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Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…

Statistics Theory · Mathematics 2021-05-06 Yunhua Xiang , Tianyu Zhang , Xu Wang , Ali Shojaie , Noah Simon

This paper studies the problem of completing a low-rank matrix from a few of its random entries with the aid of prior information. We suggest a strategy to incorporate prior information into the standard matrix completion procedure by…

Information Theory · Computer Science 2020-07-15 Xu Zhang , Wei Cui , Yulong Liu

In this paper we study covariance estimation with missing data. We consider missing data mechanisms that can be independent of the data, or have a time varying dependency. Additionally, observed variables may have arbitrary (non uniform)…

Statistics Theory · Mathematics 2021-06-17 Eduardo Pavez , Antonio Ortega

Model selection and assessment with incomplete data pose challenges in addition to the ones encountered with complete data. There are two main reasons for this. First, many models describe characteristics of the complete data, in spite of…

Methodology · Statistics 2008-08-28 Geert Verbeke , Geert Molenberghs , Caroline Beunckens

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

We present a novel algebraic combinatorial view on low-rank matrix completion based on studying relations between a few entries with tools from algebraic geometry and matroid theory. The intrinsic locality of the approach allows for the…

Machine Learning · Computer Science 2014-08-20 Franz J. Király , Louis Theran , Ryota Tomioka

This paper examines the problem of state estimation in power distribution systems under low-observability conditions. The recently proposed constrained matrix completion method which combines the standard matrix completion method and power…

Optimization and Control · Mathematics 2020-06-09 Yajing Liu , April Sagan , Andrey Bernstein , Rui Yang , Xinyang Zhou , Yingchen Zhang

In this paper, we consider matrix completion with absolute deviation loss and obtain an estimator of the median matrix. Despite several appealing properties of median, the non-smooth absolute deviation loss leads to computational challenge…

Machine Learning · Statistics 2020-06-19 Weidong Liu , Xiaojun Mao , Raymond K. W. Wong

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

Since there exist several completion methods to estimate the missing entries of pairwise comparison matrices, practitioners face a difficult task in choosing the best technique. Our paper contributes to this issue: we consider a special set…

Optimization and Control · Mathematics 2023-11-14 László Csató

We study the completion of approximately low rank matrices with entries missing not at random (MNAR). In the context of typical large-dimensional statistical settings, we establish a framework for the performance analysis of the nuclear…

Information Theory · Computer Science 2024-01-02 Agostino Capponi , Mihailo Stojnic

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

In this paper, we introduce the first method that (1) can complete kernel matrices with completely missing rows and columns as opposed to individual missing kernel values, (2) does not require any of the kernels to be complete a priori, and…

Machine Learning · Computer Science 2016-02-09 Sahely Bhadra , Samuel Kaski , Juho Rousu

Our capacity to process large complex data sources is ever-increasing, providing us with new, important applied research questions to address, such as how to handle missing values in large-scale databases. Mitra et al. (2023) noted the…

Methodology · Statistics 2023-07-07 James Jackson , Robin Mitra , Niels Hagenbuch , Sarah McGough , Chris Harbron

In this paper, we present a unified analysis of matrix completion under general low-dimensional structural constraints induced by {\em any} norm regularization. We consider two estimators for the general problem of structured matrix…

Machine Learning · Statistics 2018-11-26 Suriya Gunasekar , Arindam Banerjee , Joydeep Ghosh

Physics education researchers (PER) commonly use complete-case analysis to address missing data. For complete-case analysis, researchers discard all data from any student who is missing any data. Despite its frequent use, no PER article we…

Physics Education · Physics 2019-02-20 Jayson Nissen , Robin Donatello , Ben Van Dusen

Model-based unsupervised learning, as any learning task, stalls as soon as missing data occurs. This is even more true when the missing data are informative, or said missing not at random (MNAR). In this paper, we propose model-based…

Supervised learning with missing data aims at building the best prediction of a target output based on partially-observed inputs. Major approaches to address this problem can be decomposed into $(i)$ impute-then-predict strategies, which…

Statistics Theory · Mathematics 2024-10-14 Angel D Reyero Lobo , Alexis Ayme , Claire Boyer , Erwan Scornet

We compare two deletion-based methods for dealing with the problem of missing observations in linear regression analysis. One is the complete-case analysis (CC, or listwise deletion) that discards all incomplete observations and only uses…

Methodology · Statistics 2023-05-02 Tianchen Xu , Kun Chen , Gen Li

We offer a natural and extensible measure-theoretic treatment of missingness at random. Within the standard missing data framework, we give a novel characterisation of the observed data as a stopping-set sigma algebra. We demonstrate that…

Methodology · Statistics 2018-01-23 Daniel Farewell , Rhian Daniel , Shaun Seaman