DeepAI AI Chat
Log In Sign Up

Exact Recovery for a Family of Community-Detection Generative Models

by   Luca Corinzia, et al.

Generative models for networks with communities have been studied extensively for being a fertile ground to establish information-theoretic and computational thresholds. In this paper we propose a new simplistic model for planted generative models called planted Random Energy Model (REM), inspired by Derrida's REM. For this model we provide the asymptotic behaviour of the probability of error for the maximum likelihood estimator and hence the exact recovery threshold. As an application of it, we further consider the 2 non-equally sized community Weighted Stochastic Block Model (2-WSBM) on h-uniform hypergraphs, that is equivalent to the planted REM on both sides of the spectrum, for high and low edge cardinality h. We provide upper and lower bounds for the exact recoverability for any h, mapping these problems to the aforementioned planted-REM. To the best of our knowledge, these are the first consistency results for the 2-WSBM with non-equally sized community and for the 2-WSBM on hypergraphs.


page 1

page 2

page 3

page 4


Information Theoretic Limits of Exact Recovery in Sub-hypergraph Models for Community Detection

In this paper, we study the information theoretic bounds for exact recov...

Community detection and stochastic block models: recent developments

The stochastic block model (SBM) is a random graph model with planted cl...

Exact Recovery of Community Detection in dependent Gaussian Mixture Models

We study the community detection problem on a Gaussian mixture model, in...

Partial Recovery Bounds for the Sparse Stochastic Block Model

In this paper, we study the information-theoretic limits of community de...

Bayesian estimation from few samples: community detection and related problems

We propose an efficient meta-algorithm for Bayesian estimation problems ...

Community Detection with Graph Neural Networks

We study data-driven methods for community detection in graphs. This est...

Exact Community Recovery over Signed Graphs

Signed graphs encode similarity and dissimilarity relationships among di...