Related papers: Information Limits for Recovering a Hidden Communi…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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,…
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…
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…
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…
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…
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…