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We study the problem of detecting the presence of a single unknown spike in a rectangular data matrix, in a high-dimensional regime where the spike has fixed strength and the aspect ratio of the matrix converges to a finite limit.
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Probabilistic methods in the geometry of Banach spaces
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Some rigorous results on the Sherrington–Kirkpatrick spin glass model
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Guerra, F. and Toninelli, F. L. (2002) · 2002
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Péché, S. (2006) · 2006
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Féral, D. and Péché, S. (2007) · 2007
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Asymptotics of sample eigenstructure for a large dimensional spiked covariance model
Paul, D. (2007) · 2007
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Mean field models for spin glasses: some obnoxious problems
Talagrand, M. (2007) · 2007
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Central limit theorems for eigenvalues in a spiked population model
Bai, Z. and Yao, J.-f. (2008) · 2008
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Nadler, B. (2008) · 2008
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Amini, A. A. and Wainwright, M. J. (2009) · 2009
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Korada, S. B. and Macris, N. (2009) · 2009
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Barra, A., Genovese, G., and Guerra, F. (2011) · 2011
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Testing in high-dimensional spiked models
Johnstone, I. M. and Onatski, A. (2015) · 2015
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MMSE of probabilistic low-rank matrix estimation: Universality with respect to the output channel
Lesieur, T., Krzakala, F., and Zdeborová, L. (2015a) · 2015
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On the limitation of spectral methods: From the gaussian hidden clique problem to rank-one perturbations of gaussian tensors
Montanari, A., Reichman, D., and Zeitouni, O. (2015) · 2015
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The free energy in a multi-species Sherrington–Kirkpatrick model
Panchenko, D. (2015) · 2015
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Fluctuations of the free energy of the spherical Sherrington–Kirkpatrick model
Baik, J. and Lee, J. O. (2016) · 2016
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Benaych-Georges, F. and Nadakuditi, R. R. (2011) · 2011
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Bai, Z. and Yao, J. (2012) · 2012
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The singular values and vectors of low rank perturbations of large rectangular random matrices
Benaych-Georges, F. and Nadakuditi, R. R. (2012) · 2012
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Optimal detection of sparse principal components in high dimension
Berthet, Q. and Rigollet, P. (2013) · 2013
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Concentration Inequalities: A Nonasymptotic Theory of Independence
Boucheron, S., Lugosi, G., and Massart, P. (2013) · 2013
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Asymptotic power of sphericity tests for high-dimensional data
Onatski, A., Moreira, M. J., and Hallin, M. (2013) · 2013
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Free energy and complexity of spherical bipartite models
Auffinger, A. and Chen, W.-K. (2014) · 2014
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Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula
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Mutual information in rank-one matrix estimation
Krzakala, F., Xu, J., and Zdeborová, L. (2016) · 2016
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On the optimality and sub-optimality of PCA for spiked random matrix models
Perry, A., Wein, A. S., Bandeira, A. S., and Moitra, A. (2016) · 2016
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Banks, J., Moore, C., Vershynin, R., Verzelen, N., and Xu, J. (2017) · 2017
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Phase transitions, optimal errors and optimality of message-passing in generalized linear models
Barbier, J., Krzakala, F., Macris, N., Miolane, L., and Zdeborová, L. (2017) · 2017
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Dobriban, E. (2017) · 2017
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Finite size corrections and likelihood ratio fluctuations in the spiked Wigner model
El Alaoui, A., Krzakala, F., and Jordan, M. I. (2017) · 2017
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Fundamental limits of symmetric low-rank matrix estimation
Lelarge, M. and Miolane, L. (2017) · 2017
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Constrained low-rank matrix estimation: Phase transitions, approximate message passing and applications
Lesieur, T., Krzakala, F., and Zdeborová, L. (2017) · 2017
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Fundamental limits of low-rank matrix estimation
Miolane, L. (2017) · 2017
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