Related papers: Rank Minimization over Finite Fields: Fundamental …
Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…
We develop a framework that we call compressive rate estimation. We assume that the composite channel gain matrix (i.e. the matrix of all channel gains between all network nodes) is compressible which means it can be approximated by a…
This paper studies the inference about linear functionals of high-dimensional low-rank matrices. While most existing inference methods would require consistent estimation of the true rank, our procedure is robust to rank misspecification,…
We study lower bounds on adaptive sensing algorithms for recovering low rank matrices using linear measurements. Given an $n \times n$ matrix $A$, a general linear measurement $S(A)$, for an $n \times n$ matrix $S$, is just the inner…
Linear constraints for a matrix polytope with no fractional vertex are investigated as intersecting research among permutation codes, rank modulations, and linear programming methods. By focusing the discussion to the block structure of…
We consider the synthesis problem of Compressed Sensing - given s and an MXn matrix A, extract from it an mXn submatrix A', certified to be s-good, with m as small as possible. Starting from the verifiable sufficient conditions of…
Low-rank matrix completion (LRMC) problems arise in a wide variety of applications. Previous theory mainly provides conditions for completion under missing-at-random samplings. This paper studies deterministic conditions for completion. An…
The essence of distantly supervised relation extraction is that it is an incomplete multi-label classification problem with sparse and noisy features. To tackle the sparsity and noise challenges, we propose solving the classification…
As distributed systems increase in size, the need for scalable algorithms becomes more and more important. We argue that in the context of system identification, an essential building block of any scalable algorithm is the ability to…
Compared with classical block codes, efficient list decoding of rank-metric codes seems more difficult. Although the list decodability of random rank-metric codes and limits to list decodability have been completely determined, little work…
We formulate general conditions necessary for a linear-response detector to reach the quantum limit of measurement efficiency, where the measurement-induced dephasing rate takes on its minimum possible value. These conditions are applicable…
Density matrices are positively semi-definite Hermitian matrices with unit trace that describe the states of quantum systems. Many quantum systems of physical interest can be represented as high-dimensional low rank density matrices. A…
We study properties of rank metric and codes in rank metric over finite fields. We show that in rank metric perfect codes do not exist. We derive an existence bound that is the equivalent of the Gilbert--Varshamov bound in Hamming metric.…
Structural matrix-variate observations routinely arise in diverse fields such as multi-layer network analysis and brain image clustering. While data of this type have been extensively investigated with fruitful outcomes being delivered, the…
Random linear codes are a workhorse in coding theory, and are used to show the existence of codes with the best known or even near-optimal trade-offs in many noise models. However, they have little structure besides linearity, and are not…
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…
We propose a general framework for reconstructing and denoising single entries of incomplete and noisy entries. We describe: effective algorithms for deciding if and entry can be reconstructed and, if so, for reconstructing and denoising…
In this paper, we consider signals with a low-rank covariance matrix which reside in a low-dimensional subspace and can be written in terms of a finite (small) number of parameters. Although such signals do not necessarily have a sparse…
We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex…
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…