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

We consider a generalization of low-rank matrix completion to the case where the data belongs to an algebraic variety, i.e. each data point is a solution to a system of polynomial equations. In this case the original matrix is possibly…

Despite the popularity of low-rank matrix completion, the majority of its theory has been developed under the assumption of random observation patterns, whereas very little is known about the practically relevant case of non-random…

Time-series models typically assume untainted and legitimate streams of data. However, a self-interested adversary may have incentive to corrupt this data, thereby altering a decision maker's inference. Within the broader field of…

Many kernel methods suffer from high time and space complexities and are thus prohibitive in big-data applications. To tackle the computational challenge, the Nystr\"om method has been extensively used to reduce time and space complexities…

A new algorithm, termed subspace evolution and transfer (SET), is proposed for solving the consistent matrix completion problem. In this setting, one is given a subset of the entries of a low-rank matrix, and asked to find one low-rank…

The problem of completing a large low rank matrix using a subset of revealed entries has received much attention in the last ten years. The main result of this paper gives a necessary and sufficient condition, stated in the language of…

CUR matrix decomposition is a randomized algorithm that can efficiently compute the low rank approximation for a given rectangle matrix. One limitation with the existing CUR algorithms is that they require an access to the full matrix A for…

Submodular maximization subject to matroid constraints is a central problem with many applications in machine learning. As algorithms are increasingly used in decision-making over datapoints with sensitive attributes such as gender or race,…

A cumbersome operation in numerical analysis and linear algebra, optimization, machine learning and engineering algorithms; is inverting large full-rank matrices which appears in various processes and applications. This has both numerical…

Matrix completion has received vast amount of attention and research due to its wide applications in various study fields. Existing methods of matrix completion consider only nonlinear (or linear) relations among entries in a data matrix…

In this paper, we study the problem of matrix recovery, which aims to restore a target matrix of authentic samples from grossly corrupted observations. Most of the existing methods, such as the well-known Robust Principal Component Analysis…

In the construction of low-rank matrix approximation and maximum element search it is effective to use maxvol algorithm. Nevertheless, even in the case of rank 1 approximation the algorithm does not always converge to the maximum matrix…

This paper examines the problem of locating outlier columns in a large, otherwise low-rank, matrix. We propose a simple two-step adaptive sensing and inference approach and establish theoretical guarantees for its performance; our results…

This paper studies the low-rank matrix completion problem from an information theoretic perspective. The completion problem is rephrased as a communication problem of an (uncoded) low-rank matrix source over an erasure channel. The paper…

Matrix completion results deal with the question of when a partially specified symmetric matrix can be completed to a member of certain matrix cones. Results from positive semidefinite matrix completion and completely positive matrix…

Matrix completion aims to predict missing elements in a partially observed data matrix which in typical applications, such as collaborative filtering, is large and extremely sparsely observed. A standard solution is matrix factorization,…

We consider the problem of noisy matrix completion, in which the goal is to reconstruct a structured matrix whose entries are partially observed in noise. Standard approaches to this underdetermined inverse problem are based on assuming…

A usual way to model a recommendation system is as a matrix completion problem. There are several matrix completion methods, typically using optimization approaches or collaborative filtering. Most approaches assume that the matrix is…

We extend the theory of low-rank matrix recovery and completion to the case when Poisson observations for a linear combination or a subset of the entries of a matrix are available, which arises in various applications with count data. We…

We consider the problem of recovering a low-rank matrix when some of its entries, whose locations are not known a priori, are corrupted by errors of arbitrarily large magnitude. It has recently been shown that this problem can be solved…