Estimation and Prediction for Stochastic Blockmodels for Graphs with Latent Block Structure

By Tom A. B. Snijders, Krzysztof Nowicki. 1997

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In Graph Learning

Citations in the corpus

Revisiting Semi-Supervised Learning with Graph Embeddings (2016, background): “Features Labels Paradigm Embeddings Graph TSVM (Joachims, 1999) (Zhu et al., 2003) × √ Transductive × Regularization Manifold Reg (Belkin et al., 2006) √ √ Inductive × Regularization ICA (Sen et al., 2008) × √ Transductive × Features MAD (Talukdar & Crammer, 2009) (Snijders & Nowicki, 1997).”
Community detection in graphs (2009, methodology): “The method bears some resemblance with an a posteriori blockmodel previously introduced by Snijders and Nowicki (Nowicki and Snijders, 2001; Snijders and Nowicki, 1997).”
Community detection in networks: A user guide (2016, background): “The most famous model of networks with group structure is the stochastic block model (SBM) (Fienberg and Wasserman, 1981; Holland et al., 1983; Snijders and Nowicki, 1997).”
A Survey of Community Detection Approaches: From Statistical Modeling to Deep Learning (2021, methodology): “basic SBMmay also employ a Poisson distribution [45].”
Statistical Models for Social Networks (2011, methodology): “In Snijders (2001) this formula is motivated based on myopic stochastic optimization of the objective function, as is often used in game-theoretical models of network formation (e.”
Modeling relational events via latent classes (2010, methodology): “Statistical learning approaches can be used to infer both likely partitions of actors and the probability of block-wise interactions [25].”
Mixed Membership Stochastic Blockmodels (2007, background): “Rather, the latent stochastic blockmodel (Wang and Wong, 1987; Snijders and Nowicki, 1997) is an adaptation of mixture modeling to relational data.”
Constrained Graph Variational Autoencoders for Molecule Design (2018, methodology): “Stochastic block models [31] add community structure to the Erdős-Rényi model, but retain uncorrelated edge sampling.”
Statistical Inference on Random Dot Product Graphs: a Survey (2017, methodology): “Fortunato [36] provides an overview of partitioning techniques for graphs in general, and consistent partitioning of stochastic block models for two blocks was accomplished by Snijders and Nowicki [87] and for equal-sized blocks by Condon and Karp in 2001.”
Spectral clustering and the high-dimensional stochastic blockmodel (2010, background): “Snijders and Nowicki (1997) showed the consistency under the two block Stochastic Blockmodel of a clustering routine that clusters the nodes based on their degree distributions.”
Consistency of maximum-likelihood and variational estimators in the Stochastic Block Model (2011, methodology): “For instance Snijders and Nowicki (1997) study maximum-likelihood estimators of SBM with only two classes and binary undirected graphs, while Nowicki and Snijders (2001) perform Gibbs sampling for more than two classes at the price of a large computational cost.”
Exact Recovery in the Stochastic Block Model (2014, background): “A large body of literature in statistics and computer science [5], [6], [8], [9], [11], [13], [16], [25], [30], [34], [35]”
Matrix estimation by Universal Singular Value Thresholding (2012, methodology): “Early analysis of the stochastic blockmodel was carried out by Snijders and Nowicki [77, 91], who provided consistent parameter estimates when there are exactly two blocks.”
Limit theorems for eigenvectors of the normalized Laplacian for random graphs (2016, background): “The stochastic blockmodel [20] is a popular generative model for random graphs with latent community structure and many results are known regarding consistent recovery of the block assignments; see for example [7, 13, 24, 28, 29, 31, 35, 37, 40] and the references therein.”
Asymptotic Normality of Maximum Likelihood and its Variational Approximation for Stochastic Blockmodels (2012, methodology): “We consider a class of latent variable models considered by various authors [Karrer and Newman (2011), Latouche, Birmel´e and Ambroise (2011), Snijders and Nowicki (1997), Bickel and Chen (2009)], which we describe as follows.”