# Modeling Information Cascades with Self-exciting Processes via Generalized Epidemic Models

arXiv: https://arxiv.org/abs/1910.05451 · HTML: https://mlsanity.com/paper/1910.05451/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Oct 2019.

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

- [Long Horizon Forecasting With Temporal Point Processes](https://mlsanity.com/paper/2101.02815/) (2021)
- [DanmakuTPPBench: A Multi-modal Benchmark for Temporal Point Process Modeling and Understanding](https://mlsanity.com/paper/2505.18411/) (2025)
- [Before It's Too Late: A State Space Model for the Early Prediction of Misinformation and Disinformation Engagement](https://mlsanity.com/paper/2502.04655/) (2025)
- [Interval-censored Hawkes processes](https://mlsanity.com/paper/2104.07932/) (2021)
- [Revisiting Information Cascades in Online Social Networks](https://mlsanity.com/paper/2208.00904/) (2022)
- [Incomplete Gamma Integrals for Deep Cascade Prediction using Content, Network, and Exogenous Signals](https://mlsanity.com/paper/2106.07012/) (2021)

## Abstract (arXiv)

Epidemic models and self-exciting processes are two types of models used to describe diffusion phenomena online and offline. These models were originally developed in different scientific communities, and their commonalities are under-explored. This work establishes, for the first time, a general connection between the two model classes via three new mathematical components. The first is a generalized version of stochastic Susceptible-Infected-Recovered (SIR) model with arbitrary recovery time distributions; the second is the relationship between the (latent and arbitrary) recovery time distribution, recovery hazard function, and the infection kernel of self-exciting processes; the third includes methods for simulating, fitting, evaluating and predicting the generalized process. On three large Twitter diffusion datasets, we conduct goodness-of-fit tests and holdout log-likelihood evaluation of self-exciting processes with three infection kernels --- exponential, power-law and Tsallis Q-exponential. We show that the modeling performance of the infection kernels varies with respect to the temporal structures of diffusions, and also with respect to user behavior, such as the likelihood of being bots. We further improve the prediction of popularity by combining two models that are identified as complementary by the goodness-of-fit tests.