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We study the effect of the quality and quantity of side information on the recovery of a hidden community of size $K=o(n)$ in a graph of size $n$. Side information for each node in the graph is modeled by a random vector with the following…

Information Theory · Computer Science 2018-09-07 Hussein Saad , Aria Nosratinia

We consider the problem of detecting a community of densely connected vertices in a high-dimensional bipartite graph of size $n_1 \times n_2$. Under the null hypothesis, the observed graph is drawn from a bipartite Erd\H{o}s-Renyi…

Statistics Theory · Mathematics 2025-05-27 Julien Chhor , Parker Knight

In this paper, we study the exact recovery problem in the Gaussian weighted version of the Stochastic block model with two symmetric communities. We provide the information-theoretic threshold in terms of the signal-to-noise ratio (SNR) of…

Statistics Theory · Mathematics 2024-02-21 Aaradhya Pandey , Sanjeev Kulkarni

Empirical observations suggest that in practice, community membership does not completely explain the dependency between the edges of an observation graph. The residual dependence of the graph edges are modeled in this paper, to first…

Social and Information Networks · Computer Science 2023-01-11 Mohammad Esmaeili , Aria Nosratinia

Consider a $d$-uniform random hypergraph on $n$ vertices in which hyperedges are included iid so that the average degree is $n^\delta$. The projection of a hypergraph is a graph on the same $n$ vertices where an edge connects two vertices…

Combinatorics · Mathematics 2025-02-24 Guy Bresler , Chenghao Guo , Yury Polyanskiy , Andrew Yao

We investigate the number of maximal independent set queries required to reconstruct the edges of a hidden graph. We show that randomised adaptive algorithms need at least $\Omega(\Delta^2 \log(n / \Delta) / \log \Delta)$ queries to…

Data Structures and Algorithms · Computer Science 2024-04-05 Lukas Michel , Alex Scott

The binary symmetric stochastic block model deals with a random graph of $n$ vertices partitioned into two equal-sized clusters, such that each pair of vertices is connected independently with probability $p$ within clusters and $q$ across…

Machine Learning · Statistics 2016-01-07 Bruce Hajek , Yihong Wu , Jiaming Xu

This paper builds theoretical foundations for the recovery of a newly proposed class of smooth graph signals, approximately bandlimited graph signals, under three sampling strategies: uniform sampling, experimentally designed sampling and…

Information Theory · Computer Science 2017-02-21 Siheng Chen , Rohan Varma , Aarti Singh , Jelena Kovačević

Random graph alignment refers to recovering the underlying vertex correspondence between two random graphs with correlated edges. This can be viewed as an average-case and noisy version of the well-known graph isomorphism problem. For the…

Machine Learning · Statistics 2021-08-18 Luca Ganassali , Laurent Massoulié , Marc Lelarge

Graph reconstruction can efficiently detect the underlying topology of massive networks such as the Internet. Given a query oracle and a set of nodes, the goal is to obtain the edge set by performing as few queries as possible. An algorithm…

Data Structures and Algorithms · Computer Science 2024-07-29 Clara Stegehuis , Lotte Weedage

Graph alignment refers to the task of finding the vertex correspondence between two correlated graphs of $n$ vertices. Extensive study has been done on polynomial-time algorithms for the graph alignment problem under the Erd\H{o}s-R\'enyi…

Data Structures and Algorithms · Computer Science 2024-06-12 Ziao Wang , Weina Wang , Lele Wang

We study the problem of learning latent community structure from multiple correlated networks, focusing on edge-correlated stochastic block models with two balanced communities. Recent work of Gaudio, R\'acz, and Sridhar (COLT 2022)…

Statistics Theory · Mathematics 2024-12-05 Miklós Z. Rácz , Jifan Zhang

We study a semidefinite programming (SDP) relaxation of the maximum likelihood estimation for exactly recovering a hidden community of cardinality $K$ from an $n \times n$ symmetric data matrix $A$, where for distinct indices $i,j$, $A_{ij}…

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

We consider the problem of learning latent community structure from multiple correlated networks. We study edge-correlated stochastic block models with two balanced communities, focusing on the regime where the average degree is logarithmic…

Statistics Theory · Mathematics 2022-03-30 Julia Gaudio , Miklos Z. Racz , Anirudh Sridhar

We consider the task of learning latent community structure from multiple correlated networks. First, we study the problem of learning the latent vertex correspondence between two edge-correlated stochastic block models, focusing on the…

Statistics Theory · Mathematics 2021-07-15 Miklos Z. Racz , Anirudh Sridhar

We consider the densest $k$-subgraph problem, which seeks to identify the $k$-node subgraph of a given input graph with maximum number of edges. This problem is well-known to be NP-hard, by reduction to the maximum clique problem. We…

Optimization and Control · Mathematics 2019-04-09 Polina Bombina , Brendan Ames

We consider the statistical inference problem of recovering an unknown perfect matching, hidden in a weighted random graph, by exploiting the information arising from the use of two different distributions for the weights on the edges…

Disordered Systems and Neural Networks · Physics 2020-08-10 Guilhem Semerjian , Gabriele Sicuro , Lenka Zdeborová

We investigate the problem of recovering a latent directed Erd\H{o}s-R\'enyi graph $G^*\sim \mathcal G(n,p)$ from observations of discrete voter model trajectories on $G^*$, where $np$ grows polynomially in $n$. Given access to $M$…

Probability · Mathematics 2025-04-08 Hang Du , Seokmin Ha , Oriol Solé-Pi

In this paper, we aim at recovering an undirected weighted graph of $N$ vertices from the knowledge of a perturbed version of the eigenspaces of its adjacency matrix $W$. For instance, this situation arises for stationary signals on graphs…

Statistics Theory · Mathematics 2017-03-16 Yohann De Castro , Thibault Espinasse , Paul Rochet

This paper studies the problem of matching two complete graphs with edge weights correlated through latent geometries, extending a recent line of research on random graph matching with independent edge weights to geometric models.…

Statistics Theory · Mathematics 2022-02-25 Haoyu Wang , Yihong Wu , Jiaming Xu , Israel Yolou