Roman Vershynin
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Roman Vershyninmathematics Degrees
Mathematics
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Functional Analysis
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Probability Theory
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Measure Theory
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Mathematics
Roman Vershynin's Degrees
- PhD Mathematics University of California, Davis
- Masters Mathematics University of California, Davis
- Bachelors Mathematics University of California, Davis
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(Suggest an Edit or Addition)Roman Vershynin's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Introduction to the non-asymptotic analysis of random matrices (2010) (2747)
- Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit (2007) (996)
- On sparse reconstruction from Fourier and Gaussian measurements (2008) (876)
- Signal Recovery From Incomplete and Inaccurate Measurements Via Regularized Orthogonal Matching Pursuit (2007) (875)
- High-Dimensional Probability (2018) (747)
- A Randomized Kaczmarz Algorithm with Exponential Convergence (2007) (723)
- Hanson-Wright inequality and sub-gaussian concentration (2013) (608)
- Robust 1-bit Compressed Sensing and Sparse Logistic Regression: A Convex Programming Approach (2012) (427)
- One‐Bit Compressed Sensing by Linear Programming (2011) (394)
- The Littlewood-Offord problem and invertibility of random matrices (2007) (390)
- Non-asymptotic theory of random matrices: extreme singular values (2010) (383)
- Smallest singular value of a random rectangular matrix (2008) (349)
- Sampling from large matrices: An approach through geometric functional analysis (2005) (343)
- One sketch for all: fast algorithms for compressed sensing (2007) (310)
- Error correction via linear programming (2005) (301)
- Sparse reconstruction by convex relaxation: Fourier and Gaussian measurements (2006) (274)
- How Close is the Sample Covariance Matrix to the Actual Covariance Matrix? (2010) (261)
- Community detection in sparse networks via Grothendieck’s inequality (2014) (193)
- Geometric approach to error-correcting codes and reconstruction of signals (2005) (191)
- The Generalized Lasso With Non-Linear Observations (2015) (179)
- Algorithmic linear dimension reduction in the l_1 norm for sparse vectors (2006) (160)
- One-bit compressed sensing with non-Gaussian measurements (2012) (140)
- Concentration and regularization of random graphs (2015) (135)
- Dimension Reduction by Random Hyperplane Tessellations (2011) (134)
- High-dimensional estimation with geometric constraints (2014) (131)
- Estimation in High Dimensions: A Geometric Perspective (2014) (126)
- Entropy and the combinatorial dimension (2002) (120)
- Invertibility of symmetric random matrices (2011) (112)
- Covariance estimation for distributions with 2+ε moments (2011) (108)
- Greedy signal recovery review (2008) (101)
- Frames and the Feichtinger conjecture (2004) (93)
- Uncertainty Principles and Vector Quantization (2006) (92)
- Phase Retrieval via Randomized Kaczmarz: Theoretical Guarantees (2017) (85)
- Small Ball Probabilities for Linear Images of High-Dimensional Distributions (2014) (82)
- Beyond Hirsch Conjecture: Walks on Random Polytopes and Smoothed Complexity of the Simplex Method (2006) (80)
- Signal Recovery from Inaccurate and Incomplete Measurements via Regularized Orthogonal Matching Pursuit (2010) (78)
- Spectral norm of products of random and deterministic matrices (2008) (76)
- John's decompositions: Selecting a large part (1999) (71)
- Delocalization of eigenvectors of random matrices with independent entries (2013) (70)
- A simple tool for bounding the deviation of random matrices on geometric sets (2016) (69)
- Information-Theoretic Bounds and Phase Transitions in Clustering, Sparse PCA, and Submatrix Localization (2016) (65)
- The least singular value of a random square matrix is O(n−1/2) (2008) (60)
- A Randomized Solver for Linear Systems with Exponential Convergence (2006) (57)
- Sparse random graphs: regularization and concentration of the Laplacian (2015) (56)
- Small ball probability and Dvoretzky’s Theorem (2004) (56)
- Lectures in Geometric Functional Analysis (2012) (55)
- No-gaps delocalization for general random matrices (2015) (53)
- Combinatorics of random processes and sections of convex bodies (2004) (52)
- The capacity of feedforward neural networks (2019) (43)
- Partial estimation of covariance matrices (2010) (41)
- Invertibility of random matrices: Unitary and orthogonal perturbations (2012) (39)
- Greedy signal recovery and uncertainty principles (2008) (36)
- Concentration inequalities for random tensors (2019) (35)
- Memory Capacity of Neural Networks with Threshold and Rectified Linear Unit Activations (2020) (34)
- Optimization via Low-rank Approximation for Community Detection in Networks (2014) (33)
- Comments on the Randomized Kaczmarz Method (2009) (32)
- The smallest singular value of inhomogeneous square random matrices (2019) (30)
- Online Stochastic Gradient Descent with Arbitrary Initialization Solves Non-smooth, Non-convex Phase Retrieval (2019) (28)
- Frame expansions with erasures: an approach through the non-commutative operator theory (2004) (27)
- Euclidean embeddings in spaces of finite volume ratio via random matrices (2005) (24)
- Four lectures on probabilistic methods for data science (2016) (23)
- Norms of random matrices: local and global problems (2016) (21)
- CONCENTRATION OF RANDOM GRAPHS AND APPLICATION TO COMMUNITY DETECTION (2018) (18)
- Random Euclidean embeddings in spaces of bounded volume ratio (2004) (18)
- Approximating the moments of marginals of high-dimensional distributions (2009) (18)
- Polynomial Threshold Functions, Hyperplane Arrangements, and Random Tensors (2018) (15)
- On the Effective Measure of Dimension in the Analysis Cosparse Model (2014) (14)
- Smoothed analysis of symmetric random matrices with continuous distributions (2012) (14)
- ON LARGE RANDOM ALMOST EUCLIDEAN BASES (2000) (14)
- Signal recovery from incomplete and inaccurate measurements via ROMP (2007) (14)
- On the role of sparsity in Compressed Sensing and random matrix theory (2009) (14)
- Memory capacity of neural networks with threshold and ReLU activations (2020) (13)
- Marchenko–Pastur law with relaxed independence conditions (2019) (13)
- Isoperimetry of waists and local versus global asymptotic convex geometries (2004) (12)
- KADISON-SINGER MEETS BOURGAIN-TZAFRIRI (12)
- On neuronal capacity (2019) (11)
- Information-theoretic bounds and phase transitions in clustering, sparse PCA, and submatrix localization (2017) (11)
- Entropy, Combinatorial Dimensions and Random Averages (2002) (10)
- Random sets of isomorphism of linear operators on Hilbert space (2006) (10)
- Covariance's Loss is Privacy's Gain: Computationally Efficient, Private and Accurate Synthetic Data (2021) (7)
- Polynomial Time and Sample Complexity for Non-Gaussian Component Analysis: Spectral Methods (2017) (7)
- Remarks on the geometry of coordinate projections in ℝn (2003) (7)
- Subsequences of frames (1999) (6)
- On random intersections of two convex bodies. Appendix to: "Isoperimetry of waists and local versus global asymptotic convex geometries" by R.Vershynin (2004) (6)
- Private sampling: a noiseless approach for generating differentially private synthetic data (2021) (5)
- Optimization via Low-rank Approximation, with Applications to Community Detection in Networks (2014) (5)
- Sublinear approximation of signals (2006) (5)
- Boolean polynomial threshold functions and random tensors (2018) (4)
- Privacy of Synthetic Data: A Statistical Framework (2021) (4)
- Some problems in asymptotic convex geometry and random matrices motivated by numerical algorithms (2007) (4)
- Coordinate restrictions of linear operators in $l_2^n$ (2000) (3)
- Concentration of Sums of Independent Random Variables (2018) (3)
- Private measures, random walks, and synthetic data (2022) (3)
- Absolutely representing systems, uniform smoothness and type (1998) (3)
- On constructions of strong and uniformly minimal M-bases in Banach spaces (1998) (3)
- Embedding Levy families into Banach spaces (2002) (3)
- On the effective measure of dimension in total variation minimization (2015) (2)
- Approximation of matrices (2003) (2)
- Integer cells in convex sets (2004) (2)
- A theory of capacity and sparse neural encoding (2021) (2)
- Non-Asymptotic Theory of Random Matrices Lecture (2006) (2)
- Community detection in sparse networks via Grothendieck’s inequality (2015) (1)
- Non-Asymptotic Theory of Random Matrices Lecture 15: Invertibility of Square Gaussian Matrices, Sparse Vectors (2006) (1)
- Random Matrices: Invertibility, Structure, and Applications (2011) (1)
- Signal Recovery with Regularized OMP (2009) (1)
- Covariance loss, Szemeredi regularity, and differential privacy (2023) (1)
- Non-Asymptotic Theory of Random Matrices Lecture 17 : Invertibility of Subgaussian Matrices (2007) (1)
- High Dimensional Probability for Mathematicians and Data Scientists Working draft – not for distribution (2016) (1)
- Algorithmically Effective Differentially Private Synthetic Data (2023) (1)
- Entropy, dimension and the Elton-Pajor Theorem (2002) (1)
- The Quarks of Attention (2022) (1)
- Dimension Reduction by Random Hyperplane Tessellations (2013) (1)
- No-gaps delocalization for general random matrices (2016) (0)
- N A ] 1 1 D ec 2 00 8 GREEDY SIGNAL RECOVERY REVIEW (2018) (0)
- Probabilistic Signal Recovery and Random Matrices (2016) (0)
- Random processes via the combinatorial dimension: introductory notes (2004) (0)
- Algorithm: Regularized Orthogonal Matching Pursuit (ROMP) (2007) (0)
- Non-Asymptotic Theory of Random Matrices Lecture 9 : Applications of Dudley ’ s Inequality : Sharper bounds for random matrices (2002) (0)
- FA ] 3 0 Se p 20 04 Small ball probability and Dvoretzky Theorem (2022) (0)
- AFRL-AFOSR-VA-TR-2016-0369 Probabilistic Signal Recovery and Random Matrices (2016) (0)
- Non-Asymptotic Theory of Random Matrices Lecture 12 : Sudakov ’ s Minoration (2007) (0)
- Non-Asymptotic Theory of Random Matrices Lecture 18: Strong invertibility of subgaussian matrices and Small ball probability via arithmetic progression (2007) (0)
- Preliminaries on Random Variables (2018) (0)
- The selection problem for bases with brackets and for strong M-bases (0)
- Partial estimation of covariance matrices (2011) (0)
- Gafa Geometric and Functional Analysis Embedding Levy Families into Banach Spaces (2002) (0)
- How Close is the Sample Covariance Matrix to the Actual Covariance Matrix? (2011) (0)
- Estimation in High Dimensions : a Geometric (2014) (0)
- Four on probabilistic methods for data science (2016) (0)
- Maximal $ ℓ p n $$\ell_p^n$-Structures in Spaces with Extremal Parameters (2003) (0)
- AVIDA: Alternating method for Visualizing and Integrating Data (2022) (0)
- EMBEDDINGS OF LEVY FAMILIES INTO BANACH SPACES (2001) (0)
- The quarks of attention: Structure and capacity of neural attention building blocks (2023) (0)
- THE SMALLEST SINGULAR VALUE OF INHOMOGENEOUS SQUARE (2021) (0)
- Hints for Exercises (2018) (0)
- 2 2 Ju n 20 03 Remarks on the Geometry of Coordinate Projections in (2004) (0)
- ANALYSIS OF RANDOM MEASUREMENTS COMMENTARY AND BIBLIOGRAPHY FOR THE IPAM SHORT COURSE (2007) (0)
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What Schools Are Affiliated With Roman Vershynin?
Roman Vershynin is affiliated with the following schools:
