Thermodynamics of network model fitting with spectral entropies

TL;DR

This paper introduces a thermodynamics-inspired, entropy-based framework for network model fitting that offers a topologically agnostic approach to assess network likelihoods, with practical estimation procedures demonstrated on synthetic and brain networks.

Contribution

It presents a novel thermodynamics analogy for network model inference using spectral entropies, including analytical hyperparameter estimation methods.

Findings

Effective in synthetic modular networks

Successfully applied to brain connectivity data

Provides a topologically agnostic assessment of network models

Abstract

An information theoretic approach inspired by quantum statistical mechanics was recently proposed as a means to optimize network models and to assess their likelihood against synthetic and real-world networks. Importantly, this method does not rely on specific topological features or network descriptors, but leverages entropy-based measures of network distance. Entertaining the analogy with thermodynamics, we provide a physical interpretation of model hyperparameters and propose analytical procedures for their estimate. These results enable the practical application of this novel and powerful framework to network model inference. We demonstrate this method in synthetic networks endowed with a modular structure, and in real-world brain connectivity networks.