메뉴 건너뛰기




Volumn 57, Issue 12, 2011, Pages 7818-7839

Accuracy guarantees for ℓ1-recovery

Author keywords

Linear estimation; nonparametric estimation by convex optimization; oracle inequalities; sparse recovery

Indexed keywords

BASIS PURSUITS; DANTZIG SELECTOR; ESTIMATION PERFORMANCE; LINEAR ESTIMATION; NOISY OBSERVATIONS; NON-EUCLIDEAN; NON-PARAMETRIC ESTIMATIONS; ORACLE INEQUALITIES; PERFORMANCE ESTIMATION; RECOVERY ALGORITHMS; SIGNAL SUPPORT; SPARSE RECOVERY; SPARSE SIGNALS; STATISTICAL PROPERTIES;

EID: 83255193471     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2011.2162569     Document Type: Article
Times cited : (27)

References (21)
  • 2
    • 68649086910 scopus 로고    scopus 로고
    • Simultaneous analysis of Lasso and Dantzig selector
    • P. Bickel, Y. Ritov, and A. B. Tsybakov, "Simultaneous analysis of Lasso and Dantzig selector" Ann. Statist., vol. 37, pp. 1705-1732, 2009.
    • (2009) Ann. Statist. , vol.37 , pp. 1705-1732
    • Bickel, P.1    Ritov, Y.2    Tsybakov, A.B.3
  • 3
    • 77955054299 scopus 로고    scopus 로고
    • On the conditions used to prove oracle results for the Lasso
    • P. Bühlmann and S. van de Geer, "On the conditions used to prove oracle results for the Lasso" Electron. J. Statist., vol. 3, pp. 1360-1392, 2009.
    • (2009) Electron. J. Statist. , vol.3 , pp. 1360-1392
    • Bühlmann, P.1    Van De Geer, S.2
  • 4
    • 50849114939 scopus 로고    scopus 로고
    • Sparsity oracle inequalities for the Lasso
    • F. Bunea, A. B. Tsybakov, and M. H. Wegkamp, "Sparsity oracle inequalities for the Lasso" Electron. J. Stat., vol. 1, pp. 169-194, 2007.
    • (2007) Electron. J. Stat. , vol.1 , pp. 169-194
    • Bunea, F.1    Tsybakov, A.B.2    Wegkamp, M.H.3
  • 5
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
    • Feb
    • E. Candès, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information" IEEE Trans. Inf. Theory, vol. 52, no. 2, pp. 489-509, Feb. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.2 , pp. 489-509
    • Candès, E.1    Romberg, J.2    Tao, T.3
  • 6
    • 33745604236 scopus 로고    scopus 로고
    • Stable signal recovery from incomplete and inaccurate measurements
    • E. Candès, J. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements" Comm. Pure Appl. Math., vol. 59, pp. 1207-1223, 2006.
    • (2006) Comm. Pure Appl. Math. , vol.59 , pp. 1207-1223
    • Candès, E.1    Romberg, J.2    Tao, T.3
  • 7
    • 34548275795 scopus 로고    scopus 로고
    • The Dantzig selector: Statistical estimation when p is much larger than n
    • E. Candès and T. Tao, "The Dantzig selector: Statistical estimation when p is much larger than n" Ann. Statist., vol. 35, pp. 2313-2351, 2007.
    • (2007) Ann. Statist. , vol.35 , pp. 2313-2351
    • Candès, E.1    Tao, T.2
  • 8
    • 42649140570 scopus 로고    scopus 로고
    • The restricted isometry property and its implications for compressed sensing
    • E. Candès, "The restricted isometry property and its implications for compressed sensing" Comptes Rendus de l'Acad. des Sci., ser. I, vol. 346, pp. 589-592, 2008.
    • (2008) Comptes Rendus de l'Acad. des Sci., ser. I , vol.346 , pp. 589-592
    • Candès, E.1
  • 9
    • 21344492321 scopus 로고
    • Statistical estimation and optimal recovery
    • D. Donoho, "Statistical estimation and optimal recovery" Ann. Statist., vol. 22, no. 1, pp. 238-270, 1995.
    • (1995) Ann. Statist. , vol.22 , Issue.1 , pp. 238-270
    • Donoho, D.1
  • 11
    • 0036714214 scopus 로고    scopus 로고
    • A generalized uncertainty principle and sparse representation in pairs of p bases
    • Sep
    • M. Elad and A. M. Bruckstein, "A generalized uncertainty principle and sparse representation in pairs of p bases" IEEE Trans. Inf. Theory, vol. 48, no. 9, pp. 2558-2567, Sep. 2002.
    • (2002) IEEE Trans. Inf. Theory , vol.48 , Issue.9 , pp. 2558-2567
    • Elad, M.1    Bruckstein, A.M.2
  • 12
    • 0347968052 scopus 로고    scopus 로고
    • Sparse representations in unions of bases
    • Dec
    • R. Gribonval and M. Nielsen, "Sparse representations in unions of bases" IEEE Trans. Inf. Theory, vol. 49, no. 12, pp. 3320-3325, Dec. 2003.
    • (2003) IEEE Trans. Inf. Theory , vol.49 , Issue.12 , pp. 3320-3325
    • Gribonval, R.1    Nielsen, M.2
  • 13
    • 69049088837 scopus 로고    scopus 로고
    • Nonparametric estimation by convex programming
    • A. Juditsky and A. Nemirovski, "Nonparametric estimation by convex programming" Ann. Statist., vol. 37, no. 5a, pp. 2278-2300, 2009.
    • (2009) Ann. Statist. , vol.37 , Issue.5 A , pp. 2278-2300
    • Juditsky, A.1    Nemirovski, A.2
  • 16
    • 72249100613 scopus 로고    scopus 로고
    • The Dantzig selector and sparsity oracle inequalities
    • V.Koltchinskii, "The Dantzig selector and sparsity oracle inequalities" Bernoulli, vol. 15, pp. 799-828, 2009.
    • (2009) Bernoulli , vol.15 , pp. 799-828
    • Koltchinskii, V.1
  • 17
    • 56449113372 scopus 로고    scopus 로고
    • Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators
    • K. Lounici, "Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators" Elect. J. Statist., vol. 2, pp. 90-102, 2008.
    • (2008) Elect. J. Statist. , vol.2 , pp. 90-102
    • Lounici, K.1
  • 18
    • 65349193793 scopus 로고    scopus 로고
    • Lasso-type recovery of sparse representations for high-dimensional data
    • N. Meinshausen and B. Yu, "Lasso-type recovery of sparse representations for high-dimensional data" Ann. Statist., vol. 37, pp. 246-270, 2009.
    • (2009) Ann. Statist. , vol.37 , pp. 246-270
    • Meinshausen, N.1    Yu, B.2
  • 20
    • 50949096321 scopus 로고    scopus 로고
    • The sparsity and bias of the Lasso selection in highdimensional linear regression
    • C.-H. Zhang and J. Huang, "The sparsity and bias of the Lasso selection in highdimensional linear regression" Ann. Statist., vol. 36, pp. 1567-1594, 2008.
    • (2008) Ann. Statist. , vol.36 , pp. 1567-1594
    • Zhang, C.-H.1    Huang, J.2
  • 21
    • 69049086702 scopus 로고    scopus 로고
    • q regularization
    • q regularization" Ann. Statist., vol. 37, pp. 2109-2144, 2009.
    • (2009) Ann. Statist. , vol.37 , pp. 2109-2144
    • Zhang, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.