Related papers: Sparse Bayesian Methods for Low-Rank Matrix Estima…

Low-rank matrix regression is a fundamental problem in data science with various applications in systems and control. Nuclear norm regularization has been widely applied to solve this problem due to its convexity. However, it suffers from…

Low-rank matrix factorizations arise in a wide variety of applications -- including recommendation systems, topic models, and source separation, to name just a few. In these and many other applications, it has been widely noted that by…

The topic of recovery of a structured model given a small number of linear observations has been well-studied in recent years. Examples include recovering sparse or group-sparse vectors, low-rank matrices, and the sum of sparse and low-rank…

In this paper, we investigate the recovery of a sparse weight vector (parameters vector) from a set of noisy linear combinations. However, only partial information about the matrix representing the linear combinations is available. Assuming…

Wisely utilizing the internal and external learning methods is a new challenge in super-resolution problem. To address this issue, we analyze the attributes of two methodologies and find two observations of their recovered details: 1) they…

Square matrices appear in many machine learning problems and models. Optimization over a large square matrix is expensive in memory and in time. Therefore an economic approximation is needed. Conventional approximation approaches factorize…

The task of reconstructing a low rank matrix from incomplete linear measurements arises in areas such as machine learning, quantum state tomography and in the phase retrieval problem. In this note, we study the particular setup that the…

We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices. A salient feature of the proposed factorization scheme is it decouples the…

We study the problem of estimating a low-rank positive semidefinite (PSD) matrix from a set of rank-one measurements using sensing vectors composed of i.i.d. standard Gaussian entries, which are possibly corrupted by arbitrary outliers.…

We examine the recovery of block sparse signals and extend the framework in two important directions; one by exploiting signals' intra-block correlation and the other by generalizing signals' block structure. We propose two families of…

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…

We investigate the methods that simultaneously enforce sparsity and low-rank structure in a matrix as often employed for sparse phase retrieval problems or phase calibration problems in compressive sensing. We propose a new approach for…

This paper begins with considering the identification of sparse linear time-invariant networks described by multivariable ARX models. Such models possess relatively simple structure thus used as a benchmark to promote further research. With…

The problem of low-rank matrix estimation recently received a lot of attention due to challenging applications. A lot of work has been done on rank-penalized methods and convex relaxation, both on the theoretical and applied sides. However,…

Large language models (LLMs) have shown impressive capabilities across various tasks. However, training LLMs from scratch requires significant computational power and extensive memory capacity. Recent studies have explored low-rank…

Standard regularization methods that are used to compute solutions to ill-posed inverse problems require knowledge of the forward model. In many real-life applications, the forward model is not known, but training data is readily available.…

In this paper, we consider the challenge of reconstructing jointly sparse vectors from linear measurements. Firstly, we show that by utilizing the rank of the output data matrix we can reduce the problem to a full column rank case. This…

Matrix completion aims to recover an unknown low-rank matrix from a small subset of its entries. In many applications, the rank of the unknown target matrix is known in advance. In this paper, first we revisit a recently proposed rank-based…

Sparse reduced rank regression is an essential statistical learning method. In the contemporary literature, estimation is typically formulated as a nonconvex optimization that often yields to a local optimum in numerical computation. Yet,…

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…