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We consider the related tasks of matrix completion and matrix approximation from missing data and propose adaptive sampling procedures for both problems.
Fast monte-carlo algorithms for finding low-rank approximations
Alan Frieze, Ravi Kannan, and Santosh Vempala · 2004
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A fast random sampling algorithm for sparsifying matrices
Sanjeev Arora, Elad Hazan, and Satyen Kale · 2006
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Fast computation of low-rank matrix approximations
Dimitris Achlioptas and Frank Mcsherry · 2007
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Sampling from large matrices: An approach through geometric functional analysis
Mark Rudelson and Roman Vershynin · 2007
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An introduction to compressive sampling
Emmanuel J. Candès and Michael .B. Wakin · 2008
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Relative-error CUR matrix decompositions
Petros Drineas, Michael W. Mahoney, and S. Muthukrishnan · 2008
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An improved approximation algorithm for the column subset selection problem
Christos Boutsidis, Michael W. Mahoney, and Petros Drineas · 2009
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Exact matrix completion via convex optimization
Emmanuel J. Candès and Benjamin Recht · 2009
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High-dimensional matched subspace detection when data are missing
Laura Balzano, Benjamin Recht, and Robert Nowak · 2010
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A singular value thresholding algorithm for matrix completion
Jian-Feng Cai, Emmanuel J. Candès, and Zuowei Shen · 2010
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Matrix completion with noise
Emmanuel J Candès and Yaniv Plan · 2010
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The power of convex relaxation: Near-optimal matrix completion
Emmanuel J. Candès and Terence Tao · 2010
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Matrix completion from a few entries
Raghunandan H. Keshavan, Andrea Montanari, and Sewoong Oh · 2010
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Near optimal column-based matrix reconstruction
Christos Boutsidis, Petros Drineas, and Malik Magdon-Ismail · 2011
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The spectral norm error of the naive Nystrom extension
Alex Gittens · 2011
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Recovering low-rank matrices from few coefficients in any basis
David Gross · 2011
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Distilled sensing: Adaptive sampling for sparse detection and estimation
Jarvis Haupt, Rui Castro, and Robert Nowak · 2011
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Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion
Vladimir Koltchinskii, Karim Lounici, and Alexandre B. Tsybakov · 2011
Efficient active algorithms for hierarchical clustering
Akshay Krishnamurthy, Sivaraman Balakrishnan, Min Xu, and Aarti Singh · 2012
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Restricted strong convexity and weighted matrix completion: optimal bounds with noise
Sahand Negahban and Martin J. Wainwright · 2012
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Completion of high-rank ultrametric matrices using selective entries
Aarti Singh, Akshay Krishnamurthy, Sivaraman Balakrishnan, and Min Xu · 2012
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Near-optimal entrywise sampling for data matrices
Dimitris Achlioptas, Zohar S. Karnin, and Edo Liberty · 2013
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Incoherence-optimal matrix completion
Yudong Chen · 2013
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Understanding alternating minimization for matrix completion
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Sequential analysis in high-dimensional multiple testing and sparse recovery
Matthew Malloy and Robert Nowak · 2011
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A simpler approach to matrix completion
Benjamin Recht · 2011
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User-friendly tail bounds for sums of random matrices
Joel A. Tropp · 2011
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Recovering block-structured activations using compressive measurements
Sivaraman Balakrishnan, Mladen Kolar, Alessandro Rinaldo, and Aarti Singh · 2012
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Optimal column-based low-rank matrix reconstruction
Venkatesan Guruswami and Ali Kemal Sinop · 2012
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Fast Monte Carlo Algorithms for matrices II: Computing a low-rank approximation to a matrix
Petros Drineas, Ravi Kannan, and Michael W. Mahoney
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Moritz Hardt · 2013
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Low-rank matrix completion using alternating minimization
Prateek Jain, Praneeth Netrapalli, and Sujay Sanghavi · 2013
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Low-rank matrix and tensor completion via adaptive sampling
Akshay Krishnamurthy and Aarti Singh · 2013
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Recovering graph-structured activations using adaptive compressive measurements
Akshay Krishnamurthy, James Sharpnack, and Aarti Singh · 2013
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Adaptive sensing for estimation of structured sparse signals
Ervin Tánczos and Rui Castro · 2013
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Coherent matrix completion
Yudong Chen, Srinadh Bhojanapalli, Sujay Sanghavi, and Rachel Ward · 2014
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