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Volumn 43, Issue 1, 2015, Pages 299-322

Sparsistency and agnostic inference in sparse PCA

Author keywords

Agnostic inference; Principal components analysis; Sparsity; Subspace estimation; Variable selection

Indexed keywords


EID: 84922565321     PISSN: 00905364     EISSN: 21688966     Source Type: Journal    
DOI: 10.1214/14-AOS1273     Document Type: Article
Times cited : (44)

References (45)
  • 2
    • 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
    • 0002269120 scopus 로고
    • Limiting behavior of posterior distributions when the model is incorrect
    • Correction, Ibid 37 745-746. MR0189176
    • BERK, R. H. (1966). Limiting behavior of posterior distributions when the model is incorrect. Ann. Math. Statist. 37 51-58; Correction, Ibid 37 745-746. MR0189176
    • (1966) Ann. Math. Statist. , vol.37 , pp. 51-58
    • Berk, R.H.1
  • 4
    • 84885061765 scopus 로고    scopus 로고
    • Optimal detection of sparse principal components in high dimension
    • MR3127849
    • BERTHET, Q. and RIGOLLET, P. (2013a). Optimal detection of sparse principal components in high dimension. Ann. Statist. 41 1780-1815. MR3127849
    • (2013) Ann. Statist. , vol.41 , pp. 1780-1815
    • Berthet, Q.1    Rigollet, P.2
  • 6
    • 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
  • 7
    • 80051762104 scopus 로고    scopus 로고
    • Distributed optimization and statistical learning via the alternating direction method of multipliers
    • BOYD, S., PARIKH, N., CHU, E., PELEATO, B. and ECKSTEIN, J. (2010). Distributed optimization and statistical learning via the alternating direction method of multipliers. Faund. Trends Mach. Learn. 3 1-122.
    • (2010) Faund. Trends Mach. Learn. , vol.3 , pp. 1-122
    • Boyd, S.1    Parikh, N.2    Chu, E.3    Peleato, B.4    Eckstein, J.5
  • 9
    • 0000014224 scopus 로고
    • Linear smoothers and additive models
    • MR0994249
    • BUJA, A., HASTIE, T. and TIBSHIRANI, R. (1989). Linear smoothers and additive models. Ann. Statist. 17 453-555. MR0994249
    • (1989) Ann. Statist. , vol.17 , pp. 453-555
    • Buja, A.1    Hastie, T.2    Tibshirani, R.3
  • 10
    • 84891928504 scopus 로고    scopus 로고
    • Sparse PCA: Optimal rates and adaptive estimation
    • MR3161458
    • CAI, T. T., M A, Z. and W U, Y. (2013). Sparse PCA: Optimal rates and adaptive estimation. Ann. Statist. 41 3074-3110. MR3161458
    • (2013) Ann. Statist. , vol.41 , pp. 3074-3110
    • Cai, T.T.1
  • 11
    • 48849086355 scopus 로고    scopus 로고
    • Optimal solutions for sparse principal component analysis
    • MR2426043
    • D 'A SPREMONT, A., BACH, F. and E L GHAOUI, L. (2008). Optimal solutions for sparse principal component analysis. J. Mach. Learn. Res. 9 1269-1294. MR2426043
    • (2008) J. Mach. Learn. Res. , vol.9 , pp. 1269-1294
    • 'A Spremont A, D.1    Bach, F.2    Ghaoui L, E.L.3
  • 12
    • 34548514458 scopus 로고    scopus 로고
    • A direct formulation for sparse PCA using semidefinite programming
    • (electronic). MR2353806
    • D 'A SPREMONT, A., E L 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
    • 'A Spremont A, D.1    Ghaoui L, E.L.2    Jordan, M.I.3    Lanckriet, G.R.G.4
  • 14
    • 1542784498 scopus 로고    scopus 로고
    • Variable selection via nonconcave penalized likelihood and its oracle properties
    • MR1946581
    • FAN, J. and L I, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. J. Amer. Statist. Assoc. 96 1348-1360. MR1946581
    • (2001) J. Amer. Statist. Assoc. , vol.96 , pp. 1348-1360
    • Fan, J.1
  • 15
    • 31344454903 scopus 로고    scopus 로고
    • Persistence in high-dimensional linear predictor selection and the virtue of overparametrization
    • MR2108039
    • GREENSHTEIN, E. and RITOV, Y. (2004). Persistence in high-dimensional linear predictor selection and the virtue of overparametrization. Bernoulli 10 971-988. MR2108039
    • (2004) Bernoulli , vol.10 , pp. 971-988
    • Greenshtein, E.1    Ritov, Y.2
  • 17
    • 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. J. Educ. Psychol. 498-520.
    • (1933) J. Educ. Psychol. , pp. 498-520
    • Hotelling, H.1
  • 19
    • 66549088006 scopus 로고    scopus 로고
    • On consistency and sparsity for principal components analysis in high dimensions
    • MR2751448
    • JOHNSTONE, I. M. and L U, 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
  • 20
    • 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
  • 21
    • 77949527718 scopus 로고    scopus 로고
    • Generalized power method for sparse principal component analysis
    • MR2600619
    • JOURNÉE, M., NESTEROV, Y., R ICHTÁRIK, 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    Ichtárik P, R.3    Sepulchre, R.4
  • 24
    • 73949122606 scopus 로고    scopus 로고
    • Sparsistency and rates of convergence in large covariance matrix estimation
    • MR2572459
    • LAM, C. and FAN, J. (2009). Sparsistency and rates of convergence in large covariance matrix estimation. Ann. Statist. 37 4254-4278. MR2572459
    • (2009) Ann. Statist. , vol.37 , pp. 4254-4278
    • Lam, C.1    Fan, J.2
  • 25
    • 85015082750 scopus 로고    scopus 로고
    • Sparse principal component analysis with missing observations
    • LOUNICI, K. (2013). Sparse principal component analysis with missing observations. Progr. Probab. 66 327-356.
    • (2013) Progr. Probab. , vol.66 , pp. 327-356
    • Lounici, K.1
  • 26
    • 84877623616 scopus 로고    scopus 로고
    • Sparse principal component analysis and iterative thresholding
    • M A MR3099121
    • M A, Z. (2013). Sparse principal component analysis and iterative thresholding. Ann. Statist. 41 772-801. MR3099121
    • (2013) Ann. Statist. , vol.41 , pp. 772-801
  • 27
    • 80053050337 scopus 로고    scopus 로고
    • Deflation methods for sparse PCA
    • D. Koller, D. Schuurmans, Y. Bengio and L. Bottou Curran Associates, Red Hook, NY
    • MACKEY, L. W. (2009). Deflation methods for sparse PCA. In Advances in Neural Information Processing Systems 21 (D. Koller, D. Schuurmans, Y. Bengio and L. Bottou, eds.) 1017-1024. Curran Associates, Red Hook, NY.
    • (2009) Advances in Neural Information Processing Systems 21 , pp. 1017-1024
    • Mackey, L.W.1
  • 28
    • 33747163541 scopus 로고    scopus 로고
    • High-dimensional graphs and variable selection with the lasso
    • MR2278363
    • MEINSHAUSEN, N. and BÜHLMANN, P. (2006). High-dimensional graphs and variable selection with the lasso. Ann. Statist. 34 1436-1462. MR2278363
    • (2006) Ann. Statist. , vol.34 , pp. 1436-1462
    • Meinshausen, N.1    Bühlmann, P.2
  • 29
    • 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 Y U, 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
  • 30
    • 0039907084 scopus 로고
    • On the sum of the largest eigenvalues of a symmetric matrix
    • MR1146651
    • OVERTON, M. L. and WOMERSLEY, R. S. (1992). On the sum of the largest eigenvalues of a symmetric matrix. SIAM J. Matrix Anal. Appl. 13 41-45. MR1146651
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 41-45
    • Overton, M.L.1    Womersley, R.S.2
  • 32
    • 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. Philos. Mag. 2 559-572.
    • (1901) Philos. Mag. , vol.2 , pp. 559-572
    • Pearson, K.1
  • 33
    • 80555142374 scopus 로고    scopus 로고
    • High-dimensional covariance estimation by minimizingℓ1 -penalized log-determinant divergence
    • MR2836766
    • RAVIKUMAR, P.,WAINWRIGHT, M. J., RASKUTTI, G. and Y U, B. (2011). High-dimensional covariance estimation by minimizingℓ1 -penalized log-determinant divergence. Electron. J. Stat. 5 935-980. MR2836766
    • (2011) Electron. J. Stat. , vol.5 , pp. 935-980
    • Ravikumar, P.1    Wainwright, M.J.2    Raskutti, G.3
  • 34
    • 62349119614 scopus 로고    scopus 로고
    • Sparse permutation invariant covariance estimation
    • MR2417391
    • ROTHMAN, A. J., BICKEL, P. J., LEVINA, E. and ZHU, J. (2008). Sparse permutation invariant covariance estimation. Electron. J. Stat. 2 494-515. MR2417391
    • (2008) Electron. J. Stat. , vol.2 , pp. 494-515
    • Rothman, A.J.1    Bickel, P.J.2    Levina, E.3    Zhu, J.4
  • 35
    • 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
  • 38
    • 84891937960 scopus 로고    scopus 로고
    • Minimax sparse principal subspace estimation in high dimensions
    • MR3161452
    • V U, V. Q. and LEI, J. (2013). Minimax sparse principal subspace estimation in high dimensions. Ann. Statist. 41 2905-2947. MR3161452
    • (2013) Ann. Statist. , vol.41 , pp. 2905-2947
    • Lei, J.1
  • 39
    • 84898989473 scopus 로고    scopus 로고
    • Fantope projection and selection: A near-optimal convex relaxation of sparse PCA
    • (C. J. C. Burges, L. Bottou, M. Welling, Z. Ghahramani and K. Q. Weinberger, eds.) Curran Associates, Red Hook, NY
    • V U, V. Q., CHO, J., LEI, J. and ROHE, K. (2013). Fantope projection and selection: A near-optimal convex relaxation of sparse PCA. In Advances in Neural Information Processing Systems (NIPS) 26 (C. J. C. Burges, L. Bottou, M. Welling, Z. Ghahramani and K. Q. Weinberger, eds.) 2670-2678. Curran Associates, Red Hook, NY.
    • (2013) Advances in Neural Information Processing Systems (NIPS) , vol.26 , pp. 2670-2678
    • Cho, J.1    Lei, J.2    Rohe, K.3
  • 40
    • 65749083666 scopus 로고    scopus 로고
    • Sharp thresholds for high-dimensional and noisy sparsity recovery using ℓ1 -constrained quadratic programming (Lasso)
    • MR2729873
    • WAINWRIGHT, M. J. (2009). Sharp thresholds for high-dimensional and noisy sparsity recovery using ℓ1 -constrained quadratic programming (Lasso). IEEE Trans . Inform. Theory 55 2183-2202. MR2729873
    • (2009) IEEE Trans. Inform. Theory , vol.55 , pp. 2183-2202
    • Wainwright, M.J.1
  • 41
    • 0002644952 scopus 로고
    • Maximum likelihood estimation of misspecified models
    • MR0640163
    • WHITE, H. (1982). Maximum likelihood estimation of misspecified models. Econometrica 50 1-25. MR0640163
    • (1982) Econometrica , vol.50 , pp. 1-25
    • White, H.1
  • 42
    • 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 10 515-534.
    • (2009) Biostatistics , vol.10 , pp. 515-534
    • Witten, D.M.1    Tibshirani, R.2    Hastie, T.3
  • 43
    • 84877607371 scopus 로고    scopus 로고
    • Truncated power method for sparse eigenvalue problems
    • MR3063614
    • YUAN, X.-T. and ZHANG, T. (2013). Truncated power method for sparse eigenvalue problems. J. Mach. Learn. Res. 14 899-925. MR3063614
    • (2013) J. Mach. Learn. Res. , vol.14 , pp. 899-925
    • Yuan, X.-T.1    Zhang, T.2
  • 44
    • 33845263263 scopus 로고    scopus 로고
    • On model selection consistency of Lasso
    • MR2274449
    • ZHAO, P. and Y U, B. (2006). On model selection consistency of Lasso. J. Mach. Learn. Res. 7 2541-2563. MR2274449
    • (2006) J. Mach. Learn. Res. , vol.7 , pp. 2541-2563
    • Zhao, P.1


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