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We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix.
Karp, Richard M.R. M. (1972). Reducibility among combinatorial problems. In Complexity of Computer Computations (Proc. Sympos., IBM Thomas J. Watson Res. Center, Yorktown Heights, N.Y., 1972) 85–103. Plenum, New York
1972
Earlier work this paper cites.
Geman, StuartS. (1980). A limit theorem for the norm of random matrices. Ann. Probab. 8 252–261
1980
Earlier work this paper cites.
Ingster, Yu. I.Y. I. (1982). The asymptotic efficiency of tests for a simple hypothesis against a composite alternative. Teor. Veroyatn. Primen. 27 587–592
1982
Earlier work this paper cites.
Nesterov, Y.Y. andNemirovskii, A.A. (1987). Interior-Point Polynomial Algorithms in Convex Programming. Society for Industrial Mathematics 13. SIAM, Philadelphia, PA
1987
Earlier work this paper cites.
Yin, Y. Q.Y. Q., Bai, Z. D.Z. D. andKrishnaiah, P. R.P. R. (1988). On the limit of the largest eigenvalue of the large-dimensional sample covariance matrix. Probab. Theory Related Fields 78 509–521
1988
Earlier work this paper cites.
Jerrum, MarkM. (1992). Large cliques elude the Metropolis process. Random Structures Algorithms 3 347–359
1992
Earlier work this paper cites.
Spencer, JoelJ. (1994). Ten Lectures on the Probabilistic Method, 2nd ed. CBMS-NSF Regional Conference Series in Applied Mathematics 64. SIAM, Philadelphia, PA
1994
Earlier work this paper cites.
Goemans, Michel X.M. X. andWilliamson, David P.D. P. (1995). Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. Assoc. Comput. Mach. 42 1115–1145
1995
Earlier work this paper cites.
Kučera, LuděkL. (1995). Expected complexity of graph partitioning problems. Discrete Appl. Math. 57 193–212
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.
Alon, U.U., Barkai, N.N., Notterman, D. A.D. A., Gish, K.K., Ybarra, S.S., Mack, D.D. andLevine, A. J.A. J. (1999). Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays. Proc. Natl. Acad. Sci. USA 96 6745–6750
1999
Earlier work this paper cites.
Bai, Z. D.Z. D. (1999). Methodologies in spectral analysis of large-dimensional random matrices, a review. Statist. Sinica 9 611–677
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.
Juels, AriA. andPeinado, MarcusM. (2000). Hiding cliques for cryptographic security. Des. Codes Cryptogr. 20 269–280
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.
Baraud, YannickY. (2002). Non-asymptotic minimax rates of testing in signal detection. Bernoulli 8 577–606
2002
Earlier work this paper cites.
Krivelevich, MichaelM. andVu, Van H.V. H. (2002). Approximating the independence number and the chromatic number in expected polynomial time. J. Comb. Optim. 6 143–155
2002
Earlier work this paper cites.
Feige, UrielU. andKrauthgamer, RobertR. (2003). The probable value of the Lovász–Schrijver relaxations for maximum independent set. SIAM J. Comput. 32 345–370 (electronic)
2003
Earlier work this paper cites.
Nesterov, YuriiY. (2003). Introductory Lectures on Convex Optimization. Springer, New York
2003
Earlier work this paper cites.
Boyd, StephenS. andVandenberghe, LievenL. (2004). Convex Optimization. Cambridge Univ. Press, Cambridge
2004
Earlier work this paper cites.
Donoho, DavidD. andJin, JiashunJ. (2004). Higher criticism for detecting sparse heterogeneous mixtures. Ann. Statist. 32 962–994
2004
Earlier work this paper cites.
Tsybakov, Alexandre B.A. B. (2009). Introduction to Nonparametric Estimation. Springer, New York. Revised and extended from the 2004 French original, translated by Vladimir Zaiats
2004
Earlier work this paper cites.
Baik, JinhoJ., Ben Arous, GérardG. andPéché, SandrineS. (2005). Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices. Ann. Probab. 33 1643–1697
2005
Earlier work this paper cites.
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
Earlier work this paper cites.
Alon, NogaN., Andoni, AlexandrA., Kaufman, TaliT., Matulef, KevinK., Rubinfeld, RonittR. andXie, NingN. (2007). Testing k k -wise and almost k k -wise independence. In STOC’07—Proceedings of the 39th Annual ACM Symposium on Theory of Computing 496–505. ACM, New York
2007
Cited alongside, same era.
d’Aspremont, AlexandreA., El Ghaoui, LaurentL., Jordan, Michael I.M. I. andLanckriet, Gert R. G.G. R. G. (2007). A direct formulation for sparse PCA using semidefinite programming. SIAM Rev. 49 434–448 (electronic)
2007
Cited alongside, same era.
Paul, DebashisD. (2007). Asymptotics of sample eigenstructure for a large dimensional spiked covariance model. Statist. Sinica 17 1617–1642
2007
Cited alongside, same era.
Bickel, Peter J.P. J. andLevina, ElizavetaE. (2008). Covariance regularization by thresholding. Ann. Statist. 36 2577–2604
2008
Cited alongside, same era.
Chen, XiX. (2011). Adaptive elastic-net sparse principal component analysis for pathway association testing. Stat. Appl. Genet. Mol. Biol. 10 Art. 48, 23
2011
Later among the works it cites.
Dekel, YaelY., Gurel-Gurevich, OriO. andPeres, YuvalY. (2011). Finding hidden cliques in linear time with high probability. In ANALCO11—Workshop on Analytic Algorithmics and Combinatorics 67–75. SIAM, Philadelphia, PA
2011
Later among the works it cites.
Hazan, EladE. andKrauthgamer, RobertR. (2011). How hard is it to approximate the best Nash equilibrium? SIAM J. Comput. 40 79–91
2011
Later among the works it cites.
2011
Later among the works it cites.
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d’Aspremont, AlexandreA., Bach, FrancisF. andEl Ghaoui, LaurentL. (2008). Optimal solutions for sparse principal component analysis. J. Mach. Learn. Res. 9 1269–1294
2008
Cited alongside, same era.
El Karoui, NoureddineN. (2008). Operator norm consistent estimation of large-dimensional sparse covariance matrices. Ann. Statist. 36 2717–2756
2008
Cited alongside, same era.
Frieze, AlanA. andKannan, RaviR. (2008). A new approach to the planted clique problem. In FSTTCS 2008: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. LIPIcs. Leibniz Int. Proc. Inform. 2 187–198. Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern
2008
Cited alongside, same era.
Nadler, BoazB. (2008). Finite sample approximation results for principal component analysis: A matrix perturbation approach. Ann. Statist. 36 2791–2817
2008
Cited alongside, same era.
Sun, XingX. andNobel, Andrew B.A. B. (2008). On the size and recovery of submatrices of ones in a random binary matrix. J. Mach. Learn. Res. 9 2431–2453
2008
Cited alongside, same era.
Amini, Arash A.A. A. andWainwright, Martin J.M. J. (2009). High-dimensional analysis of semidefinite relaxations for sparse principal components. Ann. Statist. 37 2877–2921
2009
Cited alongside, same era.
Brubaker, S. CharlesS. C. andVempala, Santosh S.S. S. (2009). Random tensors and planted cliques. In Approximation, Randomization, and Combinatorial Optimization. Lecture Notes in Computer Science 5687 406–419. Springer, Berlin
2009
Cited alongside, same era.
Féral, DelphineD. andPéché, SandrineS. (2009). The largest eigenvalues of sample covariance matrices for a spiked population: Diagonal case. J. Math. Phys. 50 073302, 33
2009
Cited alongside, same era.
2011
Later among the works it cites.
Arias-Castro, EryE., Bubeck, SébastienS. andLugosi, GáborG. (2012). Detection of correlations. Ann. Statist. 40 412–435
2012
Closest in time.
2012
Closest in time.
2012
Closest in time.
2012
Closest in time.
2012
Closest in time.
Loh, Po-LingP.-L. andWainwright, Martin J.M. J. (2012). High-dimensional regression with noisy and missing data: Provable guarantees with nonconvexity. Ann. Statist. 40 1637–1664
2012
Closest in time.
Lu, ZhaosongZ. andZhang, YongY. (2012). An augmented Lagrangian approach for sparse principal component analysis. Math. Program. 135 149–193
2012
Closest in time.
2012
Closest in time.
Vershynin, RomanR. (2012). Introduction to the non-asymptotic analysis of random matrices. In Compressed Sensing 210–268. Cambridge Univ. Press, Cambridge
2012
Closest in time.
Verzelen, NicolasN. (2012). Minimax risks for sparse regressions: Ultra-high dimensional phenomenons. Electron. J. Stat. 6 38–90
2012
Closest in time.
Vu, V.V. andLei, J.J. (2012). Minimax rates of estimation for sparse pca in high dimensions. In Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics April 21–23, 2012, La Palma, Canary Islands, Vol. 22 of JMLR W&CP 1278–1286
2012
Closest in time.
Birnbaum, A.A., Johnstone, I. M.I. M., Nadler, B.B. andPaul, D.D. (2013). Minimax bounds for sparse PCA with noisy high-dimensional data. Ann. Statist. 41 1055–1084
2013
Closest in time.
2013
Closest in time.
Chandrasekaran, V.V. andJordan, M. I.M. I. (2013). Computational and statistical tradeoffs via convex relaxation. Proc. Natl. Acad. Sci. 110 E1181–E1190
2013
Closest in time.
Feldman, V.V., Grigorescu, E.E., Reyzin, L.L., Vempala, S.S. andXiao, Y.Y. (2013). Statistical algorithms and a lower bound for planted clique. In Proceedings of the 45th Annual ACM Symposium on Theory of Computing, STOC’13 655–664. ACM, New York
2013
Closest in time.
Ma, Z.Z. (2013). Sparse principal component analysis and iterative thresholding. Ann. Statist. 41 772–801
2013
Closest in time.
Onatski, A.A., Moreira, M. J.M. J. andHallin, M.M. (2013). Asymptotic power of sphericity tests for high-dimensional data. Ann. Statist. 41 1204–1231
2013
Closest in time.
Shen, DanD., Shen, HaipengH. andMarron, J. S.J. S. (2013). Consistency of sparse PCA in high dimension, low sample size contexts. J. Multivariate Anal. 115 317–333
2013
Closest in time.
Sun, X.X. andNobel, A. B.A. B. (2013). On the maximal size of large-average and ANOVA-fit submatrices in a Gaussian random matrix. Bernoulli 19 275–294
2013
Closest in time.