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We study the statistical limits of testing and estimation for a rank one deformation of a Gaussian random tensor.
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Nan Li and Baoxin Li, Tensor completion for on-board compression of hyperspectral images , Image Processing (ICIP), 2010 17th IEEE International Conference on, IEEE, 2010, pp. 517–520
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by same author, Mean field models for spin glasses: Volume i: Basic examples , vol. 54, Springer Science & Business Media, 2010
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Florent Benaych-Georges and Raj Rao Nadakuditi, The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices , Advances in Mathematics 227
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2016
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Jess Banks, Cristopher Moore, Roman Vershynin, Nicolas Verzelen, and Jiaming Xu, Information-theoretic bounds and phase transitions in clustering, sparse pca, and submatrix localization , Information Theory (ISIT), 2017 IEEE International Symposium on, IEEE, 2017, pp. 1137–1141
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2011
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F. Benaych-Georges, A. Guionnet, and M. Maida, Large deviations of the extreme eigenvalues of random deformations of matrices , Probability Theory and Related Fields 154
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Alex Bloemendal and Bálint Virág, Limits of spiked random matrices i , Probability Theory and Related Fields 156
2013
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Stéphane Boucheron, Gábor Lugosi, and Pascal Massart, Concentration inequalities: A nonasymptotic theory of independence , Oxford university press, 2013
2013
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Wei-Kuo Chen, The Aizenman-Sims-Starr scheme and Parisi formula for mixed p p -spin spherical models , Electron. J. Probab. 18
2013
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Christopher J. Hillar and Lek-Heng Lim, Most tensor problems are np-hard , J. ACM 60
2013
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Dmitry Panchenko, The sherrington-kirkpatrick model , Springer, 2013
2013
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Animashree Anandkumar, Rong Ge, Daniel Hsu, Sham M Kakade, and Matus Telgarsky, Tensor decompositions for learning latent variable models , The Journal of Machine Learning Research 15
2014
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2017
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2017
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Wei-Kuo Chen and Arnab Sen, Parisi formula, disorder chaos and fluctuation for the ground state energy in the spherical mixed p-spin models , Communications in Mathematical Physics 350
2017
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Aukosh Jagannath and Ian Tobasco, Low temperature asymptotics of spherical mean field spin glasses , Communications in Mathematical Physics 352
2017
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Chiheon Kim, Afonso S Bandeira, and Michel X Goemans, Community detection in hypergraphs, spiked tensor models, and sum-of-squares , Sampling Theory and Applications (SampTA), 2017 International Conference on, IEEE, 2017, pp. 124–128
2017
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Thibault Lesieur, Florent Krzakala, and Lenka Zdeborová, Constrained low-rank matrix estimation: phase transitions, approximate message passing and applications , Journal of Statistical Mechanics: Theory and Experiment 2017
2017
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Thibault Lesieur, Léo Miolane, Marc Lelarge, Florent Krzakala, and Lenka Zdeborová, Statistical and computational phase transitions in spiked tensor estimation , 2017 IEEE International Symposium on Information Theory (ISIT) (2017), 511–515
2017
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2018
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