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Compressed sensing and its extensions have recently triggered interest in randomized signal acquisition. A key finding is that random measurements provide sparse signal reconstruction guarantees for efficient and stable algorithms with a…

Information Theory · Computer Science 2014-07-08 Felix Krahmer , Holger Rauhut

We investigate one of the simplest multispecies generalization of the asymmetric simple exclusion process on a ring. This process has a rich combinatorial spectral structure and a matrix product form for the stationary state. In the totally…

Statistical Mechanics · Physics 2012-08-22 Chikashi Arita , Arvind Ayyer , Kirone Mallick , Sylvain Prolhac

We study the problem of finding structured low-rank matrices using nuclear norm regularization where the structure is encoded by a linear map. In contrast to most known approaches for linearly structured rank minimization, we do not (a) use…

Systems and Control · Computer Science 2015-09-09 Adams Wei Yu , Wanli Ma , Yaoliang Yu , Jaime G. Carbonell , Suvrit Sra

This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…

Statistics Theory · Mathematics 2021-02-08 Rungang Han , Rebecca Willett , Anru R. Zhang

We provide a computational framework for approximating a class of structured matrices; here, the term structure is very general, and may refer to a regular sparsity pattern (e.g., block-banded), or be more highly structured (e.g., symmetric…

Numerical Analysis · Mathematics 2021-05-05 Misha E. Kilmer , Arvind K. Saibaba

Matrix-valued optimization tasks, including those involving symmetric positive definite (SPD) matrices, arise in a wide range of applications in machine learning, data science and statistics. Classically, such problems are solved via…

Optimization and Control · Mathematics 2024-10-15 Andrew Cheng , Melanie Weber

This paper studies the problem of accurately recovering a structured signal from a small number of corrupted sub-Gaussian measurements. We consider three different procedures to reconstruct signal and corruption when different kinds of…

Information Theory · Computer Science 2017-05-23 Jinchi Chen , Yulong Liu

We consider a structured estimation problem where an observed matrix is assumed to be generated as an $s$-sparse linear combination of $N$ given $n\times n$ positive-semidefinite matrices. Recovering the unknown $N$-dimensional and…

Information Theory · Computer Science 2020-03-27 Fabian Jaensch , Peter Jung

This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix…

Statistics Theory · Mathematics 2020-07-27 T. Tony Cai , Tengyuan Liang , Alexander Rakhlin

This paper investigates efficient deep neural networks (DNNs) to replace dense unstructured weight matrices with structured ones that possess desired properties. The challenge arises because the optimal weight matrix structure in popular…

Machine Learning · Computer Science 2024-03-11 Changwoo Lee , Hun-Seok Kim

Matrix recovery from sparse observations is an extensively studied topic emerging in various applications, such as recommendation system and signal processing, which includes the matrix completion and compressed sensing models as special…

Methodology · Statistics 2026-04-13 Ziyuan Chen , Ying Yang , Fang Yao

We give unique recovery guarantees for matrices of bounded rank that have undergone permutations of their entries. We even do this for a more general matrix structure that we call ladder matrices. We use methods and results of commutative…

Information Theory · Computer Science 2022-07-25 Manolis C. Tsakiris

Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can…

Machine Learning · Computer Science 2014-09-04 Fanhua Shang , Yuanyuan Liu , Hanghang Tong , James Cheng , Hong Cheng

We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…

Instrumentation and Methods for Astrophysics · Physics 2016-05-25 Nikhil Padmanabhan , Martin White , Harrison H. Zhou , Ross O'Connell

The problem of structured matrix estimation has been studied mostly under strong noise dependence assumptions. This paper considers a general framework of noisy low-rank-plus-sparse matrix recovery, where the noise matrix may come from any…

Machine Learning · Statistics 2025-04-07 Jinhang Chai , Jianqing Fan

We propose a theory for matrix completion that goes beyond the low-rank structure commonly considered in the literature and applies to general matrices of low description complexity. Specifically, complexity of the sets of matrices…

Information Theory · Computer Science 2024-10-03 Erwin Riegler , Günther Koliander , David Stotz , Helmut Bölcskei

This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…

Statistics Theory · Mathematics 2016-07-05 Olga Klopp , Karim Lounici , Alexandre B. Tsybakov

We consider the matrix completion problem of recovering a structured low rank matrix with partially observed entries with mixed data types. Vast majority of the solutions have proposed computationally feasible estimators with strong…

Machine Learning · Statistics 2020-05-27 Daqian Sun , Martin T. Wells

Estimation of a high dimensional precision matrix is a critical problem to many areas of statistics including Gaussian graphical models and inference on high dimensional data. Working under the structural assumption of sparsity, we propose…

Methodology · Statistics 2020-12-17 Adam B Kashlak

In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected…

Applications · Statistics 2013-10-14 Fang Han , Han Liu , Brian Caffo