English
Related papers

Related papers: Information Limits for Recovering a Hidden Communi…

200 papers

We study the hardness of Approximate Query Processing (AQP) of various types of queries involving joins over multiple tables of possibly different sizes. In the case where the query result is a single value (e.g., COUNT, SUM, and…

Databases · Computer Science 2020-10-02 Tianyu Liu , Chi Wang

We investigate the clustering performances of the relaxed $K$means in the setting of sub-Gaussian Mixture Model (sGMM) and Stochastic Block Model (SBM). After identifying the appropriate signal-to-noise ratio (SNR), we prove that the…

Statistics Theory · Mathematics 2019-04-22 Christophe Giraud , Nicolas Verzelen

Exact recovery in stochastic block models (SBMs) is well understood in undirected settings, but remains considerably less developed for directed and sparse networks, particularly when the number of communities diverges. Spectral methods for…

Machine Learning · Statistics 2026-02-18 Behzad Aalipur , Yichen Qin

We study $k$-clustering problems with lower bounds, including $k$-median and $k$-means clustering with lower bounds. In addition to the point set $P$ and the number of centers $k$, a $k$-clustering problem with (uniform) lower bounds gets a…

Data Structures and Algorithms · Computer Science 2021-08-18 Anna Arutyunova , Melanie Schmidt

We derive an algorithm of optimal complexity which determines whether a given matrix is a Cauchy matrix, and which exactly recovers the Cauchy points defining a Cauchy matrix from the matrix entries. Moreover, we study how to approximate a…

Numerical Analysis · Mathematics 2015-12-22 Jörg Liesen , Robert Luce

Community detection in networks is a fundamental problem in machine learning and statistical inference, with applications in social networks, biological systems, and communication networks. The stochastic block model (SBM) serves as a…

Machine Learning · Computer Science 2026-02-06 Amir R. Asadi , Akbar Davoodi , Ramin Javadi , Farzad Parvaresh

The hypergraph community detection problem seeks to identify groups of related nodes in hypergraph data. We propose an information-theoretic hypergraph community detection algorithm which compresses the observed data in terms of community…

We give upper and lower bounds on the information-theoretic threshold for community detection in the stochastic block model. Specifically, let $k$ be the number of groups, $d$ be the average degree, the probability of edges between vertices…

Probability · Mathematics 2016-04-25 Jess Banks , Cristopher Moore

We propose a general modeling and algorithmic framework for discrete structure recovery that can be applied to a wide range of problems. Under this framework, we are able to study the recovery of clustering labels, ranks of players, signs…

Statistics Theory · Mathematics 2020-09-29 Chao Gao , Anderson Y. Zhang

The present work is concerned with community detection. Specifically, we consider a random graph drawn according to the stochastic block model~: its vertex set is partitioned into blocks, or communities, and edges are placed randomly and…

Data Structures and Algorithms · Computer Science 2019-06-27 Ludovic Stephan , Laurent Massoulié

Most recent developments on the stochastic block model (SBM) rely on the knowledge of the model parameters, or at least on the number of communities. This paper introduces efficient algorithms that do not require such knowledge and yet…

Probability · Mathematics 2015-06-12 Emmanuel Abbe , Colin Sandon

Resolving a conjecture of Abbe, Bandeira and Hall, the authors have recently shown that the semidefinite programming (SDP) relaxation of the maximum likelihood estimator achieves the sharp threshold for exactly recovering the community…

Machine Learning · Statistics 2016-06-16 Bruce Hajek , Yihong Wu , Jiaming Xu

This article studies the estimation of latent community memberships from pairwise interactions in a network of $N$ nodes, where the observed interactions can be of arbitrary type, including binary, categorical, and vector-valued, and not…

Statistics Theory · Mathematics 2022-08-31 Konstantin Avrachenkov , Maximilien Dreveton , Lasse Leskelä

A central question in quantum information theory is to determine how well lost information can be reconstructed. Crucially, the corresponding recovery operation should perform well without knowing the information to be reconstructed. In…

Quantum Physics · Physics 2016-02-08 David Sutter , Omar Fawzi , Renato Renner

The stochastic block model (SBM) is a fundamental model for studying graph clustering or community detection in networks. It has received great attention in the last decade and the balanced case, i.e., assuming all clusters have large size,…

Machine Learning · Computer Science 2023-10-24 Chandra Sekhar Mukherjee , Pan Peng , Jiapeng Zhang

The problem of PIR in graph-based replication systems has received significant attention in recent years. A systematic study was conducted by Sadeh, Gu, and Tamo, where each file is replicated across two servers and the storage topology is…

Information Theory · Computer Science 2025-10-01 Gennian Ge , Hao Wang , Zixiang Xu , Yijun Zhang

Community detection is the problem of identifying dense communities in networks. Motivated by transitive behavior in social networks ("thy friend is my friend"), an emerging line of work considers spatially-embedded networks, which…

Probability · Mathematics 2025-12-30 Julia Gaudio , Andrew Jin

This paper is motivated by the reconstruction problem on the sparse stochastic block model. Mossel, et. al. proved that a reconstruction algorithm that recovers an optimal fraction of the communities in the symmetric, 2-community case. The…

Probability · Mathematics 2023-12-20 Byron Chin , Allan Sly

This paper studies the problem of recovering a hidden vertex correspondence between two correlated graphs when both edge weights and node features are observed. While most existing work on graph alignment relies primarily on edge…

Statistics Theory · Mathematics 2026-04-07 Dong Huang , Chenyang Tian , Pengkun Yang

This paper presents the first theoretical results showing that stable identification of overcomplete $\mu$-coherent dictionaries $\Phi \in \mathbb{R}^{d\times K}$ is locally possible from training signals with sparsity levels $S$ up to the…

Information Theory · Computer Science 2015-04-03 Karin Schnass