# Hawkes Processes on Graphons

arXiv: https://arxiv.org/abs/2102.02741 · HTML: https://mlsanity.com/paper/2102.02741/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 62 references that are in the map.
- First posted on arXiv 4 Feb 2021.

## Builds on (most cited first, 30 of 30)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Gromov-Wasserstein Learning for Graph Matching and Node Embedding](https://mlsanity.com/paper/1901.06003/) (2019)
- [Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties](https://mlsanity.com/paper/1811.02834/) (2018)
- [Reward Augmented Maximum Likelihood for Neural Structured Prediction](https://mlsanity.com/paper/1609.00150/) (2016)
- [SEISMIC: A Self-Exciting Point Process Model for Predicting Tweet Popularity](https://mlsanity.com/paper/1506.02594/) (2015)
- [Learning Granger Causality for Hawkes Processes](https://mlsanity.com/paper/1602.04511/) (2016)
- [Hierarchical Optimal Transport for Document Representation](https://mlsanity.com/paper/1906.10827/) (2019)
- [Wasserstein Learning of Deep Generative Point Process Models](https://mlsanity.com/paper/1705.08051/) (2017)
- [Learning Temporal Point Processes via Reinforcement Learning](https://mlsanity.com/paper/1811.05016/) (2018)
- [Stochastic blockmodel approximation of a graphon: Theory and consistent estimation](https://mlsanity.com/paper/1311.1731/) (2013)
- [Hierarchical Optimal Transport for Multimodal Distribution Alignment](https://mlsanity.com/paper/1906.11768/) (2019)
- [A Consistent Histogram Estimator for Exchangeable Graph Models](https://mlsanity.com/paper/1402.1888/) (2014)
- [COEVOLVE: A Joint Point Process Model for Information Diffusion and Network Co-evolution](https://mlsanity.com/paper/1507.02293/) (2015)
- [Learning Graphons via Structured Gromov-Wasserstein Barycenters](https://mlsanity.com/paper/2012.05644/) (2020)
- [Sliced-Wasserstein Autoencoder: An Embarrassingly Simple Generative Model](https://mlsanity.com/paper/1804.01947/) (2018)
- [Rates of Convergence of Spectral Methods for Graphon Estimation](https://mlsanity.com/paper/1709.03183/) (2017)
- [Noise-Contrastive Estimation for Multivariate Point Processes](https://mlsanity.com/paper/2011.00717/) (2020)
- [Bregman Alternating Direction Method of Multipliers](https://mlsanity.com/paper/1306.3203/) (2013)
- [Neural Granger Causality](https://mlsanity.com/paper/1802.05842/) (2018)
- [Learning from Clinical Judgments: Semi-Markov-Modulated Marked Hawkes Processes for Risk Prognosis](https://mlsanity.com/paper/1705.05267/) (2017)
- [A Dirichlet Mixture Model of Hawkes Processes for Event Sequence Clustering](https://mlsanity.com/paper/1701.09177/) (2017)
- [Graphon Control of Large-scale Networks of Linear Systems](https://mlsanity.com/paper/1807.03412/) (2018)
- [Learning Hawkes Processes from Short Doubly-Censored Event Sequences](https://mlsanity.com/paper/1702.07013/) (2017)
- [Patient Flow Prediction via Discriminative Learning of Mutually-Correcting Processes](https://mlsanity.com/paper/1602.05112/) (2016)
- [Learning Registered Point Processes from Idiosyncratic Observations](https://mlsanity.com/paper/1710.01410/) (2017)
- [Fused Gromov-Wasserstein Alignment for Hawkes Processes](https://mlsanity.com/paper/1910.02096/) (2019)

## Abstract (arXiv)

We propose a novel framework for modeling multiple multivariate point processes, each with heterogeneous event types that share an underlying space and obey the same generative mechanism. Focusing on Hawkes processes and their variants that are associated with Granger causality graphs, our model leverages an uncountable event type space and samples the graphs with different sizes from a nonparametric model called it graphon. Given those graphs, we can generate the corresponding Hawkes processes and simulate event sequences. Learning this graphon-based Hawkes process model helps to 1) infer the underlying relations shared by different Hawkes processes; and 2) simulate event sequences with different event types but similar dynamics. We learn the proposed model by minimizing the hierarchical optimal transport distance between the generated event sequences and the observed ones, leading to a novel reward-augmented maximum likelihood estimation method. We analyze the properties of our model in-depth and demonstrate its rationality and effectiveness in both theory and experiments.