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Rank minimization over finite fields: Fundamental limits and codingtheoretic interpretations
 IEEE Trans. Inform. Theory
, 2012
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Imp: A messagepassing algorithm for matrix completion
 in Proc. 6th Int. Symp. Turbo Codes Iterative Inf. Process. (ISTC), 2010
"... Abstract—A new messagepassing (MP) method is considered for the matrix completion problem associated with recommender systems. We attack the problem using a (generative) factor graph model that is related to a probabilistic lowrank matrix factorization. Based on the model, we propose a new algorit ..."
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Abstract—A new messagepassing (MP) method is considered for the matrix completion problem associated with recommender systems. We attack the problem using a (generative) factor graph model that is related to a probabilistic lowrank matrix factorization. Based on the model, we propose a new algorithm, termed IMP, for the recovery of a data matrix from incomplete observations. The algorithm is based on a clustering followed by inference via MP (IMP). The algorithm is compared with a number of other matrix completion algorithms on real collaborative filtering (e.g., Netflix) data matrices. Our results show that, while many methods perform similarly with a large number of revealed entries, the IMP algorithm outperforms all others when the fraction of observed entries is small. This is helpful because it reduces the wellknown coldstart problem associated with collaborative filtering (CF) systems in practice. I.
Rank minimization over finite fields
 in Intl. Symp. Inf. Th., (St
, 2011
"... Abstract—This paper establishes informationtheoretic limits in estimating a finite field lowrank matrix given random linear measurements of it. Necessary and sufficient conditions on the number of measurements required are provided. It is shown that these conditions are sharp. The reliability func ..."
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Abstract—This paper establishes informationtheoretic limits in estimating a finite field lowrank matrix given random linear measurements of it. Necessary and sufficient conditions on the number of measurements required are provided. It is shown that these conditions are sharp. The reliability function associated to the minimumrank decoder is also derived. Our bounds hold even in the case where the sensing matrices are sparse. Connections to rankmetric codes are discussed.
Information theoretic bounds for tensor rank minimization
 in Proc. of Globecomm
, 2011
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Compressed Sensing, Group Testing and Matrix Completion in a Nutshell
"... Compressed sensing of sparse signals is a field that has become pervasive over the last decade, with interesting and strong theoretical guarantees, as well as practical applications across fields. The group testing problem arose several decades earlier in the context of blood testing for syphilis wh ..."
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Compressed sensing of sparse signals is a field that has become pervasive over the last decade, with interesting and strong theoretical guarantees, as well as practical applications across fields. The group testing problem arose several decades earlier in the context of blood testing for syphilis where very few patients had the disease and it was too expensive to test everyone independently. Matrix completion arises naturally in many applications due to incomplete available information. These problems share a lot of ideas, and in this survey we aim to pose the problems in a common framework and discuss the relations between them. 1
Joint Schatten pnorm and pnorm robust matrix completion for . . .
 KNOWL INF SYST
, 2013
"... The lowrank matrix completion problem is a fundamental machine learning and data mining problem with many important applications. The standard lowrank matrix completion methods relax the rank minimization problem by the trace norm minimization. However, this relaxation may make the solution ser ..."
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The lowrank matrix completion problem is a fundamental machine learning and data mining problem with many important applications. The standard lowrank matrix completion methods relax the rank minimization problem by the trace norm minimization. However, this relaxation may make the solution seriously deviate from the original solution. Meanwhile, most completion methods minimize the squared prediction errors on the observed entries, which is sensitive to outliers. In this paper, we propose a new robust matrix completion method to address these two problems. The joint Schatten pnorm and pnorm are used to better approximate the rank minimization problem and enhance the robustness to outliers. The extensive experiments are performed on both synthetic data and realworld applications in collaborative filtering prediction and social network link recovery. All empirical results show that our new method outperforms the standard matrix completion methods.