# Cardinality-Regularized Hawkes-Granger Model

arXiv: https://arxiv.org/abs/2208.10671 · HTML: https://mlsanity.com/paper/2208.10671/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 52 references that are in the map.
- First posted on arXiv 23 Aug 2022.

## Builds on (most cited first, 12 of 12)

- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [Fully Neural Network based Model for General Temporal Point Processes](https://mlsanity.com/paper/1905.09690/) (2019)
- [Modeling The Intensity Function Of Point Process Via Recurrent Neural Networks](https://mlsanity.com/paper/1705.08982/) (2017)
- [Learning Granger Causality for Hawkes Processes](https://mlsanity.com/paper/1602.04511/) (2016)
- [Uncovering Causality from Multivariate Hawkes Integrated Cumulants](https://mlsanity.com/paper/1607.06333/) (2016)
- [Neural Temporal Point Processes For Modelling Electronic Health Records](https://mlsanity.com/paper/2007.13794/) (2020)
- [Expecting to be HIP: Hawkes Intensity Processes for Social Media Popularity](https://mlsanity.com/paper/1602.06033/) (2016)
- [Sparse and low-rank multivariate Hawkes processes](https://mlsanity.com/paper/1501.00725/) (2015)
- [Learning Multivariate Hawkes Processes at Scale](https://mlsanity.com/paper/2002.12501/) (2020)
- [Hawkes Process for Understanding the Influence of Pathogenic Social Media Accounts](https://mlsanity.com/paper/1902.01970/) (2019)
- [Network Hawkes Process Models for Exploring Latent Hierarchy in Social Animal Interactions](https://mlsanity.com/paper/2012.09598/) (2020)
- [HNP3: A Hierarchical Nonparametric Point Process for Modeling Content Diffusion over Social Media](https://mlsanity.com/paper/1610.00246/) (2016)

## Built on by (most cited first, 14 of 14)

- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [MECD: Unlocking Multi-Event Causal Discovery in Video Reasoning](https://mlsanity.com/paper/2409.17647/) (2024)
- [Structural Hawkes Processes for Learning Causal Structure from Discrete-Time Event Sequences](https://mlsanity.com/paper/2305.05986/) (2023)
- [Learning Granger Causality from Instance-wise Self-attentive Hawkes Processes](https://mlsanity.com/paper/2402.03726/) (2024)
- [Granger Causal Chain Discovery for Sepsis-Associated Derangements via Continuous-Time Hawkes Processes](https://mlsanity.com/paper/2209.04480/) (2022)
- [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)
- [Causal Graph Discovery from Self and Mutually Exciting Time Series](https://mlsanity.com/paper/2301.11197/) (2023)
- [Accelerating Cutting-Plane Algorithms via Reinforcement Learning Surrogates](https://mlsanity.com/paper/2307.08816/) (2023)
- [Explainable History Distillation by Marked Temporal Point Process](https://mlsanity.com/paper/2311.07797/) (2023)
- [Causal Structure Learning in Hawkes Processes with Complex Latent Confounder Networks](https://mlsanity.com/paper/2508.11727/) (2025)
- [Learning Marked Temporal Point Process Explanations based on Counterfactual and Factual Reasoning](https://mlsanity.com/paper/2508.11943/) (2025)
- [Addressing Mark Imbalance in Integration-free Neural Marked Temporal Point Processes](https://mlsanity.com/paper/2510.20414/) (2025)
- [Resilient Concurrent Causal Discovery for Topological Event Sequences](https://mlsanity.com/paper/2608.21815/) (2026)

## Abstract (arXiv)

We propose a new sparse Granger-causal learning framework for temporal event data. We focus on a specific class of point processes called the Hawkes process. We begin by pointing out that most of the existing sparse causal learning algorithms for the Hawkes process suffer from a singularity in maximum likelihood estimation. As a result, their sparse solutions can appear only as numerical artifacts. In this paper, we propose a mathematically well-defined sparse causal learning framework based on a cardinality-regularized Hawkes process, which remedies the pathological issues of existing approaches. We leverage the proposed algorithm for the task of instance-wise causal event analysis, where sparsity plays a critical role. We validate the proposed framework with two real use-cases, one from the power grid and the other from the cloud data center management domain.