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Found 19 papers, 0 papers with code
Spectral Graph Matching and Regularized Quadratic Relaxations: Algorithm and Theory
Graph matching, also known as network alignment, aims at recovering the latent vertex correspondence between two unlabeled, edge-correlated weighted graphs.
Information-Theoretic Thresholds for Planted Dense Cycles
We study a random graph model for small-world networks which are ubiquitous in social and biological sciences.
Detection of Dense Subhypergraphs by Low-Degree Polynomials
We consider detecting the presence of a planted $G^r(n^\gamma, n^{-\alpha})$ subhypergraph in a $G^r(n, n^{-\beta})$ hypergraph, where $0< \alpha < \beta < r-1$ and $0 < \gamma < 1$.
Sharp analysis of EM for learning mixtures of pairwise differences
We consider a symmetric mixture of linear regressions with random samples from the pairwise comparison design, which can be seen as a noisy version of a type of Euclidean distance geometry problem.
Detection-Recovery Gap for Planted Dense Cycles
Planted dense cycles are a type of latent structure that appears in many applications, such as small-world networks in social sciences and sequence assembly in computational biology.
Random graph matching at Otter's threshold via counting chandeliers
We propose an efficient algorithm for graph matching based on similarity scores constructed from counting a certain family of weighted trees rooted at each vertex.
Testing network correlation efficiently via counting trees
We propose a new procedure for testing whether two networks are edge-correlated through some latent vertex correspondence.
Exact Matching of Random Graphs with Constant Correlation
Let $G$ and $G'$ be $G(n, p)$ Erd\H{o}s--R\'enyi graphs marginally, identified with their adjacency matrices.
Optimal Spectral Recovery of a Planted Vector in a Subspace
Recovering a planted vector $v$ in an $n$-dimensional random subspace of $\mathbb{R}^N$ is a generic task related to many problems in machine learning and statistics, such as dictionary learning, subspace recovery, principal component analysis, and non-Gaussian component analysis.
Random Graph Matching with Improved Noise Robustness
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges.
Learning Mixtures of Permutations: Groups of Pairwise Comparisons and Combinatorial Method of Moments
In applications such as rank aggregation, mixture models for permutations are frequently used when the population exhibits heterogeneity.
Spectral Graph Matching and Regularized Quadratic Relaxations I: The Gaussian Model
Departing from prior spectral approaches that only compare top eigenvectors, or eigenvectors of the same order, GRAMPA first constructs a similarity matrix as a weighted sum of outer products between all pairs of eigenvectors of the two graphs, with weights given by a Cauchy kernel applied to the separation of the corresponding eigenvalues, then outputs a matching by a simple rounding procedure.
Spectral Graph Matching and Regularized Quadratic Relaxations II: Erdős-Rényi Graphs and Universality
We analyze a new spectral graph matching algorithm, GRAph Matching by Pairwise eigen-Alignments (GRAMPA), for recovering the latent vertex correspondence between two unlabeled, edge-correlated weighted graphs.
Estimation of Monge Matrices
Monge matrices and their permuted versions known as pre-Monge matrices naturally appear in many domains across science and engineering.
Towards Optimal Estimation of Bivariate Isotonic Matrices with Unknown Permutations
Many applications, including rank aggregation, crowd-labeling, and graphon estimation, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and/or columns.
Breaking the $1/\sqrt{n}$ Barrier: Faster Rates for Permutation-based Models in Polynomial Time
Many applications, including rank aggregation and crowd-labeling, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and columns.
Minimax Rates and Efficient Algorithms for Noisy Sorting
There has been a recent surge of interest in studying permutation-based models for ranking from pairwise comparison data.
Worst-case vs Average-case Design for Estimation from Fixed Pairwise Comparisons
We show that when the assignment of items to the topology is arbitrary, these permutation-based models, unlike their parametric counterparts, do not admit consistent estimation for most comparison topologies used in practice.
Optimal Rates of Statistical Seriation
Given a matrix the seriation problem consists in permuting its rows in such way that all its columns have the same shape, for example, they are monotone increasing.
