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We consider the low rank matrix completion problem over finite fields. This problem has been extensively studied in the domain of real/complex numbers, however, to the best of authors' knowledge, there exists merely one efficient algorithm…

Information Theory · Computer Science 2023-08-23 Mahdi Soleymani , Qiang Liu , Hessam Mahdavifar , Laura Balzano

The low-rank matrix completion problem can be succinctly stated as follows: given a subset of the entries of a matrix, find a low-rank matrix consistent with the observations. While several low-complexity algorithms for matrix completion…

Information Theory · Computer Science 2010-06-11 Wei Dai , Ely Kerman , Olgica Milenkovic

This paper provides the best bounds to date on the number of randomly sampled entries required to reconstruct an unknown low rank matrix. These results improve on prior work by Candes and Recht, Candes and Tao, and Keshavan, Montanari, and…

Information Theory · Computer Science 2009-10-21 Benjamin Recht

Compressed sensing (CS) with prior information concerns the problem of reconstructing a sparse signal with the aid of a similar signal which is known beforehand. We consider a new approach to integrate the prior information into CS via…

Information Theory · Computer Science 2017-05-23 Xu Zhang , Wei Cui , Yulong Liu

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…

Information Theory · Computer Science 2008-05-30 Emmanuel J. Candes , Benjamin Recht

Factorizing low-rank matrices is a problem with many applications in machine learning and statistics, ranging from sparse PCA to community detection and sub-matrix localization. For probabilistic models in the Bayes optimal setting, general…

Information Theory · Computer Science 2018-12-07 Jean Barbier , Mohamad Dia , Nicolas Macris , Florent Krzakala , Lenka Zdeborová

The problem of approximating a matrix by a low-rank one has been extensively studied. This problem assumes, however, that the whole matrix has a low-rank structure. This assumption is often false for real-world matrices. We consider the…

Data Structures and Algorithms · Computer Science 2025-11-05 Martino Ciaperoni , Aristides Gionis , Heikki Mannila

We consider the problem of performing matrix completion with side information on row-by-row and column-by-column similarities. We build upon recent proposals for matrix estimation with smoothness constraints with respect to row and column…

Computation · Statistics 2019-04-23 Eric Chi , Liuiyi Hu , Arvind K. Saibaba , Arvind U. K. Rao

This paper considers theoretical analysis of recovering a low rank matrix given a few expansion coefficients with respect to any basis. The current approach generalizes the existing analysis for the low-rank matrix completion problem with…

Information Theory · Computer Science 2018-12-17 Abiy Tasissa , Rongjie Lai

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…

Machine Learning · Computer Science 2023-02-24 Manolis C. Tsakiris

Consider a movie recommendation system where apart from the ratings information, side information such as user's age or movie's genre is also available. Unlike standard matrix completion, in this setting one should be able to predict…

Machine Learning · Computer Science 2013-06-05 Prateek Jain , Inderjit S. Dhillon

We study the problem of matrix completion in this paper. A spectral scaled Student prior is exploited to favour the underlying low-rank structure of the data matrix. We provide a thorough theoretical investigation for our approach through…

Machine Learning · Statistics 2022-01-10 The Tien Mai

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…

Numerical Analysis · Computer Science 2014-11-06 Prateek Jain , Praneeth Netrapalli

The problem of completing a low-rank matrix from a subset of its entries is often encountered in the analysis of incomplete data sets exhibiting an underlying factor model with applications in collaborative filtering, computer vision and…

Machine Learning · Computer Science 2009-02-24 Amit Singer , Mihai Cucuringu

In this paper, we consider optimal low-rank regularized inverse matrix approximations and their applications to inverse problems. We give an explicit solution to a generalized rank-constrained regularized inverse approximation problem,…

Numerical Analysis · Mathematics 2016-03-21 Julianne Chung , Matthias Chung

In this paper we consider the low-rank matrix completion problem with specific application to forecasting in time series analysis. Briefly, the low-rank matrix completion problem is the problem of imputing missing values of a matrix under a…

Methodology · Statistics 2018-02-23 Jonathan Gillard , Konstantin Usevich

Low-rank matrix completion is an important problem with extensive real-world applications. When observations are uniformly sampled from the underlying matrix entries, existing methods all require the matrix to be incoherent. This paper…

Machine Learning · Computer Science 2015-02-11 Shusen Wang , Tong Zhang , Zhihua Zhang

The essence of distantly supervised relation extraction is that it is an incomplete multi-label classification problem with sparse and noisy features. To tackle the sparsity and noise challenges, we propose solving the classification…

Computation and Language · Computer Science 2014-11-18 Miao Fan , Deli Zhao , Qiang Zhou , Zhiyuan Liu , Thomas Fang Zheng , Edward Y. Chang

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…

Information Theory · Computer Science 2009-03-10 Emmanuel J. Candes , Terence Tao

Matrix completion problem has been previously studied under various adaptive and passive settings. Previously, researchers have proposed passive, two-phase and single-phase algorithms using coherence parameter, and multi phase algorithm…

Machine Learning · Computer Science 2022-03-17 Ilqar Ramazanli