메뉴 건너뛰기




Volumn 45, Issue 1, 2009, Pages 7-57

Sparsity in penalized empirical risk minimization

Author keywords

p penalty; Empirical risk; Oracle inequalities; Penalized empirical risk; Sparsity

Indexed keywords


EID: 62549157465     PISSN: 02460203     EISSN: 02460203     Source Type: Journal    
DOI: 10.1214/07-AIHP146     Document Type: Article
Times cited : (77)

References (30)
  • 1
    • 0033459856 scopus 로고    scopus 로고
    • Risk bounds for model selection via penalization
    • MR1679028
    • A. Barron, L. Birgé and P. Massart. Risk bounds for model selection via penalization. Probab. Theory Related Fields 113 (1999) 301-413. MR1679028
    • (1999) Probab. Theory Related Fields , vol.113 , pp. 301-413
    • Barron, A.1    Birgé, L.2    Massart, P.3
  • 2
    • 26444592981 scopus 로고    scopus 로고
    • Local Rademacher complexities
    • MR2166554
    • P. Bartlett, O. Bousquet and S. Mendelson. Local Rademacher complexities. Ann. Statist. 33 (2005) 1497-1537. MR2166554
    • (2005) Ann. Statist. , vol.33 , pp. 1497-1537
    • Bartlett, P.1    Bousquet, O.2    Mendelson, S.3
  • 4
    • 38049043619 scopus 로고    scopus 로고
    • Aggregation for Gaussian regression
    • MR2351101
    • F. Bunea, A. Tsybakov and M. Wegkamp. Aggregation for Gaussian regression. Ann. Statist. 35 (2007) 1674-1697. MR2351101
    • (2007) Ann. Statist. , vol.35 , pp. 1674-1697
    • Bunea, F.1    Tsybakov, A.2    Wegkamp, M.3
  • 5
    • 50849114939 scopus 로고    scopus 로고
    • Sparsity oracle inequalities for the LASSO
    • MR2312149
    • F. Bunea, A. Tsybakov and M. Wegkamp. Sparsity oracle inequalities for the LASSO. Electron. J. Statist. 1 (2007) 169-194. MR2312149
    • (2007) Electron. J. Statist. , vol.1 , pp. 169-194
    • Bunea, F.1    Tsybakov, A.2    Wegkamp, M.3
  • 6
    • 34548275795 scopus 로고    scopus 로고
    • The Dantzig selector statistical estimation when p is much larger than n
    • E. Candes and T. Tao. The Dantzig selector statistical estimation when p is much larger than n. Ann. Statist. 35 (2007) 2313-2351.
    • (2007) Ann. Statist. , vol.35 , pp. 2313-2351
    • Candes, E.1    Tao, T.2
  • 8
    • 33745604236 scopus 로고    scopus 로고
    • Stable signal recovery from incomplete and inaccurate measurements
    • MR2230846
    • E. Candes, J. Romberg and T. Tao. Stable signal recovery from incomplete and inaccurate measurements. Comm. Pure Appl. Math. 59 (2006) 1207-1223. MR2230846
    • (2006) Comm. Pure Appl. Math. , vol.59 , pp. 1207-1223
    • Candes, E.1    Romberg, J.2    Tao, T.3
  • 11
    • 33646365077 scopus 로고    scopus 로고
    • 1-norm solution is also the sparsest solution
    • MR2217606
    • 1-norm solution is also the sparsest solution. Comm. Pure Appl. Math. 59 (2006) 797-829. MR2217606
    • (2006) Comm. Pure Appl. Math. , vol.59 , pp. 797-829
    • Donoho, D.L.1
  • 12
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • MR2241189
    • D. L. Donoho. Compressed sensing. IEEE Trans. Inform. Theory 52 (2006) 1289-1306. MR2241189
    • (2006) IEEE Trans. Inform. Theory , vol.52 , pp. 1289-1306
    • Donoho, D.L.1
  • 13
    • 33144483155 scopus 로고    scopus 로고
    • Stable recovery of sparse overcomplete representations in the presence of noise
    • MR2237332
    • D. L. Donoho, M. Elad and V. Temlyakov. Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Trans. Inform. Theory 52 (2006) 6-18. MR2237332
    • (2006) IEEE Trans. Inform. Theory , vol.52 , pp. 6-18
    • Donoho, D.L.1    Elad, M.2    Temlyakov, V.3
  • 14
    • 51049121146 scopus 로고    scopus 로고
    • High-dimensional generalized linear models and the Lasso
    • van de S. Geer. High-dimensional generalized linear models and the Lasso. Ann. Statist. 36 (2008) 614-645.
    • (2008) Ann. Statist. , vol.36 , pp. 614-645
    • De G.S.Van1
  • 16
    • 33746194045 scopus 로고    scopus 로고
    • Local Rademacher complexities and oracle inequalities in risk mnimization
    • MR2329442
    • V. Koltchinskii. Local Rademacher complexities and oracle inequalities in risk mnimization. Ann. Statist. 34 (2006) 2593-2656. MR2329442
    • (2006) Ann. Statist. , vol.34 , pp. 2593-2656
    • Koltchinskii, V.1
  • 17
    • 26444607491 scopus 로고    scopus 로고
    • Complexities of convex combinations and bounding the generalization error in classification
    • MR2166553
    • V. Koltchinskii and D. Panchenko. Complexities of convex combinations and bounding the generalization error in classification. Ann. Statist. 33 (2005) 1455-1496. MR2166553
    • (2005) Ann. Statist. , vol.33 , pp. 1455-1496
    • Koltchinskii, V.1    Panchenko, D.2
  • 19
    • 0000595627 scopus 로고    scopus 로고
    • Some applications of concentration inequalities to statistics
    • MR1813803
    • P. Massart. Some applications of concentration inequalities to statistics. Ann. Fac. Sci. Tolouse (IX) 9 (2000) 245-303. MR1813803
    • (2000) Ann. Fac. Sci. Tolouse (IX) , vol.9 , pp. 245-303
    • Massart, P.1
  • 21
    • 38849196916 scopus 로고    scopus 로고
    • Reconstruction and subgaussian operators in asymptotic geometric analysis
    • S. Mendelson, A. Pajor and N. Tomczak-Jaegermann. Reconstruction and subgaussian operators in Asymptotic Geometric Analysis. Geom. Funct. Anal. 17 (2007) 1248-1282.
    • (2007) Geom. Funct. Anal. , vol.17 , pp. 1248-1282
    • Mendelson, S.1    Pajor, A.2    Tomczak-Jaegermann, N.3
  • 22
    • 33747163541 scopus 로고    scopus 로고
    • High-dimensional graphs and variable selection with the LASSO
    • MR2278363
    • N. Meinshausen and P. Bühlmann. High-dimensional graphs and variable selection with the LASSO. Ann. Statist. 34 (2006) 1436-1462. MR2278363
    • (2006) Ann. Statist. , vol.34 , pp. 1436-1462
    • Meinshausen, N.1    Bühlmann, P.2
  • 23
    • 0007259908 scopus 로고    scopus 로고
    • Topics in non-parametric statistics
    • P. Bernard (Ed). Springer, New York. MR1775640
    • A. Nemirovski. Topics in non-parametric statistics. In Ecole d'Et'e de Probabilités de Saint-Flour XXVIII, 1998 85-277. P. Bernard (Ed). Springer, New York, 2000. MR1775640
    • (1998) Ecole D'Et'e de Probabilités de Saint-Flour , vol.28 , pp. 85-277
    • Nemirovski, A.1
  • 24
    • 33746801607 scopus 로고    scopus 로고
    • Geometric approach to error correcting codes and reconstruction of signals
    • MR2206919
    • M. Rudelson and R. Vershynin. Geometric approach to error correcting codes and reconstruction of signals. Int. Math. Res. Not. 64 (2005) 4019-4041. MR2206919
    • (2005) Int. Math. Res. Not. , vol.64 , pp. 4019-4041
    • Rudelson, M.1    Vershynin, R.2
  • 25
    • 0001287271 scopus 로고    scopus 로고
    • Regression shrinkage and selection via Lasso
    • Ser. B. MR1379242
    • R. Tibshirani. Regression shrinkage and selection via Lasso. J. Royal Statist. Soc. Ser. B 58 (1996) 267-288. MR1379242
    • (1996) J. Royal Statist. Soc. , vol.58 , pp. 267-288
    • Tibshirani, R.1
  • 26
    • 9444226947 scopus 로고    scopus 로고
    • Optimal rates of aggregation
    • Proc. 16th Annual Conference on Learning Theory (COLT) and 7th Annual Workshop on Kernel Machines. Springer, New York
    • A. Tsybakov. Optimal rates of aggregation. In Proc. 16th Annual Conference on Learning Theory (COLT) and 7th Annual Workshop on Kernel Machines, 303-313. Lecture Notes in Artificial Intelligence 2777. Springer, New York, 2003.
    • (2003) Lecture Notes in Artificial Intelligence , vol.2777 , pp. 303-313
    • Tsybakov, A.1
  • 28
    • 0034410225 scopus 로고    scopus 로고
    • Mixing strategies for density estimation
    • MR1762904
    • Y. Yang. Mixing strategies for density estimation. Ann. Statist. 28 (2000) 75-87. MR1762904
    • (2000) Ann. Statist. , vol.28 , pp. 75-87
    • Yang, Y.1
  • 29
    • 29144460670 scopus 로고    scopus 로고
    • Aggregating regression procedures for a better performance
    • MR2044592
    • Y. Yang. Aggregating regression procedures for a better performance. Bernoulli 10 (2004) 25-47. MR2044592
    • (2004) Bernoulli , vol.10 , pp. 25-47
    • Yang, Y.1
  • 30
    • 33845263263 scopus 로고    scopus 로고
    • On model selection consistency of LASSO
    • MR2274449
    • P. Zhao and B. Yu. On model selection consistency of LASSO. J.Mach. Learn. Res. 7 (2006) 2541-2563. MR2274449
    • (2006) J.Mach. Learn. Res. , vol.7 , pp. 2541-2563
    • Zhao, P.1    Yu, B.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.