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Related papers: Matrix Completion With Selective Sampling

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A matrix completion problem, which aims to recover a complete matrix from its partial observations, is one of the important problems in the machine learning field and has been studied actively. However, there is a discrepancy between the…

Machine Learning · Statistics 2018-03-14 Masayoshi Hayashi , Tomoya Sakai , Masashi Sugiyama

In this short note we extend some of the recent results on matrix completion under the assumption that the columns of the matrix can be grouped (clustered) into subspaces (not necessarily disjoint or independent). This model deviates from…

Information Theory · Computer Science 2017-08-04 Vaneet Aggarwal , Shuchin Aeron

Minimization of the nuclear norm is often used as a surrogate, convex relaxation, for finding the minimum rank completion (recovery) of a partial matrix. The minimum nuclear norm problem can be solved as a trace minimization semidefinite…

Optimization and Control · Mathematics 2016-08-16 Shimeng Huang , Henry Wolkowicz

In this lecture note, we discuss a fundamental concept, referred to as the {\it characteristic rank}, which suggests a general framework for characterizing the basic properties of various low-dimensional models used in signal processing.…

Statistics Theory · Mathematics 2020-11-12 Alexander Shapiro , Yao Xie , Rui Zhang

We consider the problem of recovering a low-rank matrix from its clipped observations. Clipping is conceivable in many scientific areas that obstructs statistical analyses. On the other hand, matrix completion (MC) methods can recover a…

Machine Learning · Computer Science 2019-03-05 Takeshi Teshima , Miao Xu , Issei Sato , Masashi Sugiyama

Matrix completion results deal with the question of when a partially specified symmetric matrix can be completed to a member of certain matrix cones. Results from positive semidefinite matrix completion and completely positive matrix…

General Mathematics · Mathematics 2025-09-25 Markus Gabl

Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Accordingly, Combinatorial Optimization is a sub field of this domain of…

Computational Complexity · Computer Science 2023-06-29 Anurag Dutta , K. Lakshmanan , A. Ramamoorthy , Liton Chandra Voumik , John Harshith , John Pravin Motha

We consider the multi-view data completion problem, i.e., to complete a matrix $\mathbf{U}=[\mathbf{U}_1|\mathbf{U}_2]$ where the ranks of $\mathbf{U},\mathbf{U}_1$, and $\mathbf{U}_2$ are given. In particular, we investigate the…

Information Theory · Computer Science 2017-04-27 Morteza Ashraphijuo , Xiaodong Wang , Vaneet Aggarwal

Matrix completion is a classical problem that has received recurring interest across a wide range of fields. In this paper, we revisit this problem in an ultra-sparse sampling regime, where each entry of an unknown, $n\times d$ matrix $M$…

Machine Learning · Computer Science 2026-01-21 Hongyang R. Zhang , Zhenshuo Zhang , Huy L. Nguyen , Guanghui Lan

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

Recommender systems are essential tools in the digital landscape for connecting users with content that more closely aligns with their preferences. Matrix completion is a widely used statistical framework for such systems, aiming to predict…

Machine Learning · Statistics 2025-07-30 Aurore Archimbaud , Andreas Alfons , Ines Wilms

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 completing high-dimensional matrices from a limited set of observations arises in many big data applications, especially, recommender systems. Existing matrix completion models generally follow either a memory- or a…

Machine Learning · Computer Science 2019-09-30 Duc Minh Nguyen , Robert Calderbank , Nikos Deligiannis

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

We present new deterministic algorithms for several cases of the maximum rank matrix completion problem (for short matrix completion), i.e. the problem of assigning values to the variables in a given symbolic matrix as to maximize the…

Data Structures and Algorithms · Computer Science 2014-07-11 Gábor Ivanyos , Marek Karpinski , Nitin Saxena

We consider the low rank matrix completion problem over finite fields. This problem has been extensively studied in the domain of real/complex numbers, however, to the best of authors' knowledge, there exists merely one efficient algorithm…

Information Theory · Computer Science 2023-08-23 Mahdi Soleymani , Qiang Liu , Hessam Mahdavifar , Laura Balzano

Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of…

Optimization and Control · Mathematics 2011-08-09 Venkat Chandrasekaran , Sujay Sanghavi , Pablo A. Parrilo , Alan S. Willsky

The inductive matrix completion (IMC) problem is to recover a low rank matrix from few observed entries while incorporating prior knowledge about its row and column subspaces. In this work, we make three contributions to the IMC problem:…

Machine Learning · Computer Science 2022-02-01 Pini Zilber , Boaz Nadler

The low-rank matrix completion problem asks whether a given real matrix with missing values can be completed so that the resulting matrix has low rank or is close to a low-rank matrix. The completed matrix is often required to satisfy…

Computational Complexity · Computer Science 2025-06-24 Dror Chawin , Ishay Haviv

The matrix-completion problem has attracted a lot of attention, largely as a result of the celebrated Netflix competition. Two popular approaches for solving the problem are nuclear-norm-regularized matrix approximation (Candes and Tao,…

Methodology · Statistics 2014-10-10 Trevor Hastie , Rahul Mazumder , Jason Lee , Reza Zadeh