Introduction to the non-asymptotic analysis of random matrices
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Summary
This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory, particularly for the problem of estimating covariance matrices in statistics and for validating probabilistic constructions of measurementMatrices in compressed sensing.
- Type
- preprint
- Published
- 2010-11-12
- Cited by
- 3,099
- References
- 105
- Access
- Open access
- OpenAlex
- https://openalex.org/W2131172946
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:133440
Keywords
Random matrix, Computer science, Matrix analysis, Probabilistic logic, Matrix (chemical analysis)
References
- Probability on Banach spaces
- Frames and Bases: An Introductory Course
- The Generic Chaining
- Theoretical Foundations and Numerical Methods for Sparse Recovery
- Random Matrix Theory: Invariant Ensembles and Universality
- Propriétés locales des fonctions à séries de Fourier aléatoires
- On the distribution of the largest eigenvalue in principal components analysis
- Asymptotic Theory Of Finite Dimensional Normed Spaces
- Introduction to Operator Space Theory
- Decoupling: From Dependence to Independence
- The concentration of measure phenomenon
- The least singular value of a random square matrix is O(n−1/2)
- Spectral Analysis of Large Dimensional Random Matrices
- User-Friendly Tail Bounds for Matrix Martingales
- Concentration of the adjacency matrix and of the Laplacian in random graphs with independent edges
- A Note on Universality of the Distribution of the Largest Eigenvalues in Certain Sample Covariance Matrices
- Random Vectors in the Isotropic Position
- Spectral norm of random matrices
- Concentration of measure and isoperimetric inequalities in product spaces
- Majorization of Gaussian processes and geometric applications
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- Atlas Simulation: A Numerical Scheme for Approximating Multiscale Diffusions Embedded in High Dimensions
- Model Selection in High-Dimensional Misspecified Models
- Quelques contributions à la sélection de variables et aux tests non-paramétriques
- Optimal Sparse Principal Component Analysis in High Dimensional Elliptical Model
- Gordon's inequality and condition numbers in conic optimization
- On the spectral norm of Gaussian random matrices
- Bayesian Semi-parametric Factor Models
- High-Dimensional Semiparametric Selection Models: Estimation Theory with an Application to the Retail Gasoline Market
- User-Friendly Tools for Random Matrices: An Introduction
- Recovering the Sparsest Element in a Subspace
- Proceedings of the third"international Traveling Workshop on Interactions between Sparse models and Technology"(iTWIST'16)
- Quelques aspects de l'étude quantitative de la fonction de comptage et des valeurs propres de matrices aléatoires
- Rare-event Analysis for Extremal Eigenvalues of the Beta-Laguerre Ensemble
- Robust matrix completion
- A Convex Formulation for Mixed Regression: Near Optimal Rates in the Face of Noise
- Estimating the effect of joint interventions from observational data in sparse high-dimensional settings
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