• Corpus ID: 240354807

Optimal Reconstruction of General Sparse Stochastic Block Models

  title={Optimal Reconstruction of General Sparse Stochastic Block Models},
  author={Byron Chin and Allan Sly},
Abstract. This paper is motivated by the reconstruction problem on the sparse stochastic block model. The paper “Belief Propagation, Robust Reconstruction and Optimal Recovery of Block Models” by Mossel, Neeman, and Sly [6] provided and proved a reconstruction algorithm that recovers an optimal fraction of the communities in the symmetric, 2-community case. The main contribution of their proof is to show that when the signal to noise ratio is sufficiently large, in particular λd > C, the… 

Partial recovery and weak consistency in the non-uniform hypergraph Stochastic Block Model

The community detection problem in sparse random hypergraphs under the non-uniform hypergraph stochastic block model (HSBM) is considered, a general model of random networks with community structure and higher-order interactions, and a spectral algorithm is provided that achieves weak consistency.



Belief propagation, robust reconstruction and optimal recovery of block models

A variant of Belief Propagation is used to give a reconstruction algorithm that is optimal in the sense that if (a b) 2 > C(a + b) for some constant C then the algorithm maximizes the fraction of the nodes labelled correctly.

Recovering Communities in the General Stochastic Block Model Without Knowing the Parameters

These provide the first algorithms affording efficiency, universality and information-theoretic optimality for strong and weak consistency in the general SBM with linear size communities.

Community Detection and Stochastic Block Models

  • E. Abbe
  • Computer Science
    Found. Trends Commun. Inf. Theory
  • 2018
The recent developments that establish the fundamental limits for community detection in the stochastic block model are surveyed, both with respect to information-theoretic and computational thresholds, and for various recovery requirements such as exact, partial and weak recovery.

Reconstruction and estimation in the planted partition model

This work establishes a rigorous connection between the clustering problem, spin-glass models on the Bethe lattice and the so called reconstruction problem and provides a simple and efficient algorithm for estimating a and b when clustering is possible.

Reconstruction for the Potts model

This work confirms conjectures made by Mezard and Montanari for the Potts models proving the first exact reconstruction threshold in a non-binary model establishing the so-called Kesten-Stigum bound for the 3-state Potts model on regular trees of large degree and determines asymptotics for these reconstruction thresholds.

CS 229 Supplemental Lecture notes Hoeffding ’ s inequality

The authors' first bound is perhaps the most basic of all probability inequalities, and it is known as Markov’s inequality, given its basic-ness, it is perhaps unsurprising that its proof is essentially only one line.

A short note on Poisson tail bounds. Columbia CS

  • 2019

Reconstruction for the Potts Model. The Annals of Probability

  • 2011

As the black box algorithm to provide our initial noisy estimates, we will make minor adjustments to the following theorem from Abbe and Sandon

    For any k ∈ Z, p ∈ (0, 1) k with |p| = 1. and symmetric matrix Q with no two rows equal, there exists ǫ(c) such that for all sufficiently large c