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On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be…
Most of the existing works on provable guarantees for low-rank matrix completion algorithms rely on some unrealistic assumptions such that matrix entries are sampled randomly or the sampling pattern has a specific structure. In this work,…
Matrix completion, i.e., the exact and provable recovery of a low-rank matrix from a small subset of its elements, is currently only known to be possible if the matrix satisfies a restrictive structural constraint---known as {\em…
We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover…
This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…
Low-rank matrix completion (LRMC) problems arise in a wide variety of applications. Previous theory mainly provides conditions for completion under missing-at-random samplings. This paper studies deterministic conditions for completion. An…
Matrix completion is the problem of recovering a low rank matrix by observing a small fraction of its entries. A series of recent works [KOM12,JNS13,HW14] have proposed fast non-convex optimization based iterative algorithms to solve this…
Exact matrix completion and low rank matrix estimation problems has been studied in different underlying conditions. In this work we study exact low-rank completion under non-degenerate noise model. Non-degenerate random noise model has…
The problem of recovering a matrix of low rank from an incomplete and possibly noisy set of linear measurements arises in a number of areas. In order to derive rigorous recovery results, the measurement map is usually modeled…
In this letter, we study the deterministic sampling patterns for the completion of low rank matrix, when corrupted with a sparse noise, also known as robust matrix completion. We extend the recent results on the deterministic sampling…
Let $X_0$ be an unknown $M$ by $N$ matrix. In matrix recovery, one takes $n < MN$ linear measurements $y_1,..., y_n$ of $X_0$, where $y_i = \Tr(a_i^T X_0)$ and each $a_i$ is a $M$ by $N$ matrix. For measurement matrices with Gaussian i.i.d…
The problem of low-rank matrix completion has recently generated a lot of interest leading to several results that offer exact solutions to the problem. However, in order to do so, these methods make assumptions that can be quite…
We study the problem of recovering an incomplete $m\times n$ matrix of rank $r$ with columns arriving online over time. This is known as the problem of life-long matrix completion, and is widely applied to recommendation system, computer…
In some significant applications such as data forecasting, the locations of missing entries cannot obey any non-degenerate distributions, questioning the validity of the prevalent assumption that the missing data is randomly chosen…
In this paper, we theoretically investigate the low-rank matrix recovery problem in the context of the unconstrained regularized nuclear norm minimization (RNNM) framework. Our theoretical findings show that, the RNNM method is able to…
The matrix recovery (completion) problem, a central problem in data science and theoretical computer science, is to recover a matrix $A$ from a relatively small sample of entries. While such a task is impossible in general, it has been…
Matrix Completion is the problem of recovering an unknown real-valued low-rank matrix from a subsample of its entries. Important recent results show that the problem can be solved efficiently under the assumption that the unknown matrix is…
In this paper, we consider matrix completion from non-uniformly sampled entries including fully observed and partially observed columns. Specifically, we assume that a small number of columns are randomly selected and fully observed, and…
We study deterministic matrix completion problem, i.e., recovering a low-rank matrix from a few observed entries where the sampling set is chosen as the edge set of a Ramanujan graph. We first investigate projected gradient descent (PGD)…
Recovering a low rank matrix from a subset of its entries, some of which may be corrupted, is known as the robust matrix completion (RMC) problem. Existing RMC methods have several limitations: they require a relatively large number of…