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Volumn 41, Issue 6, 2013, Pages 2905-2947

Minimax sparse principal subspace estimation in high dimensions

Author keywords

Highdimensional statistics; Minimax bounds; Principal components analysis; Random matrices; Sparsity; Subspace estimation

Indexed keywords


EID: 84891937960     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/13-AOS1151     Document Type: Article
Times cited : (193)

References (37)
  • 1
    • 69049101180 scopus 로고    scopus 로고
    • High-dimensional analysis of semidefinite relaxations for sparse principal components
    • MR2541450
    • AMINI, A. A. and WAINWRIGHT, M. J. (2009). High-dimensional analysis of semidefinite relaxations for sparse principal components. Ann. Statist. 37 2877-2921. MR2541450
    • (2009) Ann. Statist , vol.37 , pp. 2877-2921
    • Amini, A.A.1    Wainwright, M.J.2
  • 3
    • 84879351019 scopus 로고    scopus 로고
    • Minimax bounds for sparse PCA with noisy high-dimensional data
    • MR3113803
    • BIRNBAUM, A., JOHNSTONE, I.M., NADLER, B. and PAUL, D. (2013). Minimax bounds for sparse PCA with noisy high-dimensional data. Ann. Statist. 41 1055-1084. MR3113803
    • (2013) Ann. Statist , vol.41 , pp. 1055-1084
    • Birnbaum, A.1    Johnstone, I.M.2    Nadler, B.3    Paul, D.4
  • 4
    • 78349234492 scopus 로고    scopus 로고
    • Coordinate-independent sparse sufficient dimension reduction and variable selection
    • MR2766865
    • CHEN, X., ZOU, C. and COOK, R. D. (2010). Coordinate-independent sparse sufficient dimension reduction and variable selection. Ann. Statist. 38 3696-3723. MR2766865
    • (2010) Ann. Statist , vol.38 , pp. 3696-3723
    • Chen, X.1    Zou, C.2    Cook, R.D.3
  • 6
    • 34548514458 scopus 로고    scopus 로고
    • A direct formulation for sparse PCA using semidefinite programming
    • (electronic). MR2353806
    • D'ASPREMONT, A., EL GHAOUI, L., JORDAN, M. I. and LANCKRIET, G. R. G. (2007). A direct formulation for sparse PCA using semidefinite programming. SIAM Rev. 49 434-448 (electronic). MR2353806
    • (2007) SIAM Rev , vol.49 , pp. 434-448
    • D'Aspremont, A.1    El Ghaoui, L.2    Jordan, M.I.3    Lanckriet, G.R.G.4
  • 8
    • 0032216898 scopus 로고    scopus 로고
    • The geometry of algorithms with orthogonality constraints
    • MR1646856
    • EDELMAN, A., ARIAS, T. A. and SMITH, S. T. (1999). The geometry of algorithms with orthogonality constraints. SIAM J. Matrix Anal. Appl. 20 303-353. MR1646856
    • (1999) SIAM J. Matrix Anal. Appl , vol.20 , pp. 303-353
    • Edelman, A.1    Arias, T.A.2    Smith, S.T.3
  • 9
    • 0001287361 scopus 로고
    • A comparison of signalling alphabets
    • GILBERT, E. N. (1952). A comparison of signalling alphabets. Bell System Technical Journal 31 504522.
    • (1952) Bell System Technical Journal , vol.31 , pp. 504522
    • Gilbert, E.N.1
  • 10
    • 58149421595 scopus 로고
    • Analysis of a complex of statistical variables into principal components
    • HOTELLING, H. (1933). Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology 24 498520.
    • (1933) Journal of Educational Psychology , vol.24 , pp. 498520
    • Hotelling, H.1
  • 11
    • 66549088006 scopus 로고    scopus 로고
    • On consistency and sparsity for principal components analysis in high dimensions
    • MR2751448
    • JOHNSTONE, I. M. and LU, A. Y. (2009). On consistency and sparsity for principal components analysis in high dimensions. J. Amer. Statist. Assoc. 104 682-693. MR2751448
    • (2009) J. Amer. Statist. Assoc , vol.104 , pp. 682-693
    • Johnstone, I.M.1    Lu, A.Y.2
  • 12
    • 0141941674 scopus 로고    scopus 로고
    • A modified principal component technique based on the LASSO
    • MR2002634
    • JOLLIFFE, I. T., TRENDAFILOV, N. T. and UDDIN, M. (2003). A modified principal component technique based on the LASSO. J. Comput. Graph. Statist. 12 531-547. MR2002634
    • (2003) J. Comput. Graph. Statist , vol.12 , pp. 531-547
    • Jolliffe, I.T.1    Trendafilov, N.T.2    Uddin, M.3
  • 13
    • 77949527718 scopus 로고    scopus 로고
    • Generalized power method for sparse principal component analysis
    • MR2600619
    • JOURNÉE, M., NESTEROV, Y., RICHTÁRIK, P. and SEPULCHRE, R. (2010). Generalized power method for sparse principal component analysis. J. Mach. Learn. Res. 11 517-553. MR2600619
    • (2010) J. Mach. Learn. Res , vol.11 , pp. 517-553
    • Journée, M.1    Nesterov, Y.2    Richtárik, P.3    Sepulchre, R.4
  • 15
    • 85015082750 scopus 로고    scopus 로고
    • Sparse principal component analysis with missing observations
    • In High Dimensional Probability VI (C. Houdré, D. M. Mason, J. Rosínski and J. A. Wellner, eds.). Springer, Basel
    • LOUNICI, K. (2013). Sparse principal component analysis with missing observations. In High Dimensional Probability VI (C. Houdré, D. M. Mason, J. Rosínski and J. A. Wellner, eds.). Progress in Probability 66 327-356. Springer, Basel.
    • (2013) Progress in Probability , vol.66 , pp. 327-356
    • Lounici, K.1
  • 16
    • 84877623616 scopus 로고    scopus 로고
    • Sparse principal component analysis and iterative thresholding
    • MR3099121
    • MA, Z. (2013). Sparse principal component analysis and iterative thresholding. Ann. Statist. 41 772-801. MR3099121
    • (2013) Ann. Statist , vol.41 , pp. 772-801
    • Ma, Z.1
  • 18
    • 77958490141 scopus 로고    scopus 로고
    • Empirical processes with a bounded ψ1 diameter
    • MR2729283
    • MENDELSON, S. (2010). Empirical processes with a bounded ψ1 diameter. Geom. Funct. Anal. 20 988-1027. MR2729283
    • (2010) Geom. Funct. Anal , vol.20 , pp. 988-1027
    • Mendelson, S.1
  • 19
    • 62349121558 scopus 로고    scopus 로고
    • Finite sample approximation results for principal component analysis: A matrix perturbation approach
    • MR2485013
    • NADLER, B. (2008). Finite sample approximation results for principal component analysis: A matrix perturbation approach. Ann. Statist. 36 2791-2817. MR2485013
    • (2008) Ann. Statist , vol.36 , pp. 2791-2817
    • Nadler, B.1
  • 20
    • 84871600478 scopus 로고    scopus 로고
    • A unified framework for high-dimensional analysis of M-estimators with decomposable regularizers
    • MR3025133
    • NEGAHBAN, S. N., RAVIKUMAR, P., WAINWRIGHT, M. J. and YU, B. (2012). A unified framework for high-dimensional analysis of M-estimators with decomposable regularizers. Statist. Sci. 27 538-557. MR3025133
    • (2012) Statist. Sci , vol.27 , pp. 538-557
    • Negahban, S.N.1    Ravikumar, P.2    Wainwright, M.J.3    Yu, B.4
  • 21
    • 79952960554 scopus 로고    scopus 로고
    • Metric entropy of the Grassmannmanifold
    • (Berkeley, CA, 1996). Mathematical Sciences Research Institute Publications. Cambridge Univ. Press, Cambridge. MR1665590
    • PAJOR, A. (1998). Metric entropy of the Grassmannmanifold. In Convex Geometric Analysis (Berkeley, CA, 1996). Mathematical Sciences Research Institute Publications 34 181-188. Cambridge Univ. Press, Cambridge. MR1665590
    • (1998) Convex Geometric Analysis , vol.34 , pp. 181-188
    • Pajor, A.1
  • 22
    • 38549175880 scopus 로고    scopus 로고
    • Asymptotics of sample eigenstructure for a large dimensional spiked covariance model
    • MR2399865
    • PAUL, D. (2007). Asymptotics of sample eigenstructure for a large dimensional spiked covariance model. Statist. Sinica 17 1617-1642. MR2399865
    • (2007) Statist. Sinica , vol.17 , pp. 1617-1642
    • Paul, D.1
  • 23
    • 0000325341 scopus 로고
    • On lines and planes of closest fit to systems of points in space
    • PEARSON, K. (1901). On lines and planes of closest fit to systems of points in space. Philosophical Magazine 2 559572.
    • (1901) Philosophical Magazine , vol.2 , pp. 559572
    • Pearson, K.1
  • 24
    • 80053974183 scopus 로고    scopus 로고
    • Minimax rates of estimation for high-dimensional linear regression over ℓq balls
    • MR2882274
    • RASKUTTI, G., WAINWRIGHT, M. J. and YU, B. (2011). Minimax rates of estimation for high-dimensional linear regression over ℓq balls. IEEE Trans. Inform. Theory 57 6976-6994. MR2882274
    • (2011) IEEE Trans. Inform. Theory , vol.57 , pp. 6976-6994
    • Raskutti, G.1    Wainwright, M.J.2    Yu, B.3
  • 25
    • 43049086717 scopus 로고    scopus 로고
    • Sparse principal component analysis via regularized low rank matrix approximation
    • MR2419336
    • SHEN, H. and HUANG, J. Z. (2008). Sparse principal component analysis via regularized low rank matrix approximation. J. Multivariate Anal. 99 1015-1034. MR2419336
    • (2008) J. Multivariate Anal , vol.99 , pp. 1015-1034
    • Shen, H.1    Huang, J.Z.2
  • 26
    • 84869784137 scopus 로고    scopus 로고
    • Consistency of sparse PCA in high dimension, low sample size contexts
    • MR3004561
    • SHEN, D., SHEN, H. and MARRON, J. S. (2013). Consistency of sparse PCA in high dimension, low sample size contexts. J. Multivariate Anal. 115 317-333. MR3004561
    • (2013) J. Multivariate Anal , vol.115 , pp. 317-333
    • Shen, D.1    Shen, H.2    Marron, J.S.3
  • 28
    • 0001287271 scopus 로고    scopus 로고
    • Regression shrinkage and selection via the lasso
    • MR1379242
    • TIBSHIRANI, R. (1996). Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B Stat. Methodol. 58 267-288. MR1379242
    • (1996) J. R. Stat. Soc. Ser. B Stat. Methodol , vol.58 , pp. 267-288
    • Tibshirani, R.1
  • 30
    • 0000479182 scopus 로고
    • The evaluation of signals in codes with correction of errors
    • MR0095090
    • VARŠAMOV, R. R. (1957). The evaluation of signals in codes with correction of errors. Dokl. Akad. Nauk SSSR (N.S) 117 739-741. MR0095090
    • (1957) Dokl. Akad. Nauk SSSR (N.S) , vol.117 , pp. 739-741
    • Varšamov, R.R.1
  • 33
    • 70149096300 scopus 로고    scopus 로고
    • A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis
    • WITTEN, D.M., TIBSHIRANI, R. and HASTIE, T. (2009). A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis. Biostatistics 10 515534.
    • (2009) Biostatistics , vol.10 , pp. 515534
    • Witten, D.M.1    Tibshirani, R.2    Hastie, T.3
  • 34
    • 17644388356 scopus 로고    scopus 로고
    • Assouad, Fano, and Le Cam
    • (D. Pollard, E. Torgersen and G. L. Yang, eds.). Springer, New York
    • YU, B. (1997). Assouad, Fano, and Le Cam. In Festschrift for Lucien Le Cam (D. Pollard, E. Torgersen and G. L. Yang, eds.) 423-435. Springer, New York.
    • (1997) Festschrift for Lucien le Cam , pp. 423-435
    • Yu, B.1
  • 35
    • 33645035051 scopus 로고    scopus 로고
    • Model selection and estimation in regression with grouped variables
    • MR2212574
    • YUAN, M. and LIN, Y. (2006). Model selection and estimation in regression with grouped variables. J. R. Stat. Soc. Ser. B Stat. Methodol. 68 49-67. MR2212574
    • (2006) J. R. Stat. Soc. Ser. B Stat. Methodol , vol.68 , pp. 49-67
    • Yuan, M.1    Lin, Y.2
  • 36
    • 69949155103 scopus 로고    scopus 로고
    • The composite absolute penalties family for grouped and hierarchical variable selection
    • MR2549566
    • ZHAO, P., ROCHA, G. and YU, B. (2009). The composite absolute penalties family for grouped and hierarchical variable selection. Ann. Statist. 37 3468-3497. MR2549566
    • (2009) Ann. Statist , vol.37 , pp. 3468-3497
    • Zhao, P.1    Rocha, G.2    Yu, B.3


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