Related papers: On the computational and statistical complexity of…
The knowledge of end-to-end network distances is essential to many Internet applications. As active probing of all pairwise distances is infeasible in large-scale networks, a natural idea is to measure a few pairs and to predict the other…
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…
We consider covariance estimation under Toeplitz structure. Numerous sophisticated optimization methods have been developed to maximize the Gaussian log-likelihood under Toeplitz constraints. In contrast, recent advances in deep learning…
Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample…
Matrix sensing has many real-world applications in science and engineering, such as system control, distance embedding, and computer vision. The goal of matrix sensing is to recover a matrix $A_\star \in \mathbb{R}^{n \times n}$, based on a…
Similarity matrix serves as a fundamental tool at the core of numerous downstream machine-learning tasks. However, missing data is inevitable and often results in an inaccurate similarity matrix. To address this issue, Similarity Matrix…
Cost-efficient compressive sensing is challenging when facing large-scale data, {\em i.e.}, data with large sizes. Conventional compressive sensing methods for large-scale data will suffer from low computational efficiency and massive…
A classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is known to provide the best such approximation for any…
One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…
We investigate a general matrix factorization for deviance-based data losses, extending the ubiquitous singular value decomposition beyond squared error loss. While similar approaches have been explored before, our method leverages…
We present a novel recursive algorithm for reducing a symmetric matrix to a triangular factorization which reveals the rank profile matrix. That is, the algorithm computes a factorization $\mathbf{P}^T\mathbf{A}\mathbf{P} =…
We study the asymmetric low-rank factorization problem: \[\min_{\mathbf{U} \in \mathbb{R}^{m \times d}, \mathbf{V} \in \mathbb{R}^{n \times d}} \frac{1}{2}\|\mathbf{U}\mathbf{V}^\top -\mathbf{\Sigma}\|_F^2\] where $\mathbf{\Sigma}$ is a…
We address the problem of robot localization using ground penetrating radar (GPR) sensors. Current approaches for localization with GPR sensors require a priori maps of the system's environment as well as access to approximate global…
The low-rank matrix completion problem asks whether a given real matrix with missing values can be completed so that the resulting matrix has low rank or is close to a low-rank matrix. The completed matrix is often required to satisfy…
Standard rank-revealing factorizations such as the singular value decomposition and column pivoted QR factorization are challenging to implement efficiently on a GPU. A major difficulty in this regard is the inability of standard algorithms…
This article is an extended version of previous work of the authors [40, 41] on low-rank matrix estimation in the presence of constraints on the factors into which the matrix is factorized. Low-rank matrix factorization is one of the basic…
Matrix sensing is a problem in signal processing and machine learning that involves recovering a low-rank matrix from a set of linear measurements. The goal is to reconstruct the original matrix as accurately as possible, given only a set…
In this work, we develop and analyze a Gradient Descent (GD) based solution, called Alternating GD and Minimization (AltGDmin), for efficiently solving the low rank matrix completion (LRMC) in a federated setting. LRMC involves recovering…
We propose a flexible and theoretically supported framework for scalable nonnegative matrix factorization. The goal is to find nonnegative low-rank components directly from compressed measurements, accessing the original data only once or…
Factor Analysis (FA) is a technique of fundamental importance that is widely used in classical and modern multivariate statistics, psychometrics and econometrics. In this paper, we revisit the classical rank-constrained FA problem, which…