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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 completing a matrix with categorical-valued entries from partial observations. This is achieved by extending the formulation and theory of one-bit matrix completion. We recover a low-rank matrix $X$ by maximizing…

Numerical Analysis · Computer Science 2015-07-03 Yang Cao , Yao Xie

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

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

This paper considers the problem of estimating a low-rank matrix from the observation of all or a subset of its entries in the presence of Poisson noise. When we observe all entries, this is a problem of matrix denoising; when we observe…

Machine Learning · Statistics 2024-04-22 Andrew D. McRae , Mark A. Davenport

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

In this paper, we consider matrix completion from non-uniformly sampled entries including fully observed and partially observed columns. Specifically, we assume that a small number of columns are randomly selected and fully observed, and…

Machine Learning · Computer Science 2018-06-28 Yuanyu Wan , Jinfeng Yi , Lijun Zhang

We consider the problem of exact low-rank matrix completion from a geometric viewpoint: given a partially filled matrix M, we keep the positions of specified and unspecified entries fixed, and study how the minimal completion rank depends…

Statistics Theory · Mathematics 2019-09-24 Daniel Irving Bernstein , Grigoriy Blekherman , Rainer Sinn

We propose a novel and efficient algorithm for the collaborative preference completion problem, which involves jointly estimating individualized rankings for a set of entities over a shared set of items, based on a limited number of…

Machine Learning · Statistics 2016-11-16 Suriya Gunasekar , Oluwasanmi Koyejo , Joydeep Ghosh

This paper considers the problem of matrix completion when some number of the columns are completely and arbitrarily corrupted, potentially by a malicious adversary. It is well-known that standard algorithms for matrix completion can return…

Machine Learning · Statistics 2016-04-26 Yudong Chen , Huan Xu , Constantine Caramanis , Sujay Sanghavi

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) problems arise in a wide variety of applications. Previous theory mainly provides conditions for completion under missing-at-random samplings. This paper studies deterministic conditions for completion. An…

Machine Learning · Statistics 2016-10-12 Daniel L. Pimentel-Alarcón , Nigel Boston , Robert D. Nowak

Low-rank matrices play a fundamental role in modeling and computational methods for signal processing and machine learning. In many applications where low-rank matrices arise, these matrices cannot be fully sampled or directly observed, and…

Information Theory · Computer Science 2016-05-25 Mark A. Davenport , Justin Romberg

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

Matrix completion, i.e., the exact and provable recovery of a low-rank matrix from a small subset of its elements, is currently only known to be possible if the matrix satisfies a restrictive structural constraint---known as {\em…

Machine Learning · Statistics 2014-07-22 Yudong Chen , Srinadh Bhojanapalli , Sujay Sanghavi , Rachel Ward

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

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 low-rank matrix completion problem can be succinctly stated as follows: given a subset of the entries of a matrix, find a low-rank matrix consistent with the observations. While several low-complexity algorithms for matrix completion…

Information Theory · Computer Science 2010-06-11 Wei Dai , Ely Kerman , Olgica Milenkovic

Low-rank matrix completion has been studied extensively under various type of categories. The problem could be categorized as noisy completion or exact completion, also active or passive completion algorithms. In this paper we focus on…

Machine Learning · Computer Science 2022-03-17 Ilqar Ramazanli

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

Numerical Analysis · Mathematics 2016-06-07 Victor Y. Pan , Liang Zhao