메뉴 건너뛰기




Volumn 5, Issue , 2011, Pages 127-145

PAC-Bayesian bounds for sparse regression estimation with exponential weights

Author keywords

Exponential weights; High dimensional regression; Pac bayesian inequalities; References; Sparsity oracle inequality

Indexed keywords


EID: 79960999147     PISSN: 19357524     EISSN: None     Source Type: Journal    
DOI: 10.1214/11-EJS601     Document Type: Article
Times cited : (42)

References (46)
  • 3
    • 79960993628 scopus 로고    scopus 로고
    • PAC-Bayesian bounds for randomized empirical risk minimizers
    • MR2483458
    • Alquier, P. (2008). PAC-Bayesian bounds for randomized empirical risk minimizers. Mathematical Methods of Statistics 17 (4) 279-304. MR2483458
    • (2008) Mathematical Methods of Statistics , vol.17 , Issue.4 , pp. 279-304
    • Alquier, P.1
  • 6
    • 56449120785 scopus 로고    scopus 로고
    • Bolasso: Model consistent Lasso estimation through the bootstrap
    • Proceedings of the 25th International Conference On Machine Learning New-York
    • Bach, F. (2008). Bolasso: model consistent Lasso estimation through the bootstrap. Proceedings of the 25th international conference on Machine learning, ACM, New-York.
    • (2008) ACM
    • Bach, F.1
  • 7
    • 68649086910 scopus 로고    scopus 로고
    • Simultaneous Analysis of Lasso and Dantzig Selector
    • MR2533469
    • Bickel, P. J., Ritov, Y. and Tsybakov, A. (2009). Simultaneous Analysis of Lasso and Dantzig Selector. The Annals of Statistics 37 (4) 1705-1732.MR2533469
    • (2009) The Annals of Statistics , vol.37 , Issue.4 , pp. 1705-1732
    • Bickel, P.J.1    Ritov, Y.2    Tsybakov, A.3
  • 9
  • 10
    • 67650122784 scopus 로고    scopus 로고
    • On Recovery of Sparse Signals via ℓ1 Minimization
    • MR2598028
    • Cai, T., Xu, G. and Zhang, J. (2009). On Recovery of Sparse Signals via ℓ1 Minimization. IEEE Transactions on Information Theory 55 3388-3397.MR2598028
    • (2009) IEEE Transactions On Information Theory , vol.55 , pp. 3388-3397
    • Cai, T.1    Xu, G.2    Zhang, J.3
  • 11
    • 50849141334 scopus 로고    scopus 로고
    • The Dantzig selector: Statistical estimation when p is much larger than n
    • MR2382644
    • Candés, E. and Tao, T. (2007) The Dantzig selector: statistical estimation when p is much larger than n. The Annals of Statistics 35. MR2382644
    • (2007) The Annals of Statistics , vol.35
    • Candés, E.1    Tao, T.2
  • 14
    • 77956910901 scopus 로고    scopus 로고
    • PAC-Bayesian Supervised Classification (The Thermo- dynamics of Statistical Learning)
    • MR2483528
    • Catoni, O. (2007) PAC-Bayesian Supervised Classification (The Thermo- dynamics of Statistical Learning). IMS Lecture Notes - Monograph Series 56. MR2483528
    • (2007) IMS Lecture Notes - Monograph Series , pp. 56
    • Catoni, O.1
  • 15
    • 0035273106 scopus 로고    scopus 로고
    • Atomic Decomposition by Basis Pursuit
    • MR1639094
    • Chen, S. S., Donoho, D. L. and Saunders, M. A. (2001). Atomic Decomposition by Basis Pursuit. SIAM Review 43 (1) 129-159 MR1639094
    • (2001) SIAM Review , vol.43 , Issue.1 , pp. 129-159
    • Chen, S.S.1    Donoho, D.L.2    Saunders, M.A.3
  • 17
    • 70350003059 scopus 로고    scopus 로고
    • Aggregation by exponential weighting, sharp oracle inequalities and sparsity
    • Dalalyan, A. and Tsybakov, A. (2008). Aggregation by exponential weighting, sharp oracle inequalities and sparsity. Machine Learning 72 (1- 2) 39-61.
    • (2008) Machine Learning , vol.72 , Issue.1-2 , pp. 39-61
    • Dalalyan, A.1    Tsybakov, A.2
  • 22
    • 0001194220 scopus 로고
    • A Statistical View on Some Chemometrics Regression Tools
    • Frank, L. and Friedman, J. (1993). A Statistical View on Some Chemometrics Regression Tools. Technometrics 16 199-511.
    • (1993) Technometrics , vol.16 , pp. 199-511
    • Frank, L.1    Friedman, J.2
  • 25
    • 79961003838 scopus 로고    scopus 로고
    • An- nales de l'Institut Henri Poincaré B: Probability and Statistics, to appear
    • Koltchinskii, V. (2010). Sparsity in Empirical Risk Minimization. An- nales de l'Institut Henri Poincaré B: Probability and Statistics, to appear.
    • (2010) Sparsity In Empirical Risk Minimization
    • Koltchinskii, V.1
  • 28
    • 33746478298 scopus 로고    scopus 로고
    • Information theory and mixing least-squares regressions
    • MR2242356
    • Leung, G. and Barron, A. R. (2006). Information theory and mixing least-squares regressions. IEEE Transactions on Information Theory 52 (8) 3396-3410. MR2242356
    • (2006) IEEE Transactions On Information Theory , vol.52 , Issue.8 , pp. 3396-3410
    • Leung, G.1    Barron, A.R.2
  • 29
    • 79952905234 scopus 로고    scopus 로고
    • Generalized mirror averaging and d-convex aggregation
    • MR2356820
    • Lounici, K. (2007). Generalized mirror averaging and d-convex aggregation. Mathematical Methods of Statistics 16 (3). MR2356820
    • (2007) Mathematical Methods of Statistics , vol.16 , Issue.3
    • Lounici, K.1
  • 30
    • 56449113372 scopus 로고    scopus 로고
    • Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators
    • MR2386087
    • Lounici, K. (2008). Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators. Electronic Journal of Statistics 2 90-102. MR2386087
    • (2008) Electronic Journal of Statistics , vol.2 , pp. 90-102
    • Lounici, K.1
  • 31
    • 84915425007 scopus 로고
    • Some comments on cp
    • MR1365719
    • Mallows, C. L. (1973). Some comments on cp. Technometrics 15 661-676.MR1365719
    • (1973) Technometrics , vol.15 , pp. 661-676
    • Mallows, C.L.1
  • 34
    • 0031637037 scopus 로고    scopus 로고
    • Some pac-bayesian theorems
    • Proceedings of the Eleventh Annual Conference on Computational Learning Theory MR1811587
    • McAllester D. A. (1998). Some pac-bayesian theorems. Proceedings of the Eleventh Annual Conference on Computational Learning Theory. ACM, 230-234. MR1811587
    • (1998) ACM , pp. 230-234
    • McAllester, D.A.1
  • 36
    • 79961005521 scopus 로고    scopus 로고
    • Exponential Screening and optimal rates of sparse estimation
    • to appear
    • Rigollet, P. and Tsybakov, A. (2010). Exponential Screening and optimal rates of sparse estimation. The Annals of Statistics, to appear.
    • (2010) The Annals of Statistics
    • Rigollet, P.1    Tsybakov, A.2
  • 37
    • 0000120766 scopus 로고
    • Estimating the dimension of a model
    • MR0468014
    • Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6 461-464.MR0468014
    • (1978) The Annals of Statistics , vol.6 , pp. 461-464
    • Schwarz, G.1
  • 38
    • 0030684558 scopus 로고    scopus 로고
    • A PAC analysis of a bayes estimator
    • Proceedings of the Tenth Annual Conference on Computational Learning Theory
    • Shawe-Taylor, J. and Williamson, R. (1997). A PAC analysis of a bayes estimator. Proceedings of the Tenth Annual Conference on Computational Learning Theory. ACM, 2-9.
    • (1997) ACM , pp. 2-9
    • Shawe-Taylor, J.1    Williamson, R.2
  • 39
    • 85194972808 scopus 로고    scopus 로고
    • Regression shrinkage and selection via the LASSO
    • MR1379242
    • Tibshirani, R. (1996). Regression shrinkage and selection via the LASSO. Journal of the Royal Statistical Society B 58 (1) 267-288. MR1379242
    • (1996) Journal of the Royal Statistical Society B , vol.58 , Issue.1 , pp. 267-288
    • Tibshirani, R.1
  • 40
    • 9444226947 scopus 로고    scopus 로고
    • Optimal rates of aggregation. Computationnal Learning theory and Kernel Machines
    • Springer, Heidelberg
    • Tsybakov, A. (2003). Optimal rates of aggregation. Computationnal Learning theory and Kernel Machines, Lecture Notes in Artificial Intelligence n.2777, Springer, Heidelberg. 303-313.
    • (2003) Lecture Notes In Artificial Intelligence , Issue.2777 , pp. 303-313
    • Tsybakov, A.1
  • 42
    • 77955054299 scopus 로고    scopus 로고
    • On the conditions used to prove oracle results for the LASSO
    • MR2576316
    • Van de Geer, S. A. and Bühlmann, P. (2009). On the conditions used to prove oracle results for the LASSO. Electronic Journal of Statistics 3 1360-1392. MR2576316
    • (2009) Electronic Journal of Statistics , vol.3 , pp. 1360-1392
    • van de Geer, S.A.1    Bühlmann, P.2
  • 43
    • 29144460670 scopus 로고    scopus 로고
    • Aggregating regression procedures to improve performance
    • MR2044592
    • Yang, Y. (2004). Aggregating regression procedures to improve performance. Bernoulli, 10 (1) 25-47. MR2044592
    • (2004) Bernoulli , vol.10 , Issue.1 , pp. 25-47
    • Yang, Y.1
  • 44
    • 33847361463 scopus 로고    scopus 로고
    • From epsilon-entropy to KL-entropy: Analysis of minimum information complexity density estimation
    • MR2291500
    • Zhang, T. (2008). From epsilon-entropy to KL-entropy: analysis of minimum information complexity density estimation. The Annals of Statistics 34 2180-2210. MR2291500
    • (2008) The Annals of Statistics , vol.34 , pp. 2180-2210
    • Zhang, T.1
  • 45
    • 33846114377 scopus 로고    scopus 로고
    • The adaptive lasso and its oracle properties
    • MR2279469
    • Zou, H. (2006). The adaptive lasso and its oracle properties. Journal of the American Statistical Association, 101 1418-1429. MR2279469
    • (2006) Journal of the American Statistical Association , vol.101 , pp. 1418-1429
    • Zou, H.1
  • 46
    • 16244401458 scopus 로고    scopus 로고
    • Regularization and variable selection via the elastic net
    • MR2137327
    • Zou, H. and Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society B 67 (2) 301-320. MR2137327
    • (2005) Journal of the Royal Statistical Society B , vol.67 , Issue.2 , pp. 301-320
    • Zou, H.1    Hastie, T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.