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Related papers: Robust Matrix Completion with Heavy-tailed Noise

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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

We study high-dimensional least-squares regression within a subgaussian statistical learning framework with heterogeneous noise. It includes $s$-sparse and $r$-low-rank least-squares regression when a fraction $\epsilon$ of the labels are…

Statistics Theory · Mathematics 2023-11-01 Philip Thompson

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

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

We consider the problem of noisy matrix completion, in which the goal is to reconstruct a structured matrix whose entries are partially observed in noise. Standard approaches to this underdetermined inverse problem are based on assuming…

Machine Learning · Statistics 2017-09-04 Nihar B. Shah , Sivaraman Balakrishnan , Martin J. Wainwright

High-dimensional data subject to heavy-tailed phenomena and heterogeneity are commonly encountered in various scientific fields and bring new challenges to the classical statistical methods. In this paper, we combine the asymmetric square…

Statistics Theory · Mathematics 2019-10-02 Jun Zhao , Guan'ao Yan , Yi Zhang

We consider the problem of robust matrix completion, which aims to recover a low rank matrix $L_*$ and a sparse matrix $S_*$ from incomplete observations of their sum $M=L_*+S_*\in\mathbb{R}^{m\times n}$. Algorithmically, the robust matrix…

Machine Learning · Statistics 2020-03-25 Yunfeng Cai , Ping Li

We study the problem of robust matrix completion (RMC), where the partially observed entries of an underlying low-rank matrix is corrupted by sparse noise. Existing analysis of the non-convex methods for this problem either requires the…

Information Theory · Computer Science 2025-04-28 Tianming Wang , Ke Wei

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

This paper examines a general class of noisy matrix completion tasks where the goal is to estimate a matrix from observations obtained at a subset of its entries, each of which is subject to random noise or corruption. Our specific focus is…

Machine Learning · Statistics 2016-11-18 Akshay Soni , Swayambhoo Jain , Jarvis Haupt , Stefano Gonella

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

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

Matrix completion, the problem of completing missing entries in a data matrix with low dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is the tensor analog, that attempts to impute…

Numerical Analysis · Mathematics 2021-07-07 Zehan Chao , Longxiu Huang , Deanna Needell

In this letter, we study the deterministic sampling patterns for the completion of low rank matrix, when corrupted with a sparse noise, also known as robust matrix completion. We extend the recent results on the deterministic sampling…

Information Theory · Computer Science 2018-03-14 Morteza Ashraphijuo , Vaneet Aggarwal , Xiaodong Wang

This paper investigates the theoretical underpinnings of two fundamental statistical inference problems, the construction of confidence sets and large-scale simultaneous hypothesis testing, in the presence of heavy-tailed data. With…

Statistics Theory · Mathematics 2019-03-19 Xi Chen , Wen-Xin Zhou

We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general…

Machine Learning · Statistics 2016-10-18 Lingxiao Wang , Xiao Zhang , Quanquan Gu

In existing distributed stochastic optimization studies, it is usually assumed that the gradient noise has a bounded variance. However, recent research shows that the heavy-tailed noise, which allows an unbounded variance, is closer to…

Optimization and Control · Mathematics 2025-05-15 Jun Hu , Chao Sun , Bo Chen , Jianzheng Wang , Zheming Wang

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

We study the problem of linear regression where both covariates and responses are potentially (i) heavy-tailed and (ii) adversarially contaminated. Several computationally efficient estimators have been proposed for the simpler setting…

Statistics Theory · Mathematics 2021-05-18 Ankit Pensia , Varun Jog , Po-Ling Loh

Biclustering is widely used in different kinds of fields including gene information analysis, text mining, and recommendation system by effectively discovering the local correlation between samples and features. However, many biclustering…

Methodology · Statistics 2023-10-10 Yifan Chen , Chunyin Lei , Chuanquan Li , Haiqiang Ma , Ningyuan Hu