Analysis of a maximum-entropy based estimator for dynamic random graph models

arXiv (Cornell University)

Abstract

We study dynamic random graphs in which the set of nodes is fixed, but edges evolve over time according to an underlying stochastic mechanism. Using a maximum-entropy approach, we define a probability distribution on graph trajectories that is consistent with observed constraints, capturing the inherent uncertainty in partially observed networks. We introduce a moment-based estimator for the parameters of this distribution and establish its statistical properties, such as consistency and asymptotic normality, with explicit formulas for the covariance structure. Numerical experiments demonstrate the estimator's accuracy and robustness across various dynamic network scenarios. Our framework bridges probabilistic modeling and statistical inference in time-varying networks, providing practical tools for understanding and predicting complex edge dynamics.

Authors 4

1. Diego Garlaschelli

   IMT School for Advanced Studies Lucca

   Affiliation as printed

   Affiliations. DG is with IMT School for Advanced Studies , Piazza San Francesco 19 , 55100 Lucca , Italy, and

2. Michel Mandjes
3. F. P. Pijpers

   IMT School for Advanced Studies Lucca · University of Amsterdam

   Affiliation as printed

   ) Amsterdam Business School , Faculty of Economics and Business , University of Amsterdam , Amsterdam , The Netherlands

   Affiliations. DG is with IMT School for Advanced Studies , Piazza San Francesco 19 , 55100 Lucca , Italy, and

4. Jiesen Wang Aachen Lorentz Institute for Theoretical Physics

   Leiden University

   Affiliation as printed

   Lorentz Institute for Theoretical Physics , Leiden University , Niels Bohrweg 2 , 2333 CA Leiden , The Netherlands