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Matrix completion is a class of machine learning methods that concerns the prediction of missing entries in a partially observed matrix. This paper studies matrix completion for mixed data, i.e., data involving mixed types of variables…

Machine Learning · Statistics 2022-11-18 Yunxiao Chen , Xiaoou Li

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

On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be…

Information Theory · Computer Science 2009-03-19 Emmanuel J. Candes , Yaniv Plan

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

Low-rank matrix completion addresses the problem of completing a matrix from a certain set of generic specified entries. Over the complex numbers a matrix with a given entry pattern can be uniquely completed to a specific rank, called the…

Algebraic Geometry · Mathematics 2025-03-13 Mareike Dressler , Robert Krone

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

The matrix completion problem aims to reconstruct a low-rank matrix based on a revealed set of possibly noisy entries. Prior works consider completing the entire matrix with generalization error guarantees. However, the completion accuracy…

Machine Learning · Computer Science 2023-12-19 Elad Hazan , Adam Tauman Kalai , Varun Kanade , Clara Mohri , Y. Jennifer Sun

The problem of low-rank matrix completion has recently generated a lot of interest leading to several results that offer exact solutions to the problem. However, in order to do so, these methods make assumptions that can be quite…

Machine Learning · Statistics 2014-07-14 Srinadh Bhojanapalli , Prateek Jain

High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…

Statistics Theory · Mathematics 2013-03-13 Sahand N. Negahban , Pradeep Ravikumar , Martin J. Wainwright , Bin Yu

In this work, we consider the matrix completion problem, where the objective is to reconstruct a low-rank matrix from a few observed entries. A commonly employed approach involves nuclear norm minimization. For this method to succeed, the…

Signal Processing · Electrical Eng. & Systems 2024-06-25 Hamideh. Sadat Fazael Ardakani , Sajad Daei , Arash Amini , Mikael Skoglund , Gabor Fodor

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

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

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

This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…

Statistics Theory · Mathematics 2016-07-05 Olga Klopp , Karim Lounici , Alexandre B. Tsybakov

Matrix completion has been well studied under the uniform sampling model and the trace-norm regularized methods perform well both theoretically and numerically in such a setting. However, the uniform sampling model is unrealistic for a…

Machine Learning · Computer Science 2017-05-01 T. Tony Cai , Wen-Xin Zhou

Regularization plays a pivotal role when facing the challenge of solving ill-posed inverse problems, where the number of observations is smaller than the ambient dimension of the object to be estimated. A line of recent work has studied…

Optimization and Control · Mathematics 2014-07-03 Samuel Vaiter , Mohammad Golbabaee , Jalal M. Fadili , Gabriel Peyré

We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…

Machine Learning · Computer Science 2021-02-08 Abhishek Sharma , Maks Ovsjanikov

We consider the matrix completion problem with a deterministic pattern of observed entries. In this setting, we aim to answer the question: under what condition there will be (at least locally) unique solution to the matrix completion…

Machine Learning · Computer Science 2019-01-30 Alexander Shapiro , Yao Xie , Rui Zhang

Unit norm finite frames are generalizations of orthonormal bases with many applications in signal processing. An important property of a frame is its coherence, a measure of how close any two vectors of the frame are to each other. Low…

Signal Processing · Electrical Eng. & Systems 2018-06-21 Cristian Rusu , Nuria Gonzalez-Prelcic , Robert W. Heath

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