메뉴 건너뛰기




Volumn 224, Issue 1, 2009, Pages 182-192

Learning rates of gradient descent algorithm for classification

Author keywords

Classification algorithm; computational complexity; Learning rates; Reproducing kernel Hilbert space; Stochastic gradient descent

Indexed keywords

ALGORITHMS; BANACH SPACES; COMMUNICATION CHANNELS (INFORMATION THEORY); COMPUTATIONAL COMPLEXITY; HILBERT SPACES; MATHEMATICAL TECHNIQUES; TIME VARYING NETWORKS;

EID: 56449126442     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2008.04.022     Document Type: Article
Times cited : (10)

References (22)
  • 1
    • 5844297152 scopus 로고
    • Theory of reproducing kernels
    • Aronszajn N. Theory of reproducing kernels. Trans. Amer. Math. Soc. 68 (1950) 337-404
    • (1950) Trans. Amer. Math. Soc. , vol.68 , pp. 337-404
    • Aronszajn, N.1
  • 2
    • 0035370926 scopus 로고    scopus 로고
    • Relative loss bounds for on-line density estimation with exponential family of distributions
    • Azoury K.S., and Warmuth M.K. Relative loss bounds for on-line density estimation with exponential family of distributions. Mach. Learn. 43 (2001) 211-246
    • (2001) Mach. Learn. , vol.43 , pp. 211-246
    • Azoury, K.S.1    Warmuth, M.K.2
  • 4
    • 0038453192 scopus 로고    scopus 로고
    • Rademacher and Gaussian complexities: Risk bounds and structural results
    • Bartlett P.L., and Mendelson S. Rademacher and Gaussian complexities: Risk bounds and structural results. J. Mach. Learn. Res. 3 (2002) 463-482
    • (2002) J. Mach. Learn. Res. , vol.3 , pp. 463-482
    • Bartlett, P.L.1    Mendelson, S.2
  • 6
    • 0030145382 scopus 로고    scopus 로고
    • Worst-case quadratic loss bounds for prediction using linear functions and gradient descent
    • Cesa-Bianchi N., Long P., and Warmuth M.K. Worst-case quadratic loss bounds for prediction using linear functions and gradient descent. IEEE Trans. Neural Netw. 7 (1996) 604-619
    • (1996) IEEE Trans. Neural Netw. , vol.7 , pp. 604-619
    • Cesa-Bianchi, N.1    Long, P.2    Warmuth, M.K.3
  • 7
    • 84879394399 scopus 로고    scopus 로고
    • Support vector machine soft margin classifiers: Error analysis
    • Chen D.R., Wu Q., Ying Y., and Zhou D.X. Support vector machine soft margin classifiers: Error analysis. J. Mach. Learn. Res. 5 (2004) 1143-1175
    • (2004) J. Mach. Learn. Res. , vol.5 , pp. 1143-1175
    • Chen, D.R.1    Wu, Q.2    Ying, Y.3    Zhou, D.X.4
  • 8
    • 0036071370 scopus 로고    scopus 로고
    • On the mathematical foundations of learning
    • Cucker F., and Smale S. On the mathematical foundations of learning. Bull. Amer. Math. Soc. 39 (2001) 1-49
    • (2001) Bull. Amer. Math. Soc. , vol.39 , pp. 1-49
    • Cucker, F.1    Smale, S.2
  • 9
    • 38949140825 scopus 로고    scopus 로고
    • Learning gradients by a gradient descent algorithm
    • Dong X., and Zhou D.-X. Learning gradients by a gradient descent algorithm. J. Math. Anal. Appl. 2 314 (2008) 1018-1027
    • (2008) J. Math. Anal. Appl. , vol.2 , Issue.314 , pp. 1018-1027
    • Dong, X.1    Zhou, D.-X.2
  • 10
    • 0003989054 scopus 로고    scopus 로고
    • Uniform central limit theorems, covariances via gradients
    • Combridge university Press
    • Dudley R.M. Uniform central limit theorems, covariances via gradients. Combridge Studies in Advanced Mathematics vol. 63 (1999), Combridge university Press
    • (1999) Combridge Studies in Advanced Mathematics , vol.63
    • Dudley, R.M.1
  • 13
    • 34247197035 scopus 로고    scopus 로고
    • Fast rates for support vector machines using Gaussian kernels
    • 279-294
    • Scovel C., and Steinwart I. Fast rates for support vector machines using Gaussian kernels. Ann. Statist. 35 (2007) 575-607 279-294
    • (2007) Ann. Statist. , vol.35 , pp. 575-607
    • Scovel, C.1    Steinwart, I.2
  • 14
    • 0036749277 scopus 로고    scopus 로고
    • Support vector machines are uniformly consistent
    • Steinwart I. Support vector machines are uniformly consistent. J. Complexity 18 (2002) 768-791
    • (2002) J. Complexity , vol.18 , pp. 768-791
    • Steinwart, I.1
  • 15
    • 33744740175 scopus 로고    scopus 로고
    • Online learning algorithms
    • Smale S., and Yao Y. Online learning algorithms. Found. Comp. Math. 6 (2006) 145-170
    • (2006) Found. Comp. Math. , vol.6 , pp. 145-170
    • Smale, S.1    Yao, Y.2
  • 16
    • 34547455409 scopus 로고    scopus 로고
    • Learning theory estimates via integral operators and their approximations
    • Smale S., and Zhou D.X. Learning theory estimates via integral operators and their approximations. Constr. Approx. 26 (2007) 153-172
    • (2007) Constr. Approx. , vol.26 , pp. 153-172
    • Smale, S.1    Zhou, D.X.2
  • 17
    • 56449125326 scopus 로고    scopus 로고
    • S. Smale, D.X. Zhou, Online learning with Markov sampling, 2007 (submitted for publication)
    • S. Smale, D.X. Zhou, Online learning with Markov sampling, 2007 (submitted for publication)
  • 19
    • 34547435898 scopus 로고    scopus 로고
    • On early stopping in gradient descent learning
    • Yao Y., Rosasco L., and Caponnetto A. On early stopping in gradient descent learning. Constr. Approx. 26 (2007) 289-315
    • (2007) Constr. Approx. , vol.26 , pp. 289-315
    • Yao, Y.1    Rosasco, L.2    Caponnetto, A.3
  • 20
    • 34547603945 scopus 로고    scopus 로고
    • Fully online classification by regularization
    • Ye G.B., and Zhou D.X. Fully online classification by regularization. Appl. Comput. Harmon. Anal. 23 (2007) 198-214
    • (2007) Appl. Comput. Harmon. Anal. , vol.23 , pp. 198-214
    • Ye, G.B.1    Zhou, D.X.2
  • 21
    • 33750594552 scopus 로고    scopus 로고
    • Online regularized classification algorithms
    • Ying Y., and Zhou D.X. Online regularized classification algorithms. IEEE Trans. Inform. Theory 52 (2006) 4775-4788
    • (2006) IEEE Trans. Inform. Theory , vol.52 , pp. 4775-4788
    • Ying, Y.1    Zhou, D.X.2
  • 22
    • 4644257995 scopus 로고    scopus 로고
    • Statistical behavior and consistency of classification methods based on convex risk minimization
    • Zhang T. Statistical behavior and consistency of classification methods based on convex risk minimization. Ann. Statist. 32 (2004) 56-85
    • (2004) Ann. Statist. , vol.32 , pp. 56-85
    • Zhang, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.