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Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…

Statistics Theory · Mathematics 2021-05-06 Yunhua Xiang , Tianyu Zhang , Xu Wang , Ali Shojaie , Noah Simon

We describe novel subgradient methods for a broad class of matrix optimization problems involving nuclear norm regularization. Unlike existing approaches, our method executes very cheap iterations by combining low-rank stochastic…

Machine Learning · Computer Science 2012-07-03 Haim Avron , Satyen Kale , Shiva Kasiviswanathan , Vikas Sindhwani

Over the past decade, various matrix completion algorithms have been developed. Thresholded singular value decomposition (SVD) is a popular technique in implementing many of them. A sizable number of studies have shown its theoretical and…

Methodology · Statistics 2016-05-10 Juhee Cho , Donggyu Kim , Karl Rohe

An incoherent low-rank matrix can be efficiently reconstructed after observing a few of its entries at random, and then solving a convex program that minimizes the nuclear norm. In many applications, in addition to these entries,…

Information Theory · Computer Science 2018-03-14 Armin Eftekhari , Dehui Yang , Michael B. Wakin

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

Motivated by the philosophy and phenomenal success of compressed sensing, the problem of reconstructing a matrix from a sampling of its entries has attracted much attention recently. Such a problem can be viewed as an information-theoretic…

Information Theory · Computer Science 2009-05-15 Zhisu Zhu , Anthony Man-Cho So , Yinyu Ye

Top-N recommender systems have been investigated widely both in industry and academia. However, the recommendation quality is far from satisfactory. In this paper, we propose a simple yet promising algorithm. We fill the user-item matrix…

Information Retrieval · Computer Science 2016-01-20 Zhao Kang , Chong Peng , Qiang Cheng

In many applications, e.g., recommender systems and traffic monitoring, the data comes in the form of a matrix that is only partially observed and low rank. A fundamental data-analysis task for these datasets is matrix completion, where the…

Machine Learning · Computer Science 2017-05-02 Natali Ruchansky , Mark Crovella , Evimaria Terzi

This paper considers the problem of matrix completion when some number of the columns are completely and arbitrarily corrupted, potentially by a malicious adversary. It is well-known that standard algorithms for matrix completion can return…

Machine Learning · Statistics 2016-04-26 Yudong Chen , Huan Xu , Constantine Caramanis , Sujay Sanghavi

We consider the problem of robust matrix completion, which aims to recover a low rank matrix $L_*$ and a sparse matrix $S_*$ from incomplete observations of their sum $M=L_*+S_*\in\mathbb{R}^{m\times n}$. Algorithmically, the robust matrix…

Machine Learning · Statistics 2020-03-25 Yunfeng Cai , Ping Li

We study online robust matrix completion on graphs. At each iteration a vector with some entries missing is revealed and our goal is to reconstruct it by identifying the underlying low-dimensional subspace from which the vectors are drawn.…

Information Theory · Computer Science 2016-05-16 Symeon Chouvardas , Mohammed Amin Abdullah , Lucas Claude , Moez Draief

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

Matching markets face increasing needs to learn the matching qualities between demand and supply for effective design of matching policies. In practice, the matching rewards are high-dimensional due to the growing diversity of participants.…

Machine Learning · Statistics 2026-01-13 Zhiyuan Tang , Wanning Chen , Kan Xu

The process of rank aggregation is intimately intertwined with the structure of skew-symmetric matrices. We apply recent advances in the theory and algorithms of matrix completion to skew-symmetric matrices. This combination of ideas…

Numerical Analysis · Computer Science 2011-02-24 David F. Gleich , Lek-Heng Lim

The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image…

Statistics Theory · Mathematics 2014-12-20 Jean Lafond , Olga Klopp , Eric Moulines , Jospeh Salmon

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

Conventional matrix completion methods approximate the missing values by assuming the matrix to be low-rank, which leads to a linear approximation of missing values. It has been shown that enhanced performance could be attained by using…

Information Theory · Computer Science 2024-03-18 Sajad Faramarzi , Farzan Haddadi , Sajjad Amini , Masoud Ahookhosh

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…

Machine Learning · Statistics 2025-07-30 Aurore Archimbaud , Andreas Alfons , Ines Wilms

The task of predicting missing entries of a matrix, from a subset of known entries, is known as \textit{matrix completion}. In today's data-driven world, data completion is essential whether it is the main goal or a pre-processing step.…

Numerical Analysis · Mathematics 2021-05-18 Henry Adams , Lara Kassab , Deanna Needell

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,…

Machine Learning · Statistics 2023-06-06 Hanbyul Lee , Rahul Mazumder , Qifan Song , Jean Honorio