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

TL;DR

This paper establishes a novel connection between epidemic models and self-exciting processes, introducing a generalized framework that improves understanding and prediction of diffusion phenomena on social media platforms like Twitter.

Contribution

It introduces a unified mathematical framework linking epidemic models with self-exciting processes, including methods for simulation, fitting, and evaluation, and demonstrates its effectiveness on large Twitter datasets.

Findings

Model performance varies with infection kernel types and user behavior.

Combining models enhances prediction accuracy.

The generalized model captures diverse diffusion dynamics.

Abstract

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.