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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

We consider the problem of approximately reconstructing a partially-observed, approximately low-rank matrix. This problem has received much attention lately, mostly using the trace-norm as a surrogate to the rank. Here we study low-rank…

Machine Learning · Computer Science 2011-05-27 Rina Foygel , Nathan Srebro

We propose an algorithm for low rank matrix completion for matrices with binary entries which obtains explicit binary factors. Our algorithm, which we call TBMC (\emph{Tiling for Binary Matrix Completion}), gives interpretable output in the…

Numerical Analysis · Mathematics 2020-06-23 Melanie Beckerleg , Andrew Thompson

We study the completion of approximately low rank matrices with entries missing not at random (MNAR). In the context of typical large-dimensional statistical settings, we establish a framework for the performance analysis of the nuclear…

Information Theory · Computer Science 2024-01-02 Agostino Capponi , Mihailo Stojnic

In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…

Information Theory · Computer Science 2016-11-18 Mohammadreza Malek-Mohammadi , Massoud Babaie-Zadeh , Mikael Skoglund

This paper studies the problem of recovering a low-rank matrix from several noisy random linear measurements. We consider the setting where the rank of the ground-truth matrix is unknown a priori and use an objective function built from a…

Optimization and Control · Mathematics 2025-07-29 Lijun Ding , Zhen Qin , Liwei Jiang , Jinxin Zhou , Zhihui Zhu

Matrix completion algorithms recover a low rank matrix from a small fraction of the entries, each entry contaminated with additive errors. In practice, the singular vectors and singular values of the low rank matrix play a pivotal role for…

Methodology · Statistics 2016-05-03 Juhee Cho , Donggyu Kim , Karl Rohe

This paper considers the recovery of a low-rank matrix from an observed version that simultaneously contains both (a) erasures: most entries are not observed, and (b) errors: values at a constant fraction of (unknown) locations are…

Information Theory · Computer Science 2013-09-23 Yudong Chen , Ali Jalali , Sujay Sanghavi , Constantine Caramanis

This paper concerns the problem of matrix completion, which is to estimate a matrix from observations in a small subset of indices. We propose a calibrated spectrum elastic net method with a sum of the nuclear and Frobenius penalties and…

Statistics Theory · Mathematics 2012-11-13 Tingni Sun , Cun-Hui Zhang

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 paper looks at a scaled variant of the stochastic gradient descent algorithm for the matrix completion problem. Specifically, we propose a novel matrix-scaling of the partial derivatives that acts as an efficient preconditioning for the…

Machine Learning · Computer Science 2016-10-06 Bamdev Mishra , Rodolphe Sepulchre

This paper is about iteratively reweighted basis-pursuit algorithms for compressed sensing and matrix completion problems. In a first part, we give a theoretical explanation of the fact that reweighted basis pursuit can improve a lot upon…

Information Theory · Computer Science 2011-07-11 Stéphane Gaïffas , Guillaume Lecué

Tensor completion is a natural higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from sparse observations of its entries. Existing algorithms are either heuristic without provable guarantees,…

Data Structures and Algorithms · Computer Science 2023-07-14 Allen Liu , Ankur Moitra

Initially designed for independent datas, low-rank matrix completion was successfully applied in many domains to the reconstruction of partially observed high-dimensional time series. However, there is a lack of theory to support the…

Statistics Theory · Mathematics 2022-05-05 Pierre Alquier , Nicolas Marie , Amélie Rosier

This paper studies the problem of completing a low-rank matrix from a few of its random entries with the aid of prior information. We suggest a strategy to incorporate prior information into the standard matrix completion procedure by…

Information Theory · Computer Science 2020-07-15 Xu Zhang , Wei Cui , Yulong Liu

We have recently presented a method to solve an overdetermined linear system of equations with multiple right hand side vectors, where the unknown matrix is to be symmetric and positive definite. The coefficient and the right hand side…

Optimization and Control · Mathematics 2014-09-19 Negin Bagherpour , Nezam Mahdavi-Amiri

We consider the problem of high-dimensional channel estimation in fast time-varying millimeter-wave MIMO systems with a hybrid architecture. By exploiting the low-rank and sparsity properties of the channel matrix, we propose a two-phase…

Signal Processing · Electrical Eng. & Systems 2025-11-04 Tianyu Jiang , Yan Yang , Hongjin Liu , Runyu Han , Bo Ai , Mohsen Guizani

We study the problem of low-rank matrix completion for symmetric matrices. The minimum rank of a completion of a generic partially specified symmetric matrix depends only on the location of the specified entries, and not their values, if…

Combinatorics · Mathematics 2020-10-16 Daniel Irving Bernstein , Grigoriy Blekherman , Kisun Lee

We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural…

Information Theory · Computer Science 2018-12-04 Yuanxin Li , Cong Ma , Yuxin Chen , Yuejie Chi

The completion of matrices with missing values under the rank constraint is a non-convex optimization problem. A popular convex relaxation is based on minimization of the nuclear norm (sum of singular values) of the matrix. For this…

Optimization and Control · Mathematics 2015-06-11 Konstantin Usevich , Pierre Comon