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For two correlated graphs which are independently sub-sampled from a common Erd\H{o}s-R\'enyi graph $\mathbf{G}(n, p)$, we wish to recover their \emph{latent} vertex matching from the observation of these two graphs \emph{without labels}.…

Statistics Theory · Mathematics 2022-05-31 Jian Ding , Hang Du

Embedding graphs in a geographical or latent space, i.e.\ inferring locations for vertices in Euclidean space or on a smooth manifold or submanifold, is a common task in network analysis, statistical inference, and graph visualization. We…

Computational Geometry · Computer Science 2022-05-18 Varsha Dani , Josep Díaz , Thomas P. Hayes , Cristopher Moore

We study a well known noisy model of the graph isomorphism problem. In this model, the goal is to perfectly recover the vertex correspondence between two edge-correlated Erd\H{o}s-R\'{e}nyi random graphs, with an initial seed set of…

Machine Learning · Computer Science 2018-07-27 Elchanan Mossel , Jiaming Xu

We study model recovery for data classification, where the training labels are generated from a one-hidden-layer neural network with sigmoid activations, also known as a single-layer feedforward network, and the goal is to recover the…

Machine Learning · Statistics 2020-05-07 Haoyu Fu , Yuejie Chi , Yingbin Liang

The stochastic block model (SBM) is a random graph model in which the edges are generated according to the underlying cluster structure on the vertices. The (ferromagnetic) Ising model, on the other hand, assigns $\pm 1$ labels to vertices…

Probability · Mathematics 2020-10-15 Min Ye

Performing inference in graphs is a common task within several machine learning problems, e.g., image segmentation, community detection, among others. For a given undirected connected graph, we tackle the statistical problem of exactly…

Machine Learning · Computer Science 2022-09-12 Kevin Bello , Chuyang Ke , Jean Honorio

This paper presents a fast and simple new 2-approximation algorithm for minimum weighted vertex cover. The unweighted version of this algorithm is equivalent to a well-known greedy maximal independent set algorithm. We prove that this…

Data Structures and Algorithms · Computer Science 2022-09-13 Nate Veldt

The problem of computing the vertex expansion of a graph is an NP-hard problem. The current best worst-case approximation guarantees for computing the vertex expansion of a graph are a $O(\sqrt{\log n})$-approximation algorithm due to…

Data Structures and Algorithms · Computer Science 2018-05-25 Anand Louis , Rakesh Venkat

We formulate and analyze a heterogeneous random hypergraph model, and we provide an achieveability result for recovery of hyperedges from the observed projected graph. We observe a projected graph which combines random hyperedges across all…

Data Structures and Algorithms · Computer Science 2026-03-03 Alexander Morgan , Chenghao Guo

The classical setting of community detection consists of networks exhibiting a clustered structure. To more accurately model real systems we consider a class of networks (i) whose edges may carry labels and (ii) which may lack a clustered…

Statistics Theory · Mathematics 2014-06-27 Jiaming Xu , Laurent Massoulié , Marc Lelarge

We study learning problems on correlated stochastic block models with two balanced communities. Our main result gives the first efficient algorithm for graph matching in this setting. In the most interesting regime where the average degree…

Data Structures and Algorithms · Computer Science 2024-12-04 Shuwen Chai , Miklós Z. Rácz

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

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 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

The group synchronization problem is to estimate unknown group elements at the vertices of a graph when given a set of possibly noisy observations of group differences at the edges. We consider the group synchronization problem on finite…

Statistics Theory · Mathematics 2022-05-24 Bradley Stich

For two unlabeled graphs $G_1,G_2$ independently sub-sampled from an Erd\H{o}s-R\'enyi graph $\mathbf G(n,p)$ by keeping each edge with probability $s$, we aim to recover \emph{as many as possible} of the corresponding vertex pairs. We…

Probability · Mathematics 2025-02-18 Hang Du

We study differentially private (DP) algorithms for recovering clusters in well-clustered graphs, which are graphs whose vertex set can be partitioned into a small number of sets, each inducing a subgraph of high inner conductance and small…

Data Structures and Algorithms · Computer Science 2024-03-22 Weiqiang He , Hendrik Fichtenberger , Pan Peng

The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…

Optimization and Control · Mathematics 2026-05-07 Chandler Smith , HanQin Cai , Abiy Tasissa

The graph alignment problem aims to identify the vertex correspondence between two correlated graphs. Most existing studies focus on the scenario in which the two graphs share the same vertex set. However, in many real-world applications,…

Information Theory · Computer Science 2026-01-13 Chun Hei Michael Shiu , Hei Victor Cheng , Lele Wang

This paper studies the problem of recovering the hidden vertex correspondence between two correlated random graphs. We propose the partially correlated Erd\H{o}s-R\'enyi graphs model, wherein a pair of induced subgraphs with a certain…

Information Theory · Computer Science 2025-10-08 Dong Huang , Xianwen Song , Pengkun Yang