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Volumn 22, Issue , 2012, Pages 1278-1286

Minimax rates of estimation for sparse PCA in high dimensions

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE;

EID: 84898952632     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Conference Paper
Times cited : (85)

References (27)
  • 1
    • 69049101180 scopus 로고    scopus 로고
    • Highdimensional analysis of semidefinite relaxations for sparse principal components
    • A. A. Amini and M. J. Wainwright. "Highdimensional analysis of semidefinite relaxations for sparse principal components". In: Annals of Statistics 37.5B (2009), pp. 2877-2921.
    • (2009) Annals of Statistics , vol.37 , Issue.5 B , pp. 2877-2921
    • Amini, A.A.1    Wainwright, M.J.2
  • 2
    • 62349112885 scopus 로고    scopus 로고
    • Covariance regularization by thresholding
    • P. J. Bickel and E. Levina. "Covariance Regularization by Thresholding". In: Annals of Statistics 36.6 (2008), pp. 2577-2604.
    • (2008) Annals of Statistics , vol.36 , Issue.6 , pp. 2577-2604
    • Bickel, P.J.1    Levina, E.2
  • 3
    • 41549106844 scopus 로고    scopus 로고
    • Regularized estimation of large covariance matrices
    • P. J. Bickel and E. Levina. "Regularized estimation of large covariance matrices". In: Annals of Statistics 36.1 (2008), pp. 199-227.
    • (2008) Annals of Statistics , vol.36 , Issue.1 , pp. 199-227
    • Bickel, P.J.1    Levina, E.2
  • 4
    • 0000492892 scopus 로고    scopus 로고
    • Minimum contrast estimators on sieves: Exponential bounds and rates of convergence
    • L Birgé and P Massart. "Minimum contrast estimators on sieves: exponential bounds and rates of convergence". In: Bernoulli 4.3 (1998), pp. 329-375.
    • (1998) Bernoulli , vol.4 , Issue.3 , pp. 329-375
    • Birgé, L.1    Massart, P.2
  • 5
    • 77955132618 scopus 로고    scopus 로고
    • Optimal rates of convergence for covariance matrix estimation
    • T. T. Cai, C.-H. Zhang, and H. H. Zhou. "Optimal rates of convergence for covariance matrix estimation". In: Annals of Statistics 38.4 (2010), pp. 2118-2144.
    • (2010) Annals of Statistics , vol.38 , Issue.4 , pp. 2118-2144
    • Cai, T.T.1    Zhang, C.-H.2    Zhou, H.H.3
  • 6
    • 34548514458 scopus 로고    scopus 로고
    • A direct formulation for sparse PCA using semidefinite programming
    • A. d'Aspremont, L. El Ghaoui, M. I. Jordan, and G. R. G. Lanckriet. "A direct formulation for sparse PCA using semidefinite programming". In: SIAM Review 49.3 (2007), pp. 434-448.
    • (2007) SIAM Review , vol.49 , Issue.3 , pp. 434-448
    • D'Aspremont, A.1    El Ghaoui, L.2    Jordan, M.I.3    Lanckriet, G.R.N.G.4
  • 7
    • 62349123505 scopus 로고    scopus 로고
    • Operator norm consistent estimation of large-dimensional sparse covariance matrices
    • N. El Karoui. "Operator norm consistent estimation of large-dimensional sparse covariance matrices". In: Annals of Statistics 36.6 (2008), pp. 2717-2756.
    • (2008) Annals of Statistics , vol.36 , Issue.6 , pp. 2717-2756
    • El Karoui, N.1
  • 8
    • 35648994961 scopus 로고    scopus 로고
    • Gaussian averages of interpolated bodies and applications to approximate reconstruction
    • Y. Gordon, A. Litvak, S. Mendelson, and A. Pajor. "Gaussian averages of interpolated bodies and applications to approximate reconstruction". In: Journal of Approximation Theory 149 (2007), pp. 59-73.
    • (2007) Journal of Approximation Theory , vol.149 , pp. 59-73
    • Gordon, Y.1    Litvak, A.2    Mendelson, S.3    Pajor, A.4
  • 11
    • 0035641726 scopus 로고    scopus 로고
    • On the distribution of the largest eigenvalue in principal components analysis
    • I. M. Johnstone. "On the distribution of the largest eigenvalue in principal components analysis". In: Annals of Statistics 29.2 (2001), pp. 295-327.
    • (2001) Annals of Statistics , vol.29 , Issue.2 , pp. 295-327
    • Johnstone, I.M.1
  • 12
    • 66549088006 scopus 로고    scopus 로고
    • On consistency and sparsity for principal components analysis in high dimensions
    • I. M. Johnstone and A. Y. Lu. "On consistency and sparsity for principal components analysis in high dimensions". In: Journal of the American Statistical Association 104.486 (2009), pp. 682-693.
    • (2009) Journal of the American Statistical Association , vol.104 , Issue.486 , pp. 682-693
    • Johnstone, I.M.1    Lu, A.Y.2
  • 14
    • 80053050337 scopus 로고    scopus 로고
    • Deflation methods for sparse PCA
    • Ed. by D. Koller D. Schuurmans, Y. Bengio, and L. Bottou
    • L. Mackey. "Deflation methods for sparse PCA". In: Advances in Neural Information Processing Systems 21. Ed. by D. Koller, D. Schuurmans, Y. Bengio, and L. Bottou. 2009, pp. 1017-1024.
    • (2009) Advances in Neural Information Processing Systems , vol.21 , pp. 1017-1024
    • Mackey, L.1
  • 16
    • 77958490141 scopus 로고    scopus 로고
    • Empirical processes with a bounded !1 diameter
    • S. Mendelson. "Empirical processes with a bounded !1 diameter". In: Geometric and Functional Analysis 20.4 (2010), pp. 988-1027.
    • (2010) Geometric and Functional Analysis , vol.20 , Issue.4 , pp. 988-1027
    • Mendelson, S.1
  • 17
    • 62349121558 scopus 로고    scopus 로고
    • Finite sample approximation results for principal component analysis: A matrix perturbation approach
    • B. Nadler. "Finite sample approximation results for principal component analysis: A matrix perturbation approach". In: Annals of Statistics 36.6 (2008), pp. 2791-2817.
    • (2008) Annals of Statistics , vol.36 , Issue.6 , pp. 2791-2817
    • Nadler, B.1
  • 18
    • 38549175880 scopus 로고    scopus 로고
    • Asymptotics of sample eigenstructure for a large dimensional spiked covariance model
    • D. Paul. "Asymptotics of sample eigenstructure for a large dimensional spiked covariance model". In: Statistica Sinica 17 (2007), pp. 1617-1642.
    • (2007) Statistica Sinica , vol.17 , pp. 1617-1642
    • Paul, D.1
  • 20
    • 80053974183 scopus 로고    scopus 로고
    • Minimax rates of estimation for high-dimensional linear regression over Q-balls
    • to appear
    • G. Raskutti,M. J. Wainwright, and B. Yu. "Minimax rates of estimation for high-dimensional linear regression over "q-balls". In: IEEE Transactions on Information Theory (2011). to appear.
    • (2011) IEEE Transactions on Information Theory
    • Raskutti, G.1    Wainwright, M.J.2    Yu, B.3
  • 21
    • 43049086717 scopus 로고    scopus 로고
    • Sparse principal component analysis via regularized low rank matrix approximation
    • H. Shen and J. Z. Huang. "Sparse principal component analysis via regularized low rank matrix approximation". In: Journal of Multivariate Analysis 99 (2008), pp. 1015-1034.
    • (2008) Journal of Multivariate Analysis , vol.99 , pp. 1015-1034
    • Shen, H.1    Huang, J.Z.2
  • 25
    • 70149096300 scopus 로고    scopus 로고
    • A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis
    • D. M. Witten, R. Tibshirani, and T. Hastie. "A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis". In: Biostatistics 10 (2009), pp. 515-534.
    • (2009) Biostatistics , vol.10 , pp. 515-534
    • Witten, D.M.1    Tibshirani, R.2    Hastie, T.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.