2021/08/02 by Hugo Cui, Luca Saglietti, Lenka Zdeborová
Computer Science · Medicine · Physics and Astronomy · #Block (permutation group theory) #Graph #Inference #Large deviations theory #Machine Learning and Algorithms #Measure (data warehouse) #Opinion Dynamics and Social Influence #SARS-CoV-2 detection and testing #Set (abstract data type) #Statistical inference #Stochastic block model #cond-mat.dis-nn
paper · pdf · doi:10.1103/physreve.105.034108
published as Phys. Rev. E 105, 034108 (2022)
arxiv created 2021/08/02 · openalex created_date 2021/08/16 · openalex publication_date 2022/03/04 · arxiv updated 2022/03/22 · openalex updated_date 2026/08/05
In community detection on graphs, the semi-supervised learning problem entails inferring the ground-truth membership of each node in a graph, given the connectivity structure and a limited number of revealed node labels. Different subsets of revealed labels can in principle lead to higher or lower information gains and induce different reconstruction accuracies. In the framework of the dense stochastic block model, we employ statistical physics methods to derive a large deviation analysis for this problem, in the high-dimensional limit. This analysis allows the characterization of the fluctuations around the typical behaviour, capturing the effect of correlated label choices and yielding an estimate of their informativeness and their rareness among subsets of the same size. We find theoretical evidence of a non-monotonic relationship between reconstruction accuracy and the free energy associated to the posterior measure of the inference problem. We further discuss possible implications for active learning applications in community detection.