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Introduction to the non-asymptotic analysis of random matrices
  • R. Vershynin
  • Mathematics, Computer Science
  • Compressed Sensing
  • 12 November 2010
This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory. Expand
High-Dimensional Probability: An Introduction with Applications in Data Science
High-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions. Expand
A Randomized Kaczmarz Algorithm with Exponential Convergence
The Kaczmarz method for solving linear systems of equations is an iterative algorithm that has found many applications ranging from computer tomography to digital signal processing. Despite theExpand
Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit
This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements—L1-minimization methods and iterative methods (Matching Pursuits). Expand
On sparse reconstruction from Fourier and Gaussian measurements
This paper improves upon best-known guarantees for exact reconstruction of a sparse signal f from a small universal sample of Fourier measurements. The method for reconstruction that has recentlyExpand
The Littlewood-Offord problem and invertibility of random matrices
Abstract We prove two basic conjectures on the distribution of the smallest singular value of random n × n matrices with independent entries. Under minimal moment assumptions, we show that theExpand
Signal Recovery From Incomplete and Inaccurate Measurements Via Regularized Orthogonal Matching Pursuit
  • D. Needell, R. Vershynin
  • Mathematics, Computer Science
  • IEEE Journal of Selected Topics in Signal…
  • 9 December 2007
We demonstrate a simple greedy algorithm that can reliably recover a vector <i>v</i> ¿ ¿<sup>d</sup> from incomplete and inaccurate measurements . Expand
Robust 1-bit Compressed Sensing and Sparse Logistic Regression: A Convex Programming Approach
  • Y. Plan, R. Vershynin
  • Mathematics, Computer Science
  • IEEE Transactions on Information Theory
  • 6 February 2012
We show that an -sparse signal in can be accurately estimated from m = O(s log(n/s) single-bit measurements using a simple convex program. Expand
Hanson-Wright inequality and sub-gaussian concentration
In this expository note, we give a modern proof of Hanson-Wright inequality for quadratic forms in sub-gaussian random variables.We deduce a useful concentration inequality for sub-gaussian randomExpand
Smallest singular value of a random rectangular matrix
We prove an optimal estimate of the smallest singular value of a random sub- Gaussian matrix, valid for all dimensions. For an Nn matrix A with inde- pendent and identically distributed sub-GaussianExpand