Reducing Degeneracy in Maximum Entropy Models of Networks

TL;DR

This paper addresses the degeneracy problem in maximum entropy network models by identifying its link to non-log-concave density of states functions and proposing transformations to ensure log-concavity, thereby improving model reliability.

Contribution

The authors identify the cause of degeneracy in maximum entropy models and introduce a transformation method to ensure log-concavity, reducing degeneracy issues.

Findings

Transformations can make the density of states function log-concave

The method effectively reduces degeneracy in example systems

Improves the predictive reliability of maximum entropy network models

Abstract

Based on Jaynes' maximum entropy principle, exponential random graphs provide a family of principled models that allow the prediction of network properties as constrained by empirical data (observables). However, their use is often hindered by the degeneracy problem characterized by spontaneous symmetry-breaking, where predictions fail. Here we show that degeneracy appears when the corresponding density of states function is not log-concave, which is typically the consequence of nonlinear relationships between the constraining observables. Exploiting these nonlinear relationships here we propose a solution to the degeneracy problem for a large class of systems via transformations that render the density of states function log-concave. The effectiveness of the method is illustrated on examples.