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In some significant applications such as data forecasting, the locations of missing entries cannot obey any non-degenerate distributions, questioning the validity of the prevalent assumption that the missing data is randomly chosen…

Information Theory · Computer Science 2019-09-09 Guangcan Liu , Qingshan Liu , Xiao-Tong Yuan , Meng Wang

It is shown that if a probability measure $\nu$ is supported on a closed subset of $(0,\infty)$, that is, its support is bounded away from zero, then the free multiplicative convolution of $\nu$ and the semicircle law is absolutely…

Probability · Mathematics 2015-11-13 Arijit Chakrabarty

In the context of high-dimensional linear regression models, we propose an algorithm of exact support recovery in the setting of noisy compressed sensing where all entries of the design matrix are independent and identically distributed…

Statistics Theory · Mathematics 2019-10-23 Mohamed Ndaoud , Alexandre B. Tsybakov

A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…

Numerical Analysis · Mathematics 2012-12-27 Victor Y. Pan , Guoliang Qian

We prove that independent rectangular random matrices, when embedded in a space of larger square matrices, are asymptotically free with amalgamation over a commutative finite dimensional subalgebra $D$ (under an hypothesis of unitary…

Operator Algebras · Mathematics 2007-05-23 Florent Benaych-Georges

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…

Numerical Analysis · Mathematics 2014-11-04 Holger Rauhut , Reinhold Schneider , Zeljka Stojanac

In this paper we consider memoryless one-bit compressed sensing with randomly subsampled Gaussian circulant matrices. We show that in a small sparsity regime and for small enough accuracy $\delta$, $m\sim \delta^{-4} s\log(N/s\delta)$…

Information Theory · Computer Science 2017-10-11 Sjoerd Dirksen , Hans Christian Jung , Holger Rauhut

We investigate the problem of estimating the unknown degree of sparsity from compressive measurements without the need to carry out a sparse recovery step. While the sparsity order can be directly inferred from the effective rank of the…

Information Theory · Computer Science 2018-08-01 Sebastian Semper , Florian Römer , Thomas Hotz , Giovanni DelGaldo

We present a new method for constructing Hadamard matrices that combines transformer neural networks with local search in the PatternBoost framework. Our approach is designed for extremely sparse combinatorial search problems and is…

Combinatorics · Mathematics 2026-05-12 Geordie Williamson , Oded Yacobi , Paul Zinn-Justin

This paper presents new approaches for finding the determinant and inverse of a matrix. The choice of pivot selection is kept arbitrary and can be made according to the users need. So the ill conditioned matrices can be handled easily. The…

Commutative Algebra · Mathematics 2013-04-26 Hafsa Athar Jafree , Muhammad Imtiaz , Syed Inayatullah , Fozia Hanif Khan , Tajuddin Nizami

We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements. While the theoretical understanding of low rank…

Information Theory · Computer Science 2016-02-18 Holger Rauhut , Reinhold Schneider , Zeljka Stojanac

The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques.…

Signal Processing · Electrical Eng. & Systems 2023-12-29 Kartheek Kumar Reddy Nareddy , Abijith Jagannath Kamath , Chandra Sekhar Seelamantula

Let o be a 4k-length column vector whose all entries are 1s, with k a positive integer. Let V={v_i} be a set of semi-normalized Hadamard (SH)-vectors, which are 4k-length vectors whose 2k entries are -1s and the remaining 2k are 1s. We…

Discrete Mathematics · Computer Science 2016-07-01 Andriyan B. Suksmono

We study the problem of solving a linear sensing system when the observations are unlabeled. Specifically we seek a solution to a linear system of equations y = Ax when the order of the observations in the vector y is unknown. Focusing on…

Information Theory · Computer Science 2015-12-02 Jayakrishnan Unnikrishnan , Saeid Haghighatshoar , Martin Vetterli

We propose a new paradigm for designing efficient p-adaptive arbitrary high order methods. We consider arbitrary high order iterative schemes that gain one order of accuracy at each iteration and we modify them in order to match the…

Numerical Analysis · Mathematics 2023-11-09 Lorenzo Micalizzi , Davide Torlo , Walter Boscheri

Matrices satisfying the Restricted Isometry Property (RIP) play an important role in the areas of compressed sensing and statistical learning. RIP matrices with optimal parameters are mainly obtained via probabilistic arguments, as explicit…

Machine Learning · Computer Science 2019-11-01 Shiva Prasad Kasiviswanathan , Mark Rudelson

In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…

Combinatorics · Mathematics 2021-10-15 Bingchen Qian , Xin Wang , Gennian Ge

We consider the problem of recovering an unknown low-rank matrix X with (possibly) non-orthogonal, effectively sparse rank-1 decomposition from measurements y gathered in a linear measurement process A. We propose a variational formulation…

Information Theory · Computer Science 2023-06-13 Johannes Maly

Products of random transfer matrices are applied to low dimensional disordered systems to evaluate numerically extensive quantities such as entropy and overlap probability distribution. The main advantage is the possibility to avoid…

Condensed Matter · Physics 2009-10-22 A Crisanti , G Paladin , M Serva , A Vulpiani

We define a stochastic variant of the proximal point algorithm in the general setting of nonlinear (separable) Hadamard spaces for approximating zeros of the mean of a stochastically perturbed monotone vector field and prove its convergence…

Optimization and Control · Mathematics 2025-10-14 Nicholas Pischke