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In this paper, we investigate the matrix estimation problem in the multi-response regression model with measurement errors. A nonconvex error-corrected estimator based on a combination of the amended loss function and the nuclear norm…

Statistics Theory · Mathematics 2022-09-19 Xin Li , Dongya Wu

The reconstruction of low-rank matrix from its noisy observation finds its usage in many applications. It can be reformulated into a constrained nuclear norm minimization problem, where the bound $\eta$ of the constraint is explicitly given…

Optimization and Control · Mathematics 2022-04-14 Kexin Li , Hongwei Li , Raymond H. Chan , You-wei Wen

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

Given a limited number of entries from the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, recovery of the low-rank and sparse components is a fundamental task subsuming…

Multiagent Systems · Computer Science 2013-10-01 Morteza Mardani , Gonzalo Mateos , Georgios B. Giannakis

The problem of matrix sensing, or trace regression, is a problem wherein one wishes to estimate a low-rank matrix from linear measurements perturbed with noise. A number of existing works have studied both convex and nonconvex approaches to…

Statistics Theory · Mathematics 2025-06-26 Joshua Agterberg , René Vidal

We consider the high-dimensional inference problem where the signal is a low-rank matrix which is corrupted by an additive Gaussian noise. Given a probabilistic model for the low-rank matrix, we compute the limit in the large dimension…

Probability · Mathematics 2018-06-01 Léo Miolane

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

Previous work regarding low-rank matrix recovery has concentrated on the scenarios in which the matrix is noise-free and the measurements are corrupted by noise. However, in practical application, the matrix itself is usually perturbed by…

Information Theory · Computer Science 2020-03-09 Jianwen Huang , Jianjun Wang , Feng Zhang , Hailin Wang , Wendong Wang

Matrix completion refers to completing a low-rank matrix from a few observed elements of its entries and has been known as one of the significant and widely-used problems in recent years. The required number of observations for exact…

Information Theory · Computer Science 2021-11-02 Hamideh. Sadat Fazael Ardakani , Niloufar Rahmani , Sajad Daei

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

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

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

Noisy matrix completion aims at estimating a low-rank matrix given only partial and corrupted entries. Despite substantial progress in designing efficient estimation algorithms, it remains largely unclear how to assess the uncertainty of…

Machine Learning · Statistics 2019-11-15 Yuxin Chen , Jianqing Fan , Cong Ma , Yuling Yan

We propose a convex optimization formulation with the nuclear norm and $\ell_1$-norm to find a large approximately rank-one submatrix of a given nonnegative matrix. We develop optimality conditions for the formulation and characterize the…

Optimization and Control · Mathematics 2010-11-09 Xuan Vinh Doan , Stephen A. Vavasis

We consider the matrix completion problem of recovering a structured low rank matrix with partially observed entries with mixed data types. Vast majority of the solutions have proposed computationally feasible estimators with strong…

Machine Learning · Statistics 2020-05-27 Daqian Sun , Martin T. Wells

Low-rank matrix completion (LRMC) has demonstrated remarkable success in a wide range of applications. To address the NP-hard nature of the rank minimization problem, the nuclear norm is commonly used as a convex and computationally…

Computer Vision and Pattern Recognition · Computer Science 2025-12-25 Zhijie Wang , Liangtian He , Qinghua Zhang , Jifei Miao , Liang-Jian Deng , Jun Liu

The multivariate linear regression model with shuffled data and additive Gaussian noise arises in various correspondence estimation and matching problems. Focusing on the denoising aspect of this problem, we provide a characterization the…

Machine Learning · Statistics 2017-04-26 Ashwin Pananjady , Martin J. Wainwright , Thomas A. Courtade

Probabilistic approach to Boolean matrix factorization can provide solutions robustagainst noise and missing values with linear computational complexity. However,the assumption about latent factors can be problematic in real world…

Machine Learning · Statistics 2019-05-31 Lifan Liang , Songjian Lu

The low-rank matrix approximation problem is ubiquitous in computational mathematics. Traditionally, this problem is solved in spectral or Frobenius norms, where the accuracy of the approximation is related to the rate of decrease of the…

Numerical Analysis · Mathematics 2022-01-31 Stanislav Morozov , Nikolai Zamarashkin , Eugene Tyrtyshnikov

Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is…

Machine Learning · Statistics 2015-12-31 Ravi Ganti , Laura Balzano , Rebecca Willett