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Stochastic Block Models and Reconstruction by Mossel, Elchanan; Neeman, Joe; Sly, Allan is a scholarly article available to read on EtoBox.

What is Stochastic Block Models and Reconstruction about?

The planted partition model (also known as the stochastic blockmodel) is a classical cluster-exhibiting random graph model that has been extensively studied in statistics, physics, and computer science. In its simplest form, the planted partition model is a model for random graphs on $n$ nodes with two equal-sized clusters, with an between-class edge probability of $q$ and a within-class edge probability of $p$. Although most of the literature on this model has focused on the case of increasing degrees (ie.\ $pn, qn \to \infty$ as $n \to \infty$), the sparse case $p, q = O(1/n)$ is interesting both from a mathematical and an applied point of view. A striking conjecture of Decelle, Krzkala, Moore and Zdeborov\'a based on deep, non-rigorous ideas from statistical physics gave a precise prediction for the algorithmic threshold of clustering in the sparse planted partition model. In particular, if $p = a/n$ and $q = b/n$, then Decelle et al.\ conjectured that it is possible to cluster in a way correlated with the true partition if $(a - b)^2 > 2(a + b)$, and impossible if $(a - b)^2 < 2(a + b)$. By comparison, the best-known rigorous result is that of Coja-Oghlan, who showed that clust

Author

Mossel, Elchanan; Neeman, Joe; Sly, Allan

Published

2012

Language

EN