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Over the past few years, trace regression models have received considerable attention in the context of matrix completion, quantum state tomography, and compressed sensing.
Matrix Analysis
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The phase retrieval problem
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Handbook of the Geometry of Banach Spaces
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Using the Nyström method to speed up kernel machines
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Learning with kernels
B. Schölkopf and A. Smola · 2002
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Convex Optimization
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Maximum margin matrix factorization
N. Srebro, J. Rennie, and T. Jaakola · 2005
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On the uniqueness of nonnegative sparse solutions to underdetermined systems of equations
A. Bruckstein, M. Elad, and M. Zibulevsky · 2008
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Exact matrix completion via convex optimization
E. Candes and B. Recht · 2009
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Conditions for a Unique Non-negative Solution to an Underdetermined System
M. Wang and A. Tang · 2009
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Counting the faces of randomly-projected hypercubes and orthants, with applications
D. Donoho and J. Tanner · 2010
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Quantum State Tomography via Compressed Sensing
D. Gross, Y.-K. Liu, S. Flammia, S. Becker, and J. Eisert · 2010
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Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization
B. Recht, M. Fazel, and P. Parillo · 2010
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Tight oracle bounds for low-rank matrix recovery from a minimal number of noisy measurements
E. Candes and Y. Plan · 2011
A unique ’nonnegative’ solution to an underdetermined system: from vectors to matrices
M. Wang, W. Xu, and A. Tang · 2011
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PhaseLift: exact and stable signal recovery from magnitude measurements via convex programming
E. Candes, T. Strohmer, and V. Voroninski · 2012
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Topics in Random Matrix Theory
T. Tao · 2012
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How close is the sample covariance matrix to the actual covariance matrix ?
R. Vershynin · 2012
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Sign-constrained least squares estimation for high-dimensional regression
N. Meinshausen · 2013
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Non-negative least squares for high-dimensional linear models: consistency and sparse recovery without regularization
M. Slawski and M. Hein · 2013
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Von Neumann entropy penalization and low-rank matrix estimation
V. Koltchinskii · 2011
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Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion
V. Koltchinskii, K. Lounici, and A. Tsybakov · 2011
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Estimation of (near) low-rank matrices with noise and high-dimensional scaling
S. Negahban and M. Wainwright · 2011
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Estimation of high-dimensional low-rank matrices
A. Rohde and A. Tsybakov · 2011
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http://cbcl.mit.edu/software-datasets/FaceData2.html
CBCL face dataset
Cited in the paper.
Exact and Stable Covariance Estimation from Quadratic Sampling via Convex Programming
Y. Chen, Y. Chi, and A. Goldsmith
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Living on the edge: phase transitions in convex programs with random data
D. Amelunxen, M. Lotz, M. McCoy, and J. Tropp · 2014
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Solving quadratic equations via PhaseLift when there are about as many equations as unknowns
E. Candes and X. Li · 2014
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User-friendly tools for random matrices: An introduction
J. Tropp · 2014
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ROP: Matrix recovery via rank-one projections
T. Cai and A. Zhang · 2015
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