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

03/05/2021 ∙ by Lorenzo Dall'Amico, et al. ∙ 0

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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 14

page 22

Code Repositories

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.