Generalized Poisson Dynamic Network Models

2026-04-07

AI Summary

This study addresses the challenge of under- and over-dispersion commonly observed in edge weights of dynamic count networks, which traditional latent factor models—focused solely on conditional means—fail to adequately capture. To this end, the paper introduces the generalized Poisson distribution into dynamic network modeling for the first time, integrating latent factor dynamics, autoregressive mechanisms, and evolving latent positions within a unified framework that simultaneously handles both forms of dispersion. A Bayesian inference scheme is developed alongside an MCMC algorithm for posterior sampling. Theoretical analysis highlights the critical role of the dispersion parameter in shaping network connectivity, while empirical evaluations on bike-sharing and media networks demonstrate substantially improved model fit and predictive performance, underscoring the necessity and advantage of explicitly modeling non-equidispersion.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Social media analysis through the lenses of networks
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Count-weighted temporal networks often exhibit unequal dispersion in the edge weights, which cannot be fully explained by modelling observational heterogeneity through latent factors in the conditional mean. Therefore, we propose new dynamic network model classes exploiting the Generalized Poisson distribution to capture both under- and overdispersion. We consider three different dynamic specifications: latent factor dynamics, autoregressive dynamics, and latent position dynamics, and study some theoretical properties of the random networks, showing the impact of the dispersion parameter on the random network's connectivity. After discussing the parameter identification strategy, we present a Bayesian inference procedure along with a posterior sampling algorithm. A numerical illustration demonstrates the effectiveness of the designed algorithm and provides estimates of the misspecification bias when unequal dispersion is neglected. Our new models are then applied to two relevant dynamic datasets considered in previous studies: a set of bike-sharing dynamic networks and a set of dynamic media networks. Our results highlight the importance of explicitly modeling overdispersion for both an accurate in-sample fit and out-of-sample performance.

Problem

• unequal dispersion
• count-weighted temporal networks
• overdispersion
• underdispersion
• edge weights

Innovation

• Generalized Poisson distribution
• overdispersion
• dynamic network models
• Bayesian inference
• latent factor dynamics