- [Modeling Events and Interactions through Temporal Processes -- A Survey](https://mlsanity.com/paper/2303.06067/) (2023)
- [Granger Causal Inference in Multivariate Hawkes Processes by Minimum Message Length](https://mlsanity.com/paper/2309.02027/) (2023)
- [Advances in Temporal Point Processes: Bayesian, Neural, and LLM Approaches](https://mlsanity.com/paper/2501.14291/) (2025)
- [Self-supervised Adaptive Pre-training of Multilingual Speech Models for Language and Dialect Identification](https://mlsanity.com/paper/2312.07338/) (2023)
- [Your Autoregressive Model Already Reveals the Causal Graph](https://mlsanity.com/paper/2602.01135/) (2026)
- [Causal Representation Meets Stochastic Modeling under Generic Geometry](https://mlsanity.com/paper/2602.05033/) (2026)
- [A neural network based model for multi-dimensional nonlinear Hawkes processes](https://mlsanity.com/paper/2303.03073/) (2023)
- [Likelihood-Free Estimation for Spatiotemporal Hawkes processes with missing data and application to predictive policing](https://mlsanity.com/paper/2502.07111/) (2025)
- [Signal Transformer: Complex-valued Attention and Meta-Learning for Signal Recognition](https://mlsanity.com/paper/2106.04392/) (2021)
- [Local Independence Testing for Point Processes](https://mlsanity.com/paper/2110.12709/) (2021)
- [Hawkes Processes with Delayed Granger Causality](https://mlsanity.com/paper/2308.06106/) (2023)
- [Detecting Structural Shifts in Multivariate Hawkes Processes with Fr'echet Statistics](https://mlsanity.com/paper/2308.06769/) (2023)
- [Enhancing Asynchronous Time Series Forecasting with Contrastive Relational Inference](https://mlsanity.com/paper/2309.02868/) (2023)
- [Enhancing Multilingual Speech Recognition through Language Prompt Tuning and Frame-Level Language Adapter](https://mlsanity.com/paper/2309.09443/) (2023)
- [GMTR: Graph Matching Transformers](https://mlsanity.com/paper/2311.08141/) (2023)
- [DarkShot: Lighting Dark Images with Low-Compute and High-Quality](https://mlsanity.com/paper/2312.16805/) (2023)
- [TRLS: A Time Series Representation Learning Framework via Spectrogram for Medical Signal Processing](https://mlsanity.com/paper/2401.05431/) (2024)
- [TEN-GUARD: Tensor Decomposition for Backdoor Attack Detection in Deep Neural Networks](https://mlsanity.com/paper/2401.05432/) (2024)
- [T-Pixel2Mesh: Combining Global and Local Transformer for 3D Mesh Generation from a Single Image](https://mlsanity.com/paper/2403.13663/) (2024)

## Abstract (arXiv)

We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each nodes of the process, but also disentangles the causality relationships between them. Our approach is the first that leads to an estimation of this matrix without any parametric modeling and estimation of the kernels themselves. A consequence is that it can give an estimation of causality relationships between nodes (or users), based on their activity timestamps (on a social network for instance), without knowing or estimating the shape of the activities lifetime. For that purpose, we introduce a moment matching method that fits the third-order integrated cumulants of the process. We show on numerical experiments that our approach is indeed very robust to the shape of the kernels, and gives appealing results on the MemeTracker database.