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We consider the matrix completion problem under a form of row/column weighted entrywise sampling, including the case of uniform entrywise sampling as a special case. We analyze the associated random observation operator, and prove that with…

Information Theory · Computer Science 2011-05-17 Sahand Negahban , Martin J. Wainwright

Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…

Machine Learning · Statistics 2024-12-17 Ziyuan Chen , Fang Yao

A matrix completion problem is to recover the missing entries in a partially observed matrix. Most of the existing matrix completion methods assume a low rank structure of the underlying complete matrix. In this paper, we introduce an…

Machine Learning · Statistics 2020-11-16 Chencheng Cai , Rong Chen , Han Xiao

We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…

Numerical Analysis · Mathematics 2014-07-01 Gil Shabat , Yaniv Shmueli , Amir Averbuch

The problem of structured matrix estimation has been studied mostly under strong noise dependence assumptions. This paper considers a general framework of noisy low-rank-plus-sparse matrix recovery, where the noise matrix may come from any…

Machine Learning · Statistics 2025-04-07 Jinhang Chai , Jianqing Fan

This paper studies low-rank matrix completion in the presence of heavy-tailed and possibly asymmetric noise, where we aim to estimate an underlying low-rank matrix given a set of highly incomplete noisy entries. Though the matrix completion…

Statistics Theory · Mathematics 2022-06-10 Bingyan Wang , Jianqing Fan

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…

Machine Learning · Computer Science 2016-12-04 Maria-Florina Balcan , Hongyang Zhang

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…

Machine Learning · Statistics 2016-09-27 Ethan X. Fang , Han Liu , Kim-Chuan Toh , Wen-Xin Zhou

Matrix completion is a classical problem in data science wherein one attempts to reconstruct a low-rank matrix while only observing some subset of the entries. Previous authors have phrased this problem as a nuclear norm minimization…

Machine Learning · Computer Science 2019-04-19 Christian Parkinson , Kevin Huynh , Deanna Needell

The recovery of a low rank matrix from a subset of noisy low-precision quantized samples arises in several applications such as collaborative filtering, intelligent recommendation and millimeter wave channel estimation with few bit ADCs. In…

Information Theory · Computer Science 2019-11-25 Jiang Zhu , Zhennan Liu , Qi Zhang , Chunyi Song , Zhiwei Xu

We consider in this paper the problem of noisy 1-bit matrix completion under a general non-uniform sampling distribution using the max-norm as a convex relaxation for the rank. A max-norm constrained maximum likelihood estimate is…

Machine Learning · Statistics 2013-09-25 T. Tony Cai , Wen-Xin Zhou

The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem under the standard low rank assumption is NP-hard,…

Machine Learning · Computer Science 2014-12-01 Vassilis Kalofolias , Xavier Bresson , Michael Bronstein , Pierre Vandergheynst

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…

Information Theory · Computer Science 2018-03-14 Morteza Ashraphijuo , Vaneet Aggarwal , Xiaodong Wang

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…

Machine Learning · Computer Science 2021-04-19 Dong Hu , Alex Gittens , Malik Magdon-Ismail

This paper examines fundamental error characteristics for a general class of matrix completion problems, where the matrix of interest is a product of two a priori unknown matrices, one of which is sparse, and the observations are noisy. Our…

Information Theory · Computer Science 2017-10-27 Abhinav V. Sambasivan , Jarvis D. Haupt

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…

Machine Learning · Computer Science 2016-04-20 Yang Cao , Yao Xie

This paper considers the problem of estimating a low-rank matrix from the observation of all or a subset of its entries in the presence of Poisson noise. When we observe all entries, this is a problem of matrix denoising; when we observe…

Machine Learning · Statistics 2024-04-22 Andrew D. McRae , Mark A. Davenport

We propose a general framework for reconstructing and denoising single entries of incomplete and noisy entries. We describe: effective algorithms for deciding if and entry can be reconstructed and, if so, for reconstructing and denoising…

Machine Learning · Statistics 2013-04-02 Franz J. Király , Louis Theran

In this paper, we propose a novel method for matrix completion under general non-uniform missing structures. By controlling an upper bound of a novel balancing error, we construct weights that can actively adjust for the non-uniformity in…

Machine Learning · Statistics 2021-06-11 Jiayi Wang , Raymond K. W. Wong , Xiaojun Mao , Kwun Chuen Gary Chan

Matrix completion focuses on recovering missing or incomplete information in matrices. This problem arises in various applications, including image processing and network analysis. Previous research proposed Poisson matrix completion for…

Machine Learning · Computer Science 2024-08-30 Yu Lu , Kevin Bui , Roummel F. Marcia