Related papers: Matrix completion with column manipulation: Near-o…

Matrix completion is a ubiquitous tool in machine learning and data analysis. Most work in this area has focused on the number of observations necessary to obtain an accurate low-rank approximation. In practice, however, the cost of…

Recommender systems are essential tools in the digital landscape for connecting users with content that more closely aligns with their preferences. Matrix completion is a widely used statistical framework for such systems, aiming to predict…

We propose a randomized method for solving linear programs with a large number of columns but a relatively small number of constraints. Since enumerating all the columns is usually unrealistic, such linear programs are commonly solved by…

The problem of completing a large matrix with lots of missing entries has received widespread attention in the last couple of decades. Two popular approaches to the matrix completion problem are based on singular value thresholding and…

In this paper, we study the popularly dubbed matrix completion problem, where the task is to "fill in" the unobserved entries of a matrix from a small subset of observed entries, under the assumption that the underlying matrix is of…

This paper considers the recovery of a low-rank matrix from an observed version that simultaneously contains both (a) erasures: most entries are not observed, and (b) errors: values at a constant fraction of (unknown) locations are…

The Nystrom method is an efficient technique used to speed up large-scale learning applications by generating low-rank approximations. Crucial to the performance of this technique is the assumption that a matrix can be well approximated by…

We study low rank matrix and tensor completion and propose novel algorithms that employ adaptive sampling schemes to obtain strong performance guarantees. Our algorithms exploit adaptivity to identify entries that are highly informative for…

Low-rank Matrix Completion (LRMC) describes the problem where we wish to recover missing entries of partially observed low-rank matrix. Most existing matrix completion work deals with sampling procedures that are independent of the…

The Nystrom method is an efficient technique to speed up large-scale learning applications by generating low-rank approximations. Crucial to the performance of this technique is the assumption that a matrix can be well approximated by…

This paper examines a general class of noisy matrix completion tasks where the goal is to estimate a matrix from observations obtained at a subset of its entries, each of which is subject to random noise or corruption. Our specific focus is…

This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the matrix completion problem, and comes up in a great number of applications, including the famous Netflix…

Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time…

Tensor completion is a natural higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from sparse observations of its entries. Existing algorithms are either heuristic without provable guarantees,…

While the matrix completion problem has attracted considerable attention over the decades, few works address the nonignorable missing issue and all have their limitations. In this article, we propose a nuclear norm regularized row- and…

Low-rank matrix completion consists of computing a matrix of minimal complexity that recovers a given set of observations as accurately as possible. Unfortunately, existing methods for matrix completion are heuristics that, while highly…

Selecting a good column (or row) subset of massive data matrices has found many applications in data analysis and machine learning. We propose a new adaptive sampling algorithm that can be used to improve any relative-error column selection…

We consider the symmetric Toeplitz matrix completion problem, whose matrix under consideration possesses specific row and column structures. This problem, which has wide application in diverse areas, is well-known to be computationally…

We consider the problem of matrix completion on an $n \times m$ matrix. We introduce the problem of Interpretable Matrix Completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the…

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…