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A well-known method for completing low-rank matrices based on convex optimization has been established by Cand{\`e}s and Recht. Although theoretically complete, the method may not entirely solve the low-rank matrix completion problem. This…

Methodology · Statistics 2014-07-17 Guangcan Liu , Ping Li

We revisit the inductive matrix completion problem that aims to recover a rank-$r$ matrix with ambient dimension $d$ given $n$ features as the side prior information. The goal is to make use of the known $n$ features to reduce sample and…

Machine Learning · Statistics 2018-03-06 Xiao Zhang , Simon S. Du , Quanquan Gu

We propose a theory for matrix completion that goes beyond the low-rank structure commonly considered in the literature and applies to general matrices of low description complexity. Specifically, complexity of the sets of matrices…

Information Theory · Computer Science 2024-10-03 Erwin Riegler , Günther Koliander , David Stotz , Helmut Bölcskei

The problem of completing a low-rank matrix from a subset of its entries is often encountered in the analysis of incomplete data sets exhibiting an underlying factor model with applications in collaborative filtering, computer vision and…

Machine Learning · Computer Science 2009-02-24 Amit Singer , Mihai Cucuringu

This paper considers the matrix completion problem. We show that it is not necessary to assume joint incoherence, which is a standard but unintuitive and restrictive condition that is imposed by previous studies. This leads to a sample…

Information Theory · Computer Science 2016-11-15 Yudong Chen

The aim of this note (as well as of the course itself) is to give a largely self-contained proof of two of the main results in the field of low-rank matrix recovery. This field aims for identification of low-rank matrices from only limited…

Functional Analysis · Mathematics 2016-09-27 Jan Vybiral

A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to…

Numerical Analysis · Mathematics 2018-10-30 Simon Foucart , Srinivas Subramanian

Completing a data matrix X has become an ubiquitous problem in modern data science, with applications in recommender systems, computer vision, and networks inference, to name a few. One typical assumption is that X is low-rank. A more…

Machine Learning · Computer Science 2018-08-03 Daniel L. Pimentel-Alarcón

In this paper, we study the popularly dubbed matrix completion problem, where the task is to "fill in" the unobserved entries of a matrix from a small subset of observed entries, under the assumption that the underlying matrix is of…

Computation · Statistics 2020-03-04 Rahul Mazumder , Diego F. Saldana , Haolei Weng

Modern surveys with large sample sizes and growing mixed-type questionnaires require robust and scalable analysis methods. In this work, we consider recovering a mixed dataframe matrix, obtained by complex survey sampling, with entries…

Methodology · Statistics 2024-02-07 Xiaojun Mao , Hengfang Wang , Zhonglei Wang , Shu Yang

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 the low-rank matrix completion (LRMC) problem, the low-rank assumption means that the columns (or rows) of the matrix to be completed are points on a low-dimensional linear algebraic variety. This paper extends this thinking to cases…

Machine Learning · Statistics 2020-09-08 Greg Ongie , Daniel Pimentel-Alarcón , Laura Balzano , Rebecca Willett , Robert D. Nowak

Matrix completion has attracted significant recent attention in many fields including statistics, applied mathematics and electrical engineering. Current literature on matrix completion focuses primarily on independent sampling models under…

Methodology · Statistics 2015-04-09 Tianxi Cai , T. Tony Cai , Anru Zhang

Many applications, including rank aggregation, crowd-labeling, and graphon estimation, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and/or columns. We consider the problem of estimating…

Machine Learning · Statistics 2019-10-29 Cheng Mao , Ashwin Pananjady , Martin J. Wainwright

We extend the theory of matrix completion to the case where we make Poisson observations for a subset of entries of a low-rank matrix. We consider the (now) usual matrix recovery formulation through maximum likelihood with proper…

Machine Learning · Statistics 2015-03-26 Yang Cao , Yao Xie

We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex…

Machine Learning · Statistics 2017-01-17 Xiao Zhang , Lingxiao Wang , Quanquan Gu

The problem of recovering a matrix of low rank from an incomplete and possibly noisy set of linear measurements arises in a number of areas. In order to derive rigorous recovery results, the measurement map is usually modeled…

Information Theory · Computer Science 2015-07-28 Maryia Kabanava , Richard Kueng , Holger Rauhut , Ulrich Terstiege

We study the recovery of Hermitian low rank matrices $X \in \mathbb{C}^{n \times n}$ from undersampled measurements via nuclear norm minimization. We consider the particular scenario where the measurements are Frobenius inner products with…

Information Theory · Computer Science 2014-10-28 Richard Kueng , Holger Rauhut , Ulrich Terstiege

This paper studies the open problem of conformalized entry prediction in a row/column-exchangeable matrix. The matrix setting presents novel and unique challenges, but there exists little work on this interesting topic. We meticulously…

Machine Learning · Computer Science 2023-06-07 Meijia Shao , Yuan Zhang

We consider two matrix completion problems, in which we are given a matrix with missing entries and the task is to complete the matrix in a way that (1) minimizes the rank, or (2) minimizes the number of distinct rows. We study the…

Data Structures and Algorithms · Computer Science 2018-09-14 Robert Ganian , Iyad Kanj , Sebastian Ordyniak , Stefan Szeider