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Leverage scores, loosely speaking, reflect the importance of the rows and columns of a matrix. Ideally, given the leverage scores of a rank-$r$ matrix $M\in\mathbb{R}^{n\times n}$, that matrix can be reliably completed from just…

Information Theory · Computer Science 2017-11-21 Armin Eftekhari , Michael B. Wakin , Rachel A. Ward

This paper considers the matrix completion problem. We show that it is not necessary to assume joint incoherence, which is a standard but unintuitive and restrictive condition that is imposed by previous studies. This leads to a sample…

Information Theory · Computer Science 2016-11-15 Yudong Chen

Randomized iterative algorithms have attracted much attention in recent years because they can approximately solve large-scale linear systems of equations without accessing the entire coefficient matrix. In this paper, we propose two novel…

Numerical Analysis · Mathematics 2021-10-22 Kui Du , Xiao-Hui Sun

This paper presents a two-stage online algorithm for recovery of low-rank parameter matrix in non-stationary stochastic systems. The first stage applies the recursive least squares (RLS) estimator combined with its singular value…

Systems and Control · Electrical Eng. & Systems 2025-06-25 Yanxin Fu , Junbao Zhou , Yu Hu , Wenxiao Zhao

In this paper, we investigate the following question: How often is a random matrix normal? We consider a random $n\times n$ matrix, $M_n$, whose entries are i.i.d. Rademacher random variables (taking values $\{ \pm1 \}$ with probability…

Probability · Mathematics 2019-02-06 Andrei Deneanu , Van Vu

Low rank matrix recovery problems, including matrix completion and matrix sensing, appear in a broad range of applications. In this work we present GNMR -- an extremely simple iterative algorithm for low rank matrix recovery, based on a…

Optimization and Control · Mathematics 2022-04-28 Pini Zilber , Boaz Nadler

The McCarty Conjecture states that any McCarty Matrix (an $n\times n$ matrix $A$ with positive integer entries and each of the $2n$ row and column sums equal to $n$), can be additively decomposed into two other matrices, $B$ and $C$, such…

Combinatorics · Mathematics 2025-05-08 Anant Godbole , Lybitina Koene , Grant Shirley

In this paper we establish the connection between the Orthogonal Optical Codes (OOC) and binary compressed sensing matrices. We also introduce deterministic bipolar $m\times n$ RIP fulfilling $\pm 1$ matrices of order $k$ such that…

Information Theory · Computer Science 2015-03-13 Arash Amini , Farokh Marvasti

We consider the computation of the permanent of a binary n by n matrix. It is well- known that the exact computation is a #P complete problem. A variety of Markov chain Monte Carlo (MCMC) computational algorithms have been introduced in the…

Computation · Statistics 2013-05-30 Ajay Jasra , Junshan Wang

Maximizing monotone submodular functions under a matroid constraint is a classic algorithmic problem with multiple applications in data mining and machine learning. We study this classic problem in the fully dynamic setting, where elements…

Data Structures and Algorithms · Computer Science 2025-05-26 Paul Dütting , Federico Fusco , Silvio Lattanzi , Ashkan Norouzi-Fard , Morteza Zadimoghaddam

A binary contingency table is an m x n array of binary entries with prescribed row sums r=(r_1,...,r_m) and column sums c=(c_1,...,c_n). The configuration model for uniformly sampling binary contingency tables proceeds as follows. First,…

Probability · Mathematics 2011-10-13 Jose Blanchet , Alexandre Stauffer

Integer programs (IPs) on constraint matrices with bounded subdeterminants are conjectured to be solvable in polynomial time. We give a strongly polynomial time algorithm to solve IPs where the constraint matrix has bounded subdeterminants…

Data Structures and Algorithms · Computer Science 2025-03-19 Stefan Kober

We find a searching method on ordered lists that surprisingly outperforms binary searching with respect to average query complexity while retaining minmax optimality. The method is shown to require $O(\log_2\log_2 n)$ queries on average…

Data Structures and Algorithms · Computer Science 2021-05-26 I. F. D. Oliveira , R. H. C. Takahashi

We call a matrix completely mixable if the entries in its columns can be permuted so that all row sums are equal. If it is not completely mixable, we want to determine the smallest maximal and largest minimal row sum attainable. These…

Optimization and Control · Mathematics 2015-01-06 Utz-Uwe Haus

Bernstein polynomials, long a staple of approximation theory and computational geometry, have also increasingly become of interest in finite element methods. Many fundamental problems in interpolation and approximation give rise to…

Numerical Analysis · Mathematics 2019-07-15 Larray Allen , Robert C. Kirby

For obtaining optimal first-order convergence guarantee for stochastic optimization, it is necessary to use a recurrent data sampling algorithm that samples every data point with sufficient frequency. Most commonly used data sampling…

Optimization and Control · Mathematics 2024-07-23 William G. Powell , Hanbaek Lyu

We present a simple solution to a question posed by Candes, Romberg and Tao on the uniform uncertainty principle for Bernoulli random matrices. More precisely, we show that a rectangular k*n random subgaussian matrix (with k < n) has the…

Statistics Theory · Mathematics 2007-06-13 Shahar Mendelson , Alain Pajor , Nicole Tomczak-Jaegermann

Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is…

Machine Learning · Statistics 2015-12-31 Ravi Ganti , Laura Balzano , Rebecca Willett

The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image…

Statistics Theory · Mathematics 2014-12-20 Jean Lafond , Olga Klopp , Eric Moulines , Jospeh Salmon

Various types of recovery algorithms for batch codes have been investigated, such as asynchronous recovery or recovery as afforded by batch codes obtained from Almost Affinely Disjoint (AAD) families. In this paper, we offer the first…

Information Theory · Computer Science 2026-05-12 Baran Düzgün , Henk D. L. Hollmann , Ago-Erik Riet , Vitaly Skachek , Vladislav Taranchuk