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167
Matrix Completion with Noise
"... 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 incomplete, and perhaps even corrupted, information. In its simplest ..."
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Cited by 255 (13 self)
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that matrix completion is provably accurate even when the few observed entries are corrupted with a small amount of noise. A typical result is that one can recover an unknown n × n matrix of low rank r from just about nr log 2 n noisy samples with an error which is proportional to the noise level. We present
Matrix completion from noisy entries
 Journal of Machine Learning Research
"... Abstract Given a matrix M of lowrank, we consider the problem of reconstructing it from noisy observations of a small, random subset of its entries. The problem arises in a variety of applications, from collaborative filtering (the 'Netflix problem') to structurefrommotion and position ..."
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Cited by 124 (8 self)
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Abstract Given a matrix M of lowrank, we consider the problem of reconstructing it from noisy observations of a small, random subset of its entries. The problem arises in a variety of applications, from collaborative filtering (the 'Netflix problem') to structure
Nuclear norm penalization and optimal rates for noisy low rank matrix completion.
 Annals of Statistics,
, 2011
"... AbstractThis paper deals with the trace regression model where n entries or linear combinations of entries of an unknown m1 × m2 matrix A0 corrupted by noise are observed. We propose a new nuclear norm penalized estimator of A0 and establish a general sharp oracle inequality for this estimator for ..."
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Cited by 107 (7 self)
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for arbitrary values of n, m1, m2 under the condition of isometry in expectation. Then this method is applied to the matrix completion problem. In this case, the estimator admits a simple explicit form and we prove that it satisfies oracle inequalities with faster rates of convergence than in the previous works
Lowrank matrix and tensor completion via adaptive sampling,” arXiv preprint arXiv:1304.4672
, 2013
"... We study low rank matrix and tensor completion and propose novel algorithms that employ adaptive sampling schemes to obtain strong performance guarantees. Our algorithms exploit adaptivity to identify entries that are highly informative for learning the column space of the matrix (tensor) and conseq ..."
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Cited by 14 (2 self)
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We study low rank matrix and tensor completion and propose novel algorithms that employ adaptive sampling schemes to obtain strong performance guarantees. Our algorithms exploit adaptivity to identify entries that are highly informative for learning the column space of the matrix (tensor
LowRank Tensor Completion with SpatioTemporal Consistency
"... Video completion is a computer vision technique to recover the missing values in video sequences by filling the unknown regions with the known information. In recent research, tensor completion, a generalization of matrix completion for higher order data, emerges as a new solution to estimate the m ..."
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Video completion is a computer vision technique to recover the missing values in video sequences by filling the unknown regions with the known information. In recent research, tensor completion, a generalization of matrix completion for higher order data, emerges as a new solution to estimate
Lowrank matrix completion with noisy observations: A quantitative comparison
 in The 47th Annual Allerton Conference on Communication, Control, and Computing
, 2009
"... ar ..."
Noisy Tensor Completion via the SumofSquares Hierarchy
, 2016
"... Abstract In the noisy tensor completion problem we observe m entries (whose location is chosen uniformly at random) from an unknown n 1 × n 2 × n 3 tensor T . We assume that T is entrywise close to being rank r. Our goal is to fill in its missing entries using as few observations as possible. Let ..."
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Abstract In the noisy tensor completion problem we observe m entries (whose location is chosen uniformly at random) from an unknown n 1 × n 2 × n 3 tensor T . We assume that T is entrywise close to being rank r. Our goal is to fill in its missing entries using as few observations as possible. Let
Minimal Entropy of States Emerging from Noisy Quantum Channels
 IEEE Trans. Info. Theory
, 2001
"... In this paper, we consider the minimal entropy of twoqubit states transmitted through two uses of a noisy quantum channel, which is modeled by the action of a completely positive tracepreserving (or stochastic) map. We provide strong support for the conjecture that this minimal entropy is additive ..."
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Cited by 92 (21 self)
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In this paper, we consider the minimal entropy of twoqubit states transmitted through two uses of a noisy quantum channel, which is modeled by the action of a completely positive tracepreserving (or stochastic) map. We provide strong support for the conjecture that this minimal entropy
Results 1  10
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167