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Related papers: Robust Matrix Completion with Mixed Data Types

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In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our…

Machine Learning · Computer Science 2014-04-17 Zheng Wang , Ming-Jun Lai , Zhaosong Lu , Wei Fan , Hasan Davulcu , Jieping Ye

We give a new framework for solving the fundamental problem of low-rank matrix completion, i.e., approximating a rank-$r$ matrix $\mathbf{M} \in \mathbb{R}^{m \times n}$ (where $m \ge n$) from random observations. First, we provide an…

Machine Learning · Computer Science 2023-08-08 Jonathan A. Kelner , Jerry Li , Allen Liu , Aaron Sidford , Kevin Tian

We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…

Methodology · Statistics 2025-10-28 Di Wang , Xiaoyu Zhang , Guodong Li , Wenyang Zhang

Matrix completion aims to recover an unknown low-rank matrix from a small subset of its entries. In many applications, the rank of the unknown target matrix is known in advance. In this paper, first we revisit a recently proposed rank-based…

Optimization and Control · Mathematics 2024-06-11 Tacildo de Souza Araújo , Douglas S. Gonçalves , Cristiano Torezzan

The matrix completion problem consists in reconstructing a matrix from a sample of entries, possibly observed with noise. A popular class of estimator, known as nuclear norm penalized estimators, are based on minimizing the sum of a data…

Statistics Theory · Mathematics 2015-04-21 Jean Lafond

We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…

Statistics Theory · Mathematics 2015-02-03 Olga Klopp

Robust low-rank matrix completion (RMC), or robust principal component analysis with partially observed data, has been studied extensively for computer vision, signal processing and machine learning applications. This problem aims to…

Machine Learning · Computer Science 2021-06-09 Minhui Huang , Shiqian Ma , Lifeng Lai

The aim of this note (as well as of the course itself) is to give a largely self-contained proof of two of the main results in the field of low-rank matrix recovery. This field aims for identification of low-rank matrices from only limited…

Functional Analysis · Mathematics 2016-09-27 Jan Vybiral

We introduce a two step algorithm with theoretical guarantees to recover a jointly sparse and low-rank matrix from undersampled measurements of its columns. The algorithm first estimates the row subspace of the matrix using a set of common…

Machine Learning · Statistics 2015-06-03 Sampurna Biswas , Sunrita Poddar , Soura Dasgupta , Raghuraman Mudumbai , Mathews Jacob

Given only a few observed entries from a low-rank matrix $X$, matrix completion is the problem of imputing the missing entries, and it formalizes a wide range of real-world settings that involve estimating missing data. However, when there…

Machine Learning · Computer Science 2023-06-08 Steven Cao , Percy Liang , Gregory Valiant

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

Given a known matrix that is the sum of a low rank matrix and a masked sparse matrix, we wish to recover both the low rank component and the sparse component. The sparse matrix is masked in the sense that a linear transformation has been…

Information Theory · Computer Science 2025-04-29 Xuemei Chen , Rongrong Wang

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…

Computational Complexity · Computer Science 2014-04-11 Moritz Hardt , Raghu Meka , Prasad Raghavendra , Benjamin Weitz

As a paradigm to recover unknown entries of a matrix from partial observations, low-rank matrix completion (LRMC) has generated a great deal of interest. Over the years, there have been lots of works on this topic but it might not be easy…

Data Structures and Algorithms · Computer Science 2019-07-30 Luong Trung Nguyen , Junhan Kim , Byonghyo Shim

We consider the problem of low rank matrix recovery in a stochastically noisy high dimensional setting. We propose a new estimator for the low rank matrix, based on the iterative hard thresholding method, and that is computationally…

Statistics Theory · Mathematics 2016-03-02 Alexandra Carpentier , Arlene K. H. Kim

The low-rank matrix completion problem can be solved by Riemannian optimization on a fixed-rank manifold. However, a drawback of the known approaches is that the rank parameter has to be fixed a priori. In this paper, we consider the…

Optimization and Control · Mathematics 2022-02-21 Bin Gao , P. -A. Absil

For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation…

Optimization and Control · Mathematics 2015-06-23 Weimin Miao , Shaohua Pan , Defeng Sun

Low-rank tensor completion recovers missing entries based on different tensor decompositions. Due to its outstanding performance in exploiting some higher-order data structure, low rank tensor ring has been applied in tensor completion. To…

Machine Learning · Computer Science 2020-07-14 Huyan Huang , Yipeng Liu , Ce Zhu

A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to…

Numerical Analysis · Mathematics 2018-10-30 Simon Foucart , Srinivas Subramanian

Estimation of low-rank matrices is of significant interest in a range of contemporary applications. In this paper, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization…

Statistics Theory · Mathematics 2014-12-10 T. Tony Cai , Anru Zhang