메뉴 건너뛰기




Volumn 40, Issue 1, 2000, Pages 77-102

Upper and lower bounds on the learning curve for Gaussian processes

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; ERRORS; GRAPH THEORY; MARKOV PROCESSES; MATRIX ALGEBRA; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES; VECTORS;

EID: 0033686947     PISSN: 08856125     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007601601278     Document Type: Article
Times cited : (58)

References (29)
  • 2
    • 0016355478 scopus 로고
    • A new look at statistical model identification
    • Akaike, H. (1974). A new look at statistical model identification. IEEE Transactions on Automatic Control, 19, 716-723.
    • (1974) IEEE Transactions on Automatic Control , vol.19 , pp. 716-723
    • Akaike, H.1
  • 3
    • 0000308194 scopus 로고    scopus 로고
    • Gaussian processes for Bayesian classification via hybrid Monte Carlo
    • M. C. Mozer, M. I. Jordan, & T. Petsche (Eds.), MIT Press
    • Barber, D. & Williams, C. K. I. (1997). Gaussian processes for Bayesian classification via hybrid Monte Carlo. In M. C. Mozer, M. I. Jordan, & T. Petsche (Eds.), Advances in Neural Information Processing Systems, Vol. 9. MIT Press.
    • (1997) Advances in Neural Information Processing Systems , vol.9
    • Barber, D.1    Williams, C.K.I.2
  • 4
    • 0003707560 scopus 로고
    • New York: John Wiley and Sons
    • David, H. A. (1970). Order Statistics. New York: John Wiley and Sons.
    • (1970) Order Statistics
    • David, H.A.1
  • 6
    • 0027188154 scopus 로고
    • Stochastic linear learning: Exact test and training error averages
    • Hansen, L. K. (1993). Stochastic linear learning: Exact test and training error averages. Neural Networks, 6, 393-396.
    • (1993) Neural Networks , vol.6 , pp. 393-396
    • Hansen, L.K.1
  • 8
    • 0031326925 scopus 로고    scopus 로고
    • Mutual information, metric entropy and cumulative relative entropy risk
    • Haussler, D. & Opper, M. (1997). Mutual information, metric entropy and cumulative relative entropy risk. The Annals of Statistics, 25(6), 2451.
    • (1997) The Annals of Statistics , vol.25 , Issue.6 , pp. 2451
    • Haussler, D.1    Opper, M.2
  • 9
    • 0003495476 scopus 로고
    • Singapore: World Scientific Publishing
    • Ihara, S. (1993). Information Theory. Singapore: World Scientific Publishing.
    • (1993) Information Theory
    • Ihara, S.1
  • 10
    • 0004256437 scopus 로고
    • Berlin: Springer-Verlag. Lecture Notes in Statistics
    • Matérn, B. (1986). Spatial Variation, 2nd ed. Berlin: Springer-Verlag. Lecture Notes in Statistics, Vol. 36.
    • (1986) Spatial Variation, 2nd Ed. , pp. 36
    • Matérn, B.1
  • 11
    • 0002417069 scopus 로고
    • Design problems for optimal surface interpolation
    • Z. Ziegler (Ed.), Academic Press
    • Michelli, C. A. & Wahba, G. (1981). Design problems for optimal surface interpolation. In Z. Ziegler (Ed.), Approximation Theory and Applications (pp. 329-348). Academic Press.
    • (1981) Approximation Theory and Applications , pp. 329-348
    • Michelli, C.A.1    Wahba, G.2
  • 12
    • 0028544395 scopus 로고
    • Network information criterion-determining the number of hidden units for artificial neural network models
    • Murata, N., Yoshizawa, S., & Amari, S. (1994). Network information criterion-determining the number of hidden units for artificial neural network models. IEEE Transactions on Neural Networks, 5, 865-872.
    • (1994) IEEE Transactions on Neural Networks , vol.5 , pp. 865-872
    • Murata, N.1    Yoshizawa, S.2    Amari, S.3
  • 13
    • 0003301456 scopus 로고    scopus 로고
    • Bayesian Learning for Neural Networks
    • Springer
    • Neal, R. M. (1996). Bayesian Learning for Neural Networks. Springer. Lecture Notes in Statistics, Vol. 118.
    • (1996) Lecture Notes in Statistics , vol.118
    • Neal, R.M.1
  • 14
    • 84858745127 scopus 로고    scopus 로고
    • Regression with gaussian processes: Average case performance
    • M. W. Kwok-Yee, K. Irwin, & Y. Dit-Yan (Eds.), Springer-Verlag
    • Opper, M. (1997). Regression with gaussian processes: Average case performance. In M. W. Kwok-Yee, K. Irwin, & Y. Dit-Yan (Eds.), Theoretical Aspects of Neural Computation: A Multidisciplinary Perspective. Springer-Verlag.
    • (1997) Theoretical Aspects of Neural Computation: a Multidisciplinary Perspective
    • Opper, M.1
  • 15
    • 0343244538 scopus 로고    scopus 로고
    • General bounds on Bayes errors for regression with Gaussian Processes
    • M. J. Kearns, S. A. Solla, & D. A. Cohn (Eds.), MIT Press
    • Opper, M. & Vivarelli, F. (1999). General bounds on Bayes errors for regression with Gaussian Processes. In M. J. Kearns, S. A. Solla, & D. A. Cohn (Eds.), Advances in Neural Information Processing Systems, Vol. 11 (pp. 302-308). MIT Press.
    • (1999) Advances in Neural Information Processing Systems , vol.11 , pp. 302-308
    • Opper, M.1    Vivarelli, F.2
  • 18
    • 0342374925 scopus 로고    scopus 로고
    • An upper bound on the Bayesian error bars for generalized linear regression
    • S. W. Ellacott, J. C. Mason, & I. J. Anderson (Eds.), Kluwer
    • Qazaz, C. S., Williams, C. K. I., & Bishop, C. M. (1997). An upper bound on the Bayesian error bars for generalized linear regression. In S. W. Ellacott, J. C. Mason, & I. J. Anderson (Eds.), Mathematics of Neural Networks (pp. 295-299). Kluwer.
    • (1997) Mathematics of Neural Networks , pp. 295-299
    • Qazaz, C.S.1    Williams, C.K.I.2    Bishop, C.M.3
  • 20
    • 0030240964 scopus 로고    scopus 로고
    • Almost optimal differentiation using noisy data
    • Ritter, K. (1996). Almost optimal differentiation using noisy data. Journal of Approximation Theory, 86(3), 293-309.
    • (1996) Journal of Approximation Theory , vol.86 , Issue.3 , pp. 293-309
    • Ritter, K.1
  • 21
    • 0001231555 scopus 로고
    • Multivariate integration and approximation for random fields satisfying Sacks-Ylvisaker conditions
    • Ritter, K., Wasilkowski, G. W., & Wozniakowski, H. (1995). Multivariate integration and approximation for random fields satisfying Sacks-Ylvisaker conditions. Ann. Appl. Prob., 5, 518-540.
    • (1995) Ann. Appl. Prob. , vol.5 , pp. 518-540
    • Ritter, K.1    Wasilkowski, G.W.2    Wozniakowski, H.3
  • 22
    • 0001995852 scopus 로고
    • Some aspects of the spline smoothing approach to non-parametric regression curve filtering
    • Silverman, B. W. (1985). Some aspects of the spline smoothing approach to non-parametric regression curve filtering. Journal of the Royal Statistical Society B, 47(1), 1-52.
    • (1985) Journal of the Royal Statistical Society B , vol.47 , Issue.1 , pp. 1-52
    • Silverman, B.W.1
  • 23
    • 84898945810 scopus 로고    scopus 로고
    • Learning curves for Gaussian processes
    • M. J. Kearns, S. A. Solla, & D. A. Cohn (Eds.), MIT Press
    • Sollich, P. (1999). Learning curves for Gaussian processes. In M. J. Kearns, S. A. Solla, & D. A. Cohn (Eds.), Advances in Neural Information Processing Systems, Vol. 11 (pp. 344-350). MIT Press.
    • (1999) Advances in Neural Information Processing Systems , vol.11 , pp. 344-350
    • Sollich, P.1
  • 24
    • 84972499772 scopus 로고
    • Design and Analysis of Computer Experiments
    • Comment on the paper by Sacks, J. et al.
    • Stein, M. L. (1989). Comment on the paper by Sacks, J. et al. Design and Analysis of Computer Experiments. Statistical Science, 4(4):432-433.
    • (1989) Statistical Science , vol.4 , Issue.4 , pp. 432-433
    • Stein, M.L.1
  • 29
    • 84898974226 scopus 로고    scopus 로고
    • Computing with infinite networks
    • M. C. Mozer, M. I. Jordan, & T. Petsche (Eds.), MIT Press
    • Williams, C. K. I. (1997). Computing with infinite networks. In M. C. Mozer, M. I. Jordan, & T. Petsche (Eds.), Advances in Neural Information Processing Systems Vol. 9. MIT Press.
    • (1997) Advances in Neural Information Processing Systems , vol.9
    • Williams, C.K.I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.