scholarly journals Consistency of maximum-likelihood and variational estimators in the stochastic block model

2012 ◽  
Vol 6 (0) ◽  
pp. 1847-1899 ◽  
Author(s):  
Alain Celisse ◽  
Jean-Jacques Daudin ◽  
Laurent Pierre
Keyword(s):  
Maximum Likelihood ◽  
Block Model ◽  
Stochastic Block Model

scholarly journals Exact Recovery of Stochastic Block Model by Ising Model

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 65
Author(s):  
Feng Zhao ◽  
Min Ye ◽  
Shao-Lun Huang
Keyword(s):  
Phase Transition ◽  
Maximum Likelihood ◽  
Ising Model ◽  
Optimization Problem ◽  
Model Parameters ◽  
Stochastic Algorithm ◽  
Block Model ◽  
Stochastic Block Model ◽  
Special Case ◽  
Transition Property

In this paper, we study the phase transition property of an Ising model defined on a special random graph—the stochastic block model (SBM). Based on the Ising model, we propose a stochastic estimator to achieve the exact recovery for the SBM. The stochastic algorithm can be transformed into an optimization problem, which includes the special case of maximum likelihood and maximum modularity. Additionally, we give an unbiased convergent estimator for the model parameters of the SBM, which can be computed in constant time. Finally, we use metropolis sampling to realize the stochastic estimator and verify the phase transition phenomenon thfough experiments.

scholarly journals Weighted stochastic block model

2021 ◽  
Author(s):  
Tin Lok James Ng ◽  
Thomas Brendan Murphy
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Simulated Data ◽  
Important Case ◽  
Block Model ◽  
Data Set ◽  
Stochastic Block Model ◽  
Proposed Model ◽  
Variational Approaches ◽  
Number Of Classes

AbstractWe propose a weighted stochastic block model (WSBM) which extends the stochastic block model to the important case in which edges are weighted. We address the parameter estimation of the WSBM by use of maximum likelihood and variational approaches, and establish the consistency of these estimators. The problem of choosing the number of classes in a WSBM is addressed. The proposed model is applied to simulated data and an illustrative data set.

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.

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