ArticleAnnals of statistics2020
ENTRYWISE EIGENVECTOR ANALYSIS OF RANDOM MATRICES WITH LOW EXPECTED RANK.
Article in Annals of statistics, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 17 papers.
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Who cites it
17 citing papers in PubMed.
- Differentially Private Hierarchical Spectral Clustering.Entropy (Basel, Switzerland) · 2026Article
- Dimension Reduction for Large-Scale Federated Data: Statistical Rate and Asymptotic Inference.Journal of the American Statistical Association · 2026Article
- Estimating Higher-Order Mixed Memberships via theJournal of the American Statistical Association · 2025Article
- Semi-Supervised Clustering of Sparse Graphs: Crossing the Information-Theoretic Threshold.Journal of machine learning · 2024Article
- Statistical Significance of Clustering with Multidimensional Scaling.Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America · 2024Article
- Approximate message passing from random initialization with applications toProceedings of the National Academy of Sciences of the United States of America · 2023Article
- Subject clustering by IF-PCA and several recent methods.Frontiers in genetics · 2023Article
- A Useful Criterion on Studying Consistent Estimation in Community Detection.Entropy (Basel, Switzerland) · 2022Article
- Asymptotic Theory of Eigenvectors for Random Matrices with Diverging Spikes.Journal of the American Statistical Association · 2022Article
- Robust high dimensional factor models with applications to statistical machine learning.Statistical science : a review journal of the Institute of Mathematical Statistics · 2021Article
- ASYMMETRY HELPS: EIGENVALUE AND EIGENVECTOR ANALYSES OF ASYMMETRICALLY PERTURBED LOW-RANK MATRICES.Annals of statistics · 2021Article
- ENTRYWISE EIGENVECTOR ANALYSIS OF RANDOM MATRICES WITH LOW EXPECTED RANK.Annals of statistics · 2020Article
- MODEL ASSISTED VARIABLE CLUSTERING: MINIMAX-OPTIMAL RECOVERY AND ALGORITHMS.Annals of statistics · 2020Article
- NOISY MATRIX COMPLETION: UNDERSTANDING STATISTICAL GUARANTEES FOR CONVEX RELAXATION VIA NONCONVEX OPTIMIZATION.SIAM journal on optimization : a publication of the Society for Industrial and Applied Mathematics · 2020Article
- Inference and uncertainty quantification for noisy matrix completion.Proceedings of the National Academy of Sciences of the United States of America · 2019Article
- Gradient Descent with Random Initialization: Fast Global Convergence for Nonconvex Phase Retrieval.Mathematical programming · 2019Article
- SPECTRAL METHOD AND REGULARIZED MLE ARE BOTH OPTIMAL FOR TOP-Annals of statistics · 2019Article
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Authors and funding
4 authors.
Funding
Abstract
Recovering low-rank structures via eigenvector perturbation analysis is a common problem in statistical machine learning, such as in factor analysis, community detection, ranking, matrix completion, among others. While a large variety of bounds are available for average errors between empirical and population statistics of eigenvectors, few results are tight for entrywise analyses, which are critical for a number of problems such as community detection. This paper investigates entrywise behaviors of eigenvectors for a large class of random matrices whose expectations are low-rank, which helps settle the conjecture in Abbe et al. (2014b) that the spectral algorithm achieves exact recovery in the stochastic block model without any trimming or cleaning steps. The key is a first-order approximation of eigenvectors under the
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