Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors
Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional
random vectors Page 1 The Annals of Statistics 2013, Vol. 41, No. 6, 2786–2819 DOI …
random vectors Page 1 The Annals of Statistics 2013, Vol. 41, No. 6, 2786–2819 DOI …
[图书][B] Lectures on modern convex optimization: analysis, algorithms, and engineering applications
A Ben-Tal, A Nemirovski - 2001 - SIAM
To make decisions optimally is a basic human desire. Whenever the situation and the
objectives can be described quantitatively, this desire can be satisfied, to some extent, by …
objectives can be described quantitatively, this desire can be satisfied, to some extent, by …
Sparse modeling for image and vision processing
In recent years, a large amount of multi-disciplinary research has been conducted on sparse
models and their applications. In statistics and machine learning, the sparsity principle is …
models and their applications. In statistics and machine learning, the sparsity principle is …
The computational complexity of the restricted isometry property, the nullspace property, and related concepts in compressed sensing
AM Tillmann, ME Pfetsch - IEEE Transactions on Information …, 2013 - ieeexplore.ieee.org
This paper deals with the computational complexity of conditions which guarantee that the
NP-hard problem of finding the sparsest solution to an underdetermined linear system can …
NP-hard problem of finding the sparsest solution to an underdetermined linear system can …
A weighted ℓ1-minimization approach for sparse polynomial chaos expansions
This work proposes a method for sparse polynomial chaos (PC) approximation of high-
dimensional stochastic functions based on non-adapted random sampling. We modify the …
dimensional stochastic functions based on non-adapted random sampling. We modify the …
Self-concordant analysis for logistic regression
F Bach - 2010 - projecteuclid.org
Most of the non-asymptotic theoretical work in regression is carried out for the square loss,
where estimators can be obtained through closed-form expressions. In this paper, we use …
where estimators can be obtained through closed-form expressions. In this paper, we use …
The sparsest solutions to Z-tensor complementarity problems
Z Luo, L Qi, N Xiu - Optimization letters, 2017 - Springer
Finding the sparsest solutions to a tensor complementarity problem is generally NP-hard
due to the nonconvexity and noncontinuity of the involved ℓ _0 ℓ 0 norm. In this paper, a …
due to the nonconvexity and noncontinuity of the involved ℓ _0 ℓ 0 norm. In this paper, a …
An Unconstrained Minimization with for Sparse Solution of Underdetermined Linear Systems
MJ Lai, J Wang - SIAM Journal on Optimization, 2011 - SIAM
We study an unconstrained version of the \ell_q minimization for the sparse solution of
underdetermined linear systems for 0<q\leq1. Although the minimization is nonconvex when …
underdetermined linear systems for 0<q\leq1. Although the minimization is nonconvex when …
Analysis and generalizations of the linearized Bregman method
W Yin - SIAM Journal on Imaging Sciences, 2010 - SIAM
This paper analyzes and improves the linearized Bregman method for solving the basis
pursuit and related sparse optimization problems. The analysis shows that the linearized …
pursuit and related sparse optimization problems. The analysis shows that the linearized …
Various thresholds for -optimization in compressed sensing
M Stojnic - arXiv preprint arXiv:0907.3666, 2009 - arxiv.org
Recently,\cite {CRT, DonohoPol} theoretically analyzed the success of a polynomial $\ell_1
$-optimization algorithm in solving an under-determined system of linear equations. In a …
$-optimization algorithm in solving an under-determined system of linear equations. In a …