Do semidefinite relaxations solve sparse PCA up to the information limit?

Muirhead, Robb J.R. J. (1982). Aspects of Multivariate Statistical Theory. Wiley, New York

1982

Earlier work this paper cites.

Anderson, T. W.T. W. (1984). An Introduction to Multivariate Statistical Analysis, 2nd ed. Wiley, New York

1984

Earlier work this paper cites.

Stewart, G. W.G. W. andSun, Ji GuangJ. G. (1990). Matrix Perturbation Theory. Academic Press, Boston, MA

1990

Earlier work this paper cites.

Natarajan, B. K.B. K. (1995). Sparse approximate solutions to linear systems. SIAM J. Comput. 24 227–234

1995

Earlier work this paper cites.

Alon, NogaN., Krivelevich, MichaelM. andSudakov, BennyB. (1998). Finding a large hidden clique in a random graph. Random Structures Algorithms 13 457–466

1998

Earlier work this paper cites.

Sturm, Jos F.J. F. (1999). Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw. 11/12 625–653

1999

Earlier work this paper cites.

Feige, UrielU. andKrauthgamer, RobertR. (2000). Finding and certifying a large hidden clique in a semirandom graph. Random Structures Algorithms 16 195–208

2000

Earlier work this paper cites.

Laurent, B.B. andMassart, P.P. (2000). Adaptive estimation of a quadratic functional by model selection. Ann. Statist. 28 1302–1338

2000

Earlier work this paper cites.

Johnstone, Iain M.I. M. (2001). On the distribution of the largest eigenvalue in principal components analysis. Ann. Statist. 29 295–327

2001

Earlier work this paper cites.

Jolliffe, I. T.I. T. (2002). Principal Component Analysis, 2nd ed. Springer, New York

2002

Earlier work this paper cites.

Ledoit, OlivierO. andWolf, MichaelM. (2002). Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size. Ann. Statist. 30 1081–1102

2002

Earlier work this paper cites.

Zhang, ZhenyueZ., Zha, HongyuanH. andSimon, HorstH. (2002). Low-rank approximations with sparse factors. I. Basic algorithms and error analysis. SIAM J. Matrix Anal. Appl. 23 706–727 (electronic)

2002

Earlier work this paper cites.

El-Karoui, N.N. (2003). On the largest eigenvalue of wishart matrices with identity covariance when n , p n,p and p / n → ∞ p/n\to\infty . Available at \arxivurl

2003

Earlier work this paper cites.

Jolliffe, Ian T.I. T., Trendafilov, Nickolay T.N. T. andUddin, MudassirM. (2003). A modified principal component technique based on the LASSO. J. Comput. Graph. Statist. 12 531–547

2003

Earlier work this paper cites.

d’Aspremont, A.A., El-Ghaoui, L.L., Jordan, M.M. andLanckriet, G.G. (2004). A direct formulation for sparse PCA using semidefinite programming. SIAM Rev. 49 434–448

2004

Cited alongside, same era.

Baik, JinhoJ. andSilverstein, Jack W.J. W. (2006). Eigenvalues of large sample covariance matrices of spiked population models. J. Multivariate Anal. 97 1382–1408

2006

Cited alongside, same era.

Moghaddam, B.B., Weiss, S.S. andAvidan, Y.Y. (2006). Generalized spectral bounds for sparse LDA. In Proceedings of the 23rd International Conference on Machine Learning 641–648. ACM, New York

2006

Cited alongside, same era.

Moghaddam, B.B., Weiss, Y.Y. andAvidan, S.S. (2006). Spectral bounds for sparse PCA: Exact and greedy algorithms. In Advances in Neural Information Processing Systems 915–922. MIT Press, Cambridge

2006

Cited alongside, same era.

Zou, HuiH., Hastie, TrevorT. andTibshirani, RobertR. (2006). Sparse principal component analysis. J. Comput. Graph. Statist. 15 265–286

Ames, Brendan P. W.B. P. W. andVavasis, Stephen A.S. A. (2011). Nuclear norm minimization for the planted clique and biclique problems. Math. Program. 129 69–89

2011

Later among the works it cites.

Lu, ZhaosongZ. andZhang, YongY. (2012). An augmented Lagrangian approach for sparse principal component analysis. Math. Program. 135 149–193

2012

Later among the works it cites.

Berthet, QuentinQ. andRigollet, PhilippeP. (2013). Optimal detection of sparse principal components in high dimension. Ann. Statist. 41 1780–1815

2013

Closest in time.

Berthet, QuentinQ. andRigollet, PhilippeP. (2013). Complexity theoretic lower bounds for sparse principal component detection. In COLT

2013

Closest in time.

Birnbaum, AharonA., Johnstone, Iain M.I. M., Nadler, BoazB. andPaul, DebashisD. (2013). Minimax bounds for sparse PCA with noisy high-dimensional data. Ann. Statist. 41 1055–1084