A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Filters
A Short Note on Concentration Inequalities for Random Vectors with SubGaussian Norm
[article]
2019
arXiv
pre-print
Preserved Fulltext
In this note, we derive concentration inequalities for random vectors with subGaussian norm (a generalization of both subGaussian random vectors and norm bounded random vectors), which are tight up to ...
Acknowledgements We thank Gabor Lugosi and Nilesh Tripuraneni for helpful discussions.
References Joel A Tropp. User-friendly tail bounds for sums of random matrices. ...
Introduction to the non-asymptotic analysis of random matrices. arXiv preprint arXiv:1011.3027, 2010. ...
arXiv:1902.03736v1
fatcat:zday7mbfrvdvppxgqlyvr3ungm
On the concentration of subgaussian vectors and positive quadratic forms in Hilbert spaces
[article]
2023
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2023; you can also visit the original URL.
The file type is application/pdf.
Note that this fulltext copy is not of the "primary" version of this work. The version it corresponds to is:
2023 pre-print arXiv:2306.11404v1 fatcat:fj3fxpvkobcshchrqnwymqamue
In these notes, we investigate the tail behaviour of the norm of subgaussian vectors in a Hilbert space. ...
This leads to useful extensions and analogues of known Hoeffding-type inequalities and deviation bounds for positive random quadratic forms. ...
The authors wish to thank Vladimir Spokoiny for dicussions of the finite-dimensional case. ...
arXiv:2306.11404v2
fatcat:heplppsdkrafbditcluhlvlkgu
Restricted Isometry Property under High Correlations
[article]
2019
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
models (including, subgaussian, sparse, low-randomness, satisfying convex concentration property), satisfies the RIP with high probability. ...
In this paper, we construct a new broad ensemble of random matrices with dependent entries that satisfy the restricted isometry property. ...
A simple corollary of Hanson-Wright inequality from Theorem 2.1 is a concentration inequality for random vectors with independent subgaussian components. ...
arXiv:1904.05510v2
fatcat:5aq6nxdku5etnffvnvhbtugyx4
Nonuniform Sparse Recovery with Subgaussian Matrices
[article]
2011
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Other Versions
In this note we focus on nonuniform recovery using Gaussian random matrices and ℓ_1-minimization. ...
We provide a condition on the number of samples in terms of the sparsity and the signal length which guarantees that a fixed sparse signal can be recovered with a random draw of the matrix using ℓ_1-minimization ...
Indeed, the proof of Lemma E.2 is taken from a book draft that the second author is currently preparing with him. ...
arXiv:1007.2354v2
fatcat:jxqma7jukrahxgvriuvcjlbv4y
Some problems in asymptotic convex geometry and random matrices motivated by numerical algorithms
[article]
2007
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
We discuss some conjectures and known results in two related directions -- computing the size of projections of high dimensional polytopes and estimating the norms of random matrices and their inverses ...
Combining with the concentration of measure inequality, one deduces a deviation bound [7] : for every t > 0, with probability at least 1 − 2e −t 2 /2 one has (2.1) √ n − √ d − t ≤ λ min (A) ≤ λ max (A ...
Invertibility of random matrices For a one-to-one linear operator A : X → Y between two normed spaces X and Y , two quantities are central in functional analysis: the norm A and the norm of the inverse ...
arXiv:cs/0703093v1
fatcat:t2gw3yqgh5c7xplnam6dsp3rfe
Recent developments in non-asymptotic theory of random matrices
[article]
2013
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Other Versions
Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. ...
In these notes we survey some recent results in this area and describe the techniques aimed for obtaining explicit probability bounds. ...
Then Theorem 8.2 implies that, with high probability, the short Khinchin inequality holds for N independent subgaussian vectors with constant α 1 = cδ 2 . ...
arXiv:1301.2382v2
fatcat:7d62akzovfeuhcyhruiiezly2a
Non-asymptotic Theory of Random Matrices: Extreme Singular Values
2011
Proceedings of the International Congress of Mathematicians 2010 (ICM 2010)
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2016; you can also visit the original URL.
The file type is application/pdf.
We focus on recently developed geometric methods for estimating the hard edge of random matrices (the smallest singular value). ...
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. ...
The short Khinchin inequality shows also that the 1 and 2 norms are equivalent on a random subspace E := AR n ⊂ R N . ...
doi:10.1142/9789814324359_0111
fatcat:65juoo23ezapvhwt6grj33c3wy
Statistical analysis of latent generalized correlation matrix estimation in transelliptical distribution
2017
Bernoulli
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
With regard to the restricted spectral norm, we for the first time present a "sign sub-Gaussian condition" which is sufficient to guarantee that the rank-based correlation matrix estimator attains the ...
With regard to the spectral norm, we highlight the role of "effective rank" in quantifying the rate of convergence. ...
This implies that Let β > 0 be a constant defined as We have Han and Liu Page 30
Acknowledgments We sincerely thank Marten Wegkamp for his very helpful discussions and generously providing independent ...
doi:10.3150/15-bej702
pmid:28337068
pmcid:PMC5360110
fatcat:x7qj6rtqt5d2lb5jvbobkbdir4
Non-asymptotic theory of random matrices: extreme singular values
[article]
2010
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Other Versions
We focus on recently developed geometric methods for estimating the hard edge of random matrices (the smallest singular value). ...
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. ...
The short Khinchin inequality shows also that the ℓ 1 and ℓ 2 norms are equivalent on a random subspace E := AR n ⊂ R N . ...
arXiv:1003.2990v2
fatcat:khsvm4ulvrci7lg7atpzj72fjm
Hanson-Wright inequality and sub-gaussian concentration
[article]
2013
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Other Versions
We deduce a useful concentration inequality for sub-gaussian random vectors. ...
Two examples are given to illustrate these results: a concentration of distances between random vectors and subspaces, and a bound on the norms of products of random and deterministic matrices. ...
Sub-gaussian concentration Hanson-Wright inequality has a useful consequence, a concentration inequality for random vectors with independent sub-gaussian coordinates. ...
arXiv:1306.2872v3
fatcat:4uxz6wcdgbcizhqmyldqhcuq2a
Hanson-Wright inequality and sub-gaussian concentration
2013
Electronic Communications in Probability
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2015; you can also visit the original URL.
The file type is application/pdf.
We deduce a useful concentration inequality for sub-gaussian random vectors. ...
Two examples are given to illustrate these results: a concentration of distances between random vectors and subspaces, and a bound on the norms of products of random and deterministic matrices. ...
Sub-gaussian concentration Hanson-Wright inequality has a useful consequence, a concentration inequality for random vectors with independent sub-gaussian coordinates. ...
doi:10.1214/ecp.v18-2865
fatcat:4gvq62wfovhijlc3b346geaa5y
From Poincaré Inequalities to Nonlinear Matrix Concentration
[article]
2021
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
Other Versions
This paper deduces exponential matrix concentration from a Poincar\'e inequality via a short, conceptual argument. ...
The proof relies on the subadditivity of Poincar\'e inequalities and a chain rule inequality for the trace of the matrix Dirichlet form. ...
I Matrix concentration inequalities describe the probability that a random matrix is close to its expected value, with deviations measured by the ℓ 2 operator norm. ...
arXiv:2006.16561v2
fatcat:ibhkfe6vs5ditnmptr4syeyd5i
Optimal non-gaussian Dvoretzky-Milman embeddings
[article]
2023
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2024; you can also visit the original URL.
The file type is application/pdf.
We construct the first non-gaussian ensemble that yields the optimal estimate in the Dvoretzky-Milman Theorem: the ensemble exhibits almost Euclidean sections in arbitrary normed spaces of the same dimension ...
Acknowledgements: The first author is grateful for financial support through the Austrian Science Fund (FWF) projects ESP-31N and P34743N. ...
A centred random vector X in R d satisfies L p − L 2 norm equivalence with constant constant L if for any u ∈ R d , X, u Lp ≤ L X, u L 2 . (1.2) Note that if, in addition, X is isotropic (that is, X is ...
arXiv:2309.12069v1
fatcat:skhss4qvhbf5dhiu7uymn5zvgu
Convex recovery of a structured signal from independent random linear measurements
[article]
2014
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Note that this fulltext copy is not of the "primary" version of this work. The version it corresponds to is:
2014 pre-print arXiv:1405.1102v2 fatcat:y4v4vf47mndmpbqygmn5pl3fmqOther Versions
To demonstrate the power of this approach, the paper presents a short analysis of phase retrieval by trace-norm minimization. ...
This chapter develops a theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. ...
ACKNOWLEDGMENTS JAT gratefully acknowledges support from ONR award N00014-11-1002, AFOSR award FA9550-09-1-0643, and a Sloan Research Fellowship. Thanks are also due to the Moore Foundation. ...
arXiv:1405.1102v3
fatcat:lzfxtp33evb7vfiakffv7bjdoi
Convex Recovery of a Structured Signal from Independent Random Linear Measurements
[chapter]
2015
Sampling Theory, a Renaissance
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2015; you can also visit the original URL.
The file type is application/pdf.
To demonstrate the power of this approach, the paper presents a short analysis of phase retrieval by trace-norm minimization. ...
This chapter develops a theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. ...
ACKNOWLEDGMENTS JAT gratefully acknowledges support from ONR award N00014-11-1002, AFOSR award FA9550-09-1-0643, and a Sloan Research Fellowship. Thanks are also due to the Moore Foundation. ...
doi:10.1007/978-3-319-19749-4_2
fatcat:b5awmja4e5dgpetkcin6u342em
« Previous
Showing results 1 — 15 out of 655 results