Reducing degeneracy in maximum entropy models of networks.
Based on Jaynes's 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 demonstrated on examples.
Department of Physics and Interdisciplinary Center for Network Science & Applications, University of Notre Dame, Notre Dame, Indiana 46556, USA.
Szabolcs
S
Horvát
Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208, USA.
Éva
É
Czabarka
Department of Physics and Interdisciplinary Center for Network Science & Applications, University of Notre Dame, Notre Dame, Indiana 46556, USA.|Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, Indiana 46556 USA.
Zoltán
Z
Toroczkai