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arXiv · 2103.03561

Nishimori meets Bethe: a spectral method for node classification in sparse weighted graphs

Lorenzo Dall'Amico·Romain Couillet·Nicolas Tremblay
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Abstract

This article unveils a new relation between the Nishimori temperature parametrizing a distribution P and the Bethe free energy on random Erdos-Renyi graphs with edge weights distributed according to P. Estimating the Nishimori temperature being a task of major importance in Bayesian inference problems, as a practical corollary of this new relation, a numerical method is proposed to accurately estimate the Nishimori temperature from the eigenvalues of the Bethe Hessian matrix of the weighted graph. The algorithm, in turn, is used to propose a new spectral method for node classification in weighted (possibly sparse) graphs. The superiority of the method over competing state-of-the-art approaches is demonstrated both through theoretical arguments and real-world data experiments.

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BibTeXRIS

Lorenzo Dall'Amico, Romain Couillet, Nicolas Tremblay. 2021-09-24. Nishimori meets Bethe: a spectral method for node classification in sparse weighted graphs. https://doi.org/10.1088/1742-5468%2Fac21d3

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