-
2
-
-
69049101180
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
18
-
-
0000250624
-
The behavior of maximum likelihood estimates under nonstandard conditions
-
Univ. California Press, Berkeley. MR0216620
-
HUBER, P. J. (1967). The behavior of maximum likelihood estimates under nonstandard conditions. In Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), Vol. I: Statistics 221-233. Univ. California Press, Berkeley. MR0216620
-
(1967)
Proc. Fifth Berkeley Sympos. Math. Statist. And Probability (Berkeley, Calif., 1965/66), Vol. I: Statistics
, pp. 221-233
-
-
Huber, P.J.1
-
19
-
-
66549088006
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
|