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We study the problem of matrix estimation and matrix completion under a general framework. This framework includes several important models as special cases such as the gaussian mixture model, mixed membership model, bi-clustering model and…

Statistics Theory · Mathematics 2017-07-10 Olga Klopp , Yu Lu , Alexandre B. Tsybakov , Harrison H. Zhou

This paper studies low-rank matrix completion in the presence of heavy-tailed and possibly asymmetric noise, where we aim to estimate an underlying low-rank matrix given a set of highly incomplete noisy entries. Though the matrix completion…

Statistics Theory · Mathematics 2022-06-10 Bingyan Wang , Jianqing Fan

Exact matrix completion and low rank matrix estimation problems has been studied in different underlying conditions. In this work we study exact low-rank completion under non-degenerate noise model. Non-degenerate random noise model has…

Machine Learning · Computer Science 2022-04-06 Jafar Jafarov

Many results have been proved for various nuclear norm penalized estimators of the uniform sampling matrix completion problem. However, most of these estimators are not robust: in most of the cases the quadratic loss function and its…

Statistics Theory · Mathematics 2017-07-25 Andreas Elsener , Sara van de Geer

We consider the problem of noisy 1-bit matrix completion under an exact rank constraint on the true underlying matrix $M^*$. Instead of observing a subset of the noisy continuous-valued entries of a matrix $M^*$, we observe a subset of…

Machine Learning · Statistics 2015-02-25 Sonia Bhaskar , Adel Javanmard

We consider the problem of recovering a lowrank matrix M from a small number of random linear measurements. A popular and useful example of this problem is matrix completion, in which the measurements reveal the values of a subset of the…

Information Theory · Computer Science 2009-10-05 Emmanuel J. Candes , Yaniv Plan

We consider the matrix completion problem of recovering a structured matrix from noisy and partial measurements. Recent works have proposed tractable estimators with strong statistical guarantees for the case where the underlying matrix is…

Machine Learning · Statistics 2015-09-16 Suriya Gunasekar , Pradeep Ravikumar , Joydeep Ghosh

This paper studies noisy low-rank matrix completion: given partial and noisy entries of a large low-rank matrix, the goal is to estimate the underlying matrix faithfully and efficiently. Arguably one of the most popular paradigms to tackle…

Machine Learning · Statistics 2019-10-08 Yuxin Chen , Yuejie Chi , Jianqing Fan , Cong Ma , Yuling Yan

In this paper we consider the trace regression model where $n$ entries or linear combinations of entries of an unknown $m_1\times m_2$ matrix $A_0$ corrupted by noise are observed. We establish for the nuclear-norm penalized estimator of…

Statistics Theory · Mathematics 2011-10-26 Karim Lounici

Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…

Machine Learning · Statistics 2024-12-17 Ziyuan Chen , Fang Yao

Matrix learning is at the core of many machine learning problems. A number of real-world applications such as collaborative filtering and text mining can be formulated as a low-rank matrix completion problem, which recovers incomplete…

Machine Learning · Computer Science 2021-02-23 Yaqing Wang , Quanming Yao , James T. Kwok

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 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

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

We propose a new pivotal method for estimating high-dimensional matrices. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix $A\_0$ corrupted by noise. We propose a new method for estimating…

Statistics Theory · Mathematics 2015-02-03 Olga Klopp , Stéphane Gaiffas

Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries…

Machine Learning · Statistics 2022-03-18 Yuning Qiu , Guoxu Zhou , Qibin Zhao , Shengli Xie

We consider robust low rank matrix estimation as a trace regression when outputs are contaminated by adversaries. The adversaries are allowed to add arbitrary values to arbitrary outputs. Such values can depend on any samples. We deal with…

Machine Learning · Statistics 2024-05-27 Takeyuki Sasai , Hironori Fujisawa

We study the problem of recovering an incomplete $m\times n$ matrix of rank $r$ with columns arriving online over time. This is known as the problem of life-long matrix completion, and is widely applied to recommendation system, computer…

Machine Learning · Computer Science 2016-12-04 Maria-Florina Balcan , Hongyang Zhang

Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system.…

Machine Learning · Statistics 2019-10-22 Mokhtar Z. Alaya , Olga Klopp

This paper deals with the trace regression model where $n$ entries or linear combinations of entries of an unknown $m_1\times m_2$ matrix $A_0$ corrupted by noise are observed. We propose a new nuclear norm penalized estimator of $A_0$ and…

Statistics Theory · Mathematics 2016-03-24 Vladimir Koltchinskii , Alexandre B. Tsybakov , Karim Lounici