메뉴 건너뛰기




Volumn 39, Issue 2, 2011, Pages 731-771

Exponential screening and optimal rates of sparse estimation

Author keywords

Adaptation; Aggregation; Bic; High Dimensional Regression; Lasso; Minimax Rates; Sparsity; Sparsity Oracle Inequalities

Indexed keywords


EID: 79952982333     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/10-AOS854     Document Type: Article
Times cited : (165)

References (46)
  • 1
    • 33746242092 scopus 로고    scopus 로고
    • Adapting to unknown sparsity by controlling the false discovery rate
    • DOI 10.1214/009053606000000074
    • ABRAMOVICH, F., BENJAMINI, Y., DONOHO, D. L. and JOHNSTONE, I. M. (2006). Adapting to unknown sparsity by controlling the false discovery rate. Ann. Statist. 34 584-653. MR2281879 (Pubitemid 44091387)
    • (2006) Annals of Statistics , vol.34 , Issue.2 , pp. 584-653
    • Abramovich, F.1    Benjamini, Y.2    Donoho, D.L.3    Johnstone, I.M.4
  • 2
    • 79952977064 scopus 로고    scopus 로고
    • Pac-bayesian bounds for sparse regression estimation with exponential weights
    • ALQUIER, P. and LOUNICI, K. (2010). PAC-Bayesian bounds for sparse regression estimation with exponential weights. HAL.
    • HAL. , vol.2010
    • Alquier, P.1    Lounici, K.2
  • 3
    • 55649115527 scopus 로고    scopus 로고
    • A simple proof of the restricted isometry property for random matrices
    • MR2453366
    • BARANIUK, R., DAVENPORT, M., DEVORE, R. and WAKIN, M. (2008). A simple proof of the restricted isometry property for random matrices. Constr. Approx. 28 253-263. MR2453366
    • (2008) Constr. Approx. , vol.28 , pp. 253-263
    • Baraniuk, R.1    Davenport, M.2    Devore, R.3    Wakin, M.4
  • 4
    • 0027599793 scopus 로고
    • Universal approximation bounds for superpositions of a sigmoidal function
    • MR1237720
    • BARRON, A. R. (1993). Universal approximation bounds for superpositions of a sigmoidal function. IEEE Trans. Inform. Theory 39 930-945. MR1237720
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 930-945
    • Barron, A.R.1
  • 7
    • 68649086910 scopus 로고    scopus 로고
    • Simultaneous analysis of lasso and dantzig selector
    • MR2533469
    • BICKEL, P. J., RITOV, Y. and TSYBAKOV, A. B. (2009). Simultaneous analysis of Lasso and Dantzig selector. Ann. Statist. 37 1705-1732. MR2533469
    • (2009) Ann. Statist , vol.37 , pp. 1705-1732
    • Bickel, P.J.1    Ritov, Y.2    Tsybakov, A.B.3
  • 8
    • 77955054299 scopus 로고    scopus 로고
    • On the conditions used to prove oracle results for the lasso
    • MR2576316
    • BüHLMANN, P. and VAN DE GEER, S. (2009). On the conditions used to prove oracle results for the Lasso. Electron. J. Statist. 3 1360-1392. MR2576316
    • (2009) Electron. J. Statist , vol.3 , pp. 1360-1392
    • Bühlmann, P.1    Van De Geer, S.2
  • 9
    • 50849114939 scopus 로고    scopus 로고
    • Sparsity oracle inequalities for the lasso
    • electronic. MR2312149
    • BUNEA, F., TSYBAKOV, A. andWEGKAMP, M. (2007a). Sparsity oracle inequalities for the Lasso. Electron. J. Statist. 1 169-194 (electronic). MR2312149
    • (2007) Electron. J. Statist , vol.1 , pp. 169-194
    • Bunea, F.1    Tsybakov, A.2    Wegkamp, M.3
  • 10
    • 38049043619 scopus 로고    scopus 로고
    • Aggregation for gaussian regression
    • MR2351101
    • BUNEA, F., TSYBAKOV, A. B. andWEGKAMP, M. H. (2007b). Aggregation for Gaussian regression. Ann. Statist. 35 1674-1697. MR2351101
    • (2007) Ann. Statist , vol.35 , pp. 1674-1697
    • Bunea, F.1    Tsybakov, A.B.2    Wegkamp, M.H.3
  • 11
    • 42649140570 scopus 로고    scopus 로고
    • The restricted isometry property and its implications for compressed sensing
    • MR2412803
    • CANDES, E. (2008). The restricted isometry property and its implications for compressed sensing. C. R. Math. Acad. Sci. Paris 346 589-592. MR2412803
    • (2008) C. R. Math. Acad. Sci. Paris , vol.346 , pp. 589-592
    • Candes, E.1
  • 12
    • 34548275795 scopus 로고    scopus 로고
    • The dantzig selector: Statistical estimation when p is much larger than n
    • MR2382644
    • CANDES, E. and TAO, T. (2007). The Dantzig selector: Statistical estimation when p is much larger than n. Ann. Statist. 35 2313-2351. MR2382644
    • (2007) Ann. Statist , vol.35 , pp. 2313-2351
    • Candes, E.1    Tao, T.2
  • 13
    • 70350003059 scopus 로고    scopus 로고
    • Aggregation by exponential weighting, sharp pac-Bayesian bounds and sparsity
    • DALALYAN, A. and TSYBAKOV, A. (2008). Aggregation by exponential weighting, sharp pac-Bayesian bounds and sparsity. Machine Learning 72 39-61.
    • (2008) Machine Learning , vol.72 , pp. 39-61
    • Dalalyan, A.1    Tsybakov, A.2
  • 15
    • 38049046503 scopus 로고    scopus 로고
    • Aggregation by exponential weighting and sharp oracle inequalities
    • Springer, Berlin. MR2397581
    • DALALYAN, A. S. and TSYBAKOV, A. B. (2007). Aggregation by exponential weighting and sharp oracle inequalities. In Learning Theory. Lecture Notes in Computer Science 4539 97-111. Springer, Berlin. MR2397581
    • (2007) Learning Theory. Lecture Notes in Computer Science , vol.4539 , pp. 97-111
    • Dalalyan, A.S.1    Tsybakov, A.B.2
  • 17
    • 0041958932 scopus 로고
    • Ideal spatial adaptation by wavelet shrinkage
    • MR1311089
    • DONOHO, D. L. and JOHNSTONE, I. M. (1994a). Ideal spatial adaptation by wavelet shrinkage. Biometrika 81 425-455. MR1311089
    • (1994) Biometrika , vol.81 , pp. 425-455
    • Donoho, D.L.1    Johnstone, I.M.2
  • 18
    • 0012499079 scopus 로고
    • Minimax risk over lp-balls for lq -error
    • MR1278886
    • DONOHO, D. L. and JOHNSTONE, I. M. (1994b). Minimax risk over lp-balls for lq -error. Probab. Theory Related Fields 99 277-303. MR1278886
    • (1994) Probab. Theory Related Fields , vol.99 , pp. 277-303
    • Donoho, D.L.1    Johnstone, I.M.2
  • 19
    • 0002712203 scopus 로고
    • Maximum entropy and the nearly black object
    • With discussion and a reply by the authors. MR1157714
    • DONOHO, D. L., JOHNSTONE, I. M., HOCH, J. C. and STERN, A. S. (1992). Maximum entropy and the nearly black object. J. Roy. Statist. Soc. Ser. B 54 41-81. With discussion and a reply by the authors. MR1157714
    • (1992) J. Roy. Statist. Soc. Ser. B. , vol.54 , pp. 41-81
    • Donoho, D.L.1    Johnstone, I.M.2    Hoch, J.C.3    Stern, A.S.4
  • 20
    • 1542784498 scopus 로고    scopus 로고
    • Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
    • FAN, J. and LI, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. J. Amer. Statist. Assoc. 96 1348-1360. MR1946581 (Pubitemid 33695585)
    • (2001) Journal of the American Statistical Association , vol.96 , Issue.456 , pp. 1348-1360
    • Fan, J.1    Li, R.2
  • 21
    • 21844523862 scopus 로고
    • The risk inflation criterion for multiple regression
    • MR1329177
    • FOSTER, D. P. and GEORGE, E. I. (1994). The risk inflation criterion for multiple regression. Ann. Statist. 22 1947-1975. MR1329177
    • (1994) Ann. Statist , vol.22 , pp. 1947-1975
    • Foster, D.P.1    George, E.I.2
  • 22
    • 84950917142 scopus 로고
    • Combining minimax shrinkage estimators
    • MR0845881
    • GEORGE, E. I. (1986a). Combining minimax shrinkage estimators. J. Amer. Statist. Assoc. 81 437-445. MR0845881
    • (1986) J. Amer. Statist. Assoc , vol.81 , pp. 437-445
    • George, E.I.1
  • 23
    • 0000497169 scopus 로고
    • Minimax multiple shrinkage estimation
    • MR0829562
    • GEORGE, E. I. (1986b). Minimax multiple shrinkage estimation. Ann. Statist. 14 188-205. MR0829562
    • (1986) Ann. Statist , vol.14 , pp. 188-205
    • George, E.I.1
  • 24
    • 58149358999 scopus 로고    scopus 로고
    • Mixing least-squares estimators when the variance is unknown
    • MR2543587
    • GIRAUD, C. (2008). Mixing least-squares estimators when the variance is unknown. Bernoulli 14 1089-1107. MR2543587
    • (2008) Bernoulli , vol.14 , pp. 1089-1107
    • Giraud, C.1
  • 26
    • 79952950810 scopus 로고    scopus 로고
    • A Matlab solver for l1-regularized least squares problems
    • Available at
    • KOH, K., KIM, S.-J. and BOYD, S. (2008). A Matlab solver for l1-regularized least squares problems. BETA version. Stanford Univ. Available at http://www.stanford.edu/~boyd-l1-ls.
    • (2008) BETA version. Stanford Univ
    • Koh, K.1    Kim, S.-J.2    Boyd, S.3
  • 28
    • 72249100613 scopus 로고    scopus 로고
    • The Dantzig selector and sparsity oracle inequalities
    • MR2555200
    • KOLTCHINSKII, V. (2009a). The Dantzig selector and sparsity oracle inequalities. Bernoulli 15 799-828. MR2555200
    • (2009) Bernoulli , vol.15 , pp. 799-828
    • Koltchinskii, V.1
  • 29
    • 62549157465 scopus 로고    scopus 로고
    • Sparsity in penalized empirical risk minimization
    • MR2500227
    • KOLTCHINSKII, V. (2009b). Sparsity in penalized empirical risk minimization. Ann. Inst. H. Poincaré Probab. Statist. 45 7-57. MR2500227
    • (2009) Ann. Inst. H. Poincaré Probab. Statist. , vol.45 , pp. 7-57
    • Koltchinskii, V.1
  • 31
    • 33746478298 scopus 로고    scopus 로고
    • Information theory and mixing least-squares regressions
    • DOI 10.1109/TIT.2006.878172
    • Morgan Kaufmann, San Francisco. LEUNG, G. and BARRON, A. R. (2006). Information theory and mixing least-squares regressions. IEEE Trans. Inform. Theory 52 3396-3410. MR2242356 (Pubitemid 44145107)
    • (2006) IEEE Transactions on Information Theory , vol.52 , Issue.8 , pp. 3396-3410
    • Leung, G.1    Barron, A.R.2
  • 32
    • 79952905234 scopus 로고    scopus 로고
    • Generalized mirror averaging and D-convex aggregation
    • MR2356820
    • LOUNICI, K. (2007). Generalized mirror averaging and D-convex aggregation. Math. Methods Statist. 16 246-259. MR2356820
    • (2007) Math. Methods Statist. , vol.16 , pp. 246-259
    • Lounici, K.1
  • 33
    • 0007259908 scopus 로고    scopus 로고
    • Topics in non-parametric statistics. In Lectures on Probability Theory and Statistics (Saint-Flour 1998)
    • Springer, Berlin. MR1775640
    • NEMIROVSKI, A. (2000). Topics in non-parametric statistics. In Lectures on Probability Theory and Statistics (Saint-Flour, 1998). Lecture Notes in Math. 1738 85-277. Springer, Berlin. MR1775640
    • (2000) Lecture Notes in Math. , vol.1738 , pp. 85-277
    • Nemirovski, A.1
  • 35
    • 0037709670 scopus 로고    scopus 로고
    • Adaptive estimation of the intensity of inhomogeneous Poisson processes via concentration inequalities
    • DOI 10.1007/s00440-003-0259-1
    • REYNAUD-BOURET, P. (2003). Adaptive estimation of the intensity of inhomogeneous Poisson processes via concentration inequalities. Probab. Theory Related Fields 126 103-153. (Pubitemid 36737904)
    • (2003) Probability Theory and Related Fields , vol.126 , Issue.1 , pp. 103-153
    • Reynaud-Bouret, P.1
  • 36
    • 79952913575 scopus 로고    scopus 로고
    • Maximum likelihood aggregation and misspecified generalized linear models
    • Available at ArXiv: 0911.2919
    • RIGOLLET, P. (2009). Maximum likelihood aggregation and misspecified generalized linear models. Technical report. Available at ArXiv:0911.2919.
    • (2009) Technical Report
    • Rigollet, P.1
  • 39
    • 9444226947 scopus 로고    scopus 로고
    • Optimal rates of aggregation In COLT (B. Schölkopf and M. K. Warmuth
    • Springer, Berlin
    • TSYBAKOV, A. B. (2003). Optimal rates of aggregation. In COLT (B. Schölkopf and M. K. Warmuth, eds.). Lecture Notes in Computer Science 2777 303-313. Springer, Berlin.
    • (2003) Lecture Notes in Computer Science , vol.2777 , pp. 303-313
    • Tsybakov, A.B.1
  • 41
    • 51049121146 scopus 로고    scopus 로고
    • High-dimensional generalized linear models and the Lasso
    • MR2396809
    • VAN DE GEER, S. A. (2008). High-dimensional generalized linear models and the Lasso. Ann. Statist. 36 614-645. MR2396809
    • (2008) Ann. Statist , vol.36 , pp. 614-645
    • Van De Geer, S.A.1
  • 43
    • 77649284492 scopus 로고    scopus 로고
    • Nearly unbiased variable selection under minimax concave penalty
    • MR2604701
    • ZHANG, C.-H. (2010). Nearly unbiased variable selection under minimax concave penalty. Ann. Statist. 38 894-942. MR2604701
    • Ann. Statist , vol.2010 , Issue.38 , pp. 894-942
    • Zhang, C.-H.1
  • 44
    • 50949096321 scopus 로고    scopus 로고
    • The sparsity and bias of the LASSO selection in highdimensional linear regression
    • MR2435448
    • ZHANG, C.-H. and HUANG, J. (2008). The sparsity and bias of the LASSO selection in highdimensional linear regression. Ann. Statist. 36 1567-1594. MR2435448
    • (2008) Ann. Statist , vol.36 , pp. 1567-1594
    • Zhang, C.-H.1    Huang, J.2
  • 46
    • 69049086702 scopus 로고    scopus 로고
    • 1 regularization
    • MR2543687
    • 1 regularization. Ann. Statist. 37 2109-2144. MR2543687
    • (2009) Ann. Statist , vol.37 , pp. 2109-2144
    • Zhang, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.