Nishimori meets Bethe：稀疏加权图中节点分类的谱方法
Nishimori meets Bethe: a spectral method for node classification in sparse weighted graphs
摘要：
本文揭示了边权按P分布的随机Erdos-Renyi图的参数化Nishimori温度与Bethe自由能之间的一个新关系。Nishimori温度的估计是贝叶斯推断问题中的一个重要任务，作为这个新关系的一个实际推论，提出了一种从加权图的Bethe Hessian矩阵的特征值精确估计Nishimori温度的数值方法。该算法，反过来，是用来提出一个新的频谱方法的节点分类加权（可能稀疏）图。通过理论论证和实际数据实验，证明了该方法优于竞争国家的最先进的方法。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
