Related papers: Estimation of matrices with row sparsity
We consider the problem of estimating an unknown $n_1 \times n_2$ matrix $\mathbf{\theta^*}$ from noisy observations under the constraint that $\mathbf{\theta}^*$ is nondecreasing in both rows and columns. We consider the least squares…
We consider the problem of recovering a matrix from its action on a known vector in the setting where the matrix can be represented efficiently in a known matrix dictionary. Connections with sparse signal recovery allows for the use of…
We study the problem of approximating a matrix $\mathbf{A}$ with a matrix that has a fixed sparsity pattern (e.g., diagonal, banded, etc.), when $\mathbf{A}$ is accessed only by matrix-vector products. We describe a simple randomized…
Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…
We derive a sufficient condition for a sparse random matrix with given numbers of non-zero entries in the rows and columns having full row rank. The result covers both matrices over finite fields with independent non-zero entries and…
Bayesian methods for low-rank matrix completion with noise have been shown to be very efficient computationally. While the behaviour of penalized minimization methods is well understood both from the theoretical and computational points of…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a…
In this paper, we consider a well-known sparse optimization problem that aims to find a sparse solution of a possibly noisy underdetermined system of linear equations. Mathematically, it can be modeled in a unified manner by minimizing…
Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…
This paper considers sparse spiked covariance matrix models in the high-dimensional setting and studies the minimax estimation of the covariance matrix and the principal subspace as well as the minimax rank detection. The optimal rate of…
This work deals with the generation of theoretical correlation matrices with specific sparsity patterns, associated to graph structures. We present a novel approach based on convex optimization, offering greater flexibility compared to…
In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define…
This note studies a method for the efficient estimation of a finite number of unknown parameters from linear equations, which are perturbed by Gaussian noise. In case the unknown parameters have only few nonzero entries, the proposed…
We introduce a two step algorithm with theoretical guarantees to recover a jointly sparse and low-rank matrix from undersampled measurements of its columns. The algorithm first estimates the row subspace of the matrix using a set of common…
The Multi-Reference Alignment (MRA) problem aims at the recovery of an unknown signal from repeated observations under the latent action of a group of cyclic isometries, in the presence of additive noise of high intensity $\sigma$. It is a…
The paper introduces a penalized matrix estimation procedure aiming at solutions which are sparse and low-rank at the same time. Such structures arise in the context of social networks or protein interactions where underlying graphs have…
The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the…
We consider designing a robust structured sparse sensing matrix consisting of a sparse matrix with a few non-zero entries per row and a dense base matrix for capturing signals efficiently We design the robust structured sparse sensing…
We revisit the probabilistic construction of sparse random matrices where each column has a fixed number of nonzeros whose row indices are drawn uniformly at random with replacement. These matrices have a one-to-one correspondence with the…
The estimation of a precision matrix is a crucial problem in various research fields, particularly when working with high dimensional data. In such settings, the most common approach is to use the penalized maximum likelihood. The…