Proof of the Achievability Conjectures for the General Stochastic Block Model

2017 ◽  
Vol 71 (7) ◽  
pp. 1334-1406 ◽  
Author(s):  
Emmanuel Abbe ◽  
Colin Sandon
Keyword(s):  
Block Model ◽  
Stochastic Block Model ◽  
General Stochastic

Fast Algorithm on Stochastic Block Model for Exploring General Communities

2014 ◽  
Vol 24 (11) ◽  
pp. 2699-2709 ◽  
Author(s):  
Bian-Fang CHAI ◽  
Jian YU ◽  
Cai-Yan JIA ◽  
Jing-Hong WANG
Keyword(s):  
Fast Algorithm ◽  
Block Model ◽  
Stochastic Block Model

scholarly journals Active Learning in the Geometric Block Model

2020 ◽  
Vol 34 (04) ◽  
pp. 3641-3648 ◽  
Author(s):  
Eli Chien ◽  
Antonia Tulino ◽  
Jaime Llorca
Keyword(s):  
Active Learning ◽  
Community Detection ◽  
Random Graphs ◽  
State Of The Art ◽  
Superior Performance ◽  
Model Parameters ◽  
Block Model ◽  
Stochastic Block Model ◽  
Synthetic Datasets ◽  
Community Detection Problems

The geometric block model is a recently proposed generative model for random graphs that is able to capture the inherent geometric properties of many community detection problems, providing more accurate characterizations of practical community structures compared with the popular stochastic block model. Galhotra et al. recently proposed a motif-counting algorithm for unsupervised community detection in the geometric block model that is proved to be near-optimal. They also characterized the regimes of the model parameters for which the proposed algorithm can achieve exact recovery. In this work, we initiate the study of active learning in the geometric block model. That is, we are interested in the problem of exactly recovering the community structure of random graphs following the geometric block model under arbitrary model parameters, by possibly querying the labels of a limited number of chosen nodes. We propose two active learning algorithms that combine the use of motif-counting with two different label query policies. Our main contribution is to show that sampling the labels of a vanishingly small fraction of nodes (sub-linear in the total number of nodes) is sufficient to achieve exact recovery in the regimes under which the state-of-the-art unsupervised method fails. We validate the superior performance of our algorithms via numerical simulations on both real and synthetic datasets.

scholarly journals Universality of the stochastic block model

2018 ◽  
Vol 98 (3) ◽  
Author(s):  
Jean-Gabriel Young ◽  
Guillaume St-Onge ◽  
Patrick Desrosiers ◽  
Louis J. Dubé
Keyword(s):  
Block Model ◽  
Stochastic Block Model
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