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Volumn E89-D, Issue 3, 2006, Pages 1128-1138

Generalization performance of subspace bayes approach in linear neural networks

Author keywords

Empirical Bayes; James Stein; Neural networks; Reduced rank regression; Unidentifiable; Variational Bayes

Indexed keywords

APPROXIMATION THEORY; ERROR ANALYSIS; MATHEMATICAL MODELS; MAXIMUM LIKELIHOOD ESTIMATION; MONTE CARLO METHODS; REGRESSION ANALYSIS;

EID: 33645781604     PISSN: 09168532     EISSN: 17451361     Source Type: Journal    
DOI: 10.1093/ietisy/e89-d.3.1128     Document Type: Conference Paper
Times cited : (4)

References (34)
  • 1
    • 33645770499 scopus 로고    scopus 로고
    • Generalization error of linear neural networks in an empirical Bayes approach
    • Edinburgh, U.K.
    • S. Nakajima and S. Watanabe, "Generalization error of linear neural networks in an empirical Bayes approach," Proc. IJCAI, pp.804-810, Edinburgh, U.K., 2005.
    • (2005) Proc. IJCAI , pp. 804-810
    • Nakajima, S.1    Watanabe, S.2
  • 3
    • 0042777587 scopus 로고
    • A generalized Bayesian framework for neural networks with singular fisher information matrices
    • S. Watanabe, "A generalized Bayesian framework for neural networks with singular fisher information matrices," Proc. NOLTA, pp.207-210, 1995.
    • (1995) Proc. NOLTA , pp. 207-210
    • Watanabe, S.1
  • 4
    • 84898934178 scopus 로고    scopus 로고
    • Geometrical singularities in the neuromanifold of multilayer perceptrons
    • S. Amari, H. Park, and T. Ozeki, "Geometrical singularities in the neuromanifold of multilayer perceptrons," Advances in NIPS, vol.14, pp.343-350, 2002.
    • (2002) Advances in NIPS , vol.14 , pp. 343-350
    • Amari, S.1    Park, H.2    Ozeki, T.3
  • 5
    • 0040079861 scopus 로고    scopus 로고
    • On the problem in model selection of neural network regression in overrealizable scenario
    • K. Hagiwara, "On the problem in model selection of neural network regression in overrealizable scenario," Neural Comput., vol. 14, pp.1979-2002, 2002.
    • (2002) Neural Comput. , vol.14 , pp. 1979-2002
    • Hagiwara, K.1
  • 6
    • 0016355478 scopus 로고
    • A new look at statistical model
    • H. Akaike, "A new look at statistical model," IEEE Trans. Autom. Control, vol.19, no.6, pp.716-723, 1974.
    • (1974) IEEE Trans. Autom. Control , vol.19 , Issue.6 , pp. 716-723
    • Akaike, H.1
  • 7
    • 0000120766 scopus 로고
    • Estimating the dimension of a model
    • G. Schwarz, "Estimating the dimension of a model," Annals of Statistics, vol.6, no.2, pp.461-464, 1978.
    • (1978) Annals of Statistics , vol.6 , Issue.2 , pp. 461-464
    • Schwarz, G.1
  • 8
    • 0000318553 scopus 로고
    • Stochastic complexity and modeling
    • J. Rissanen, "Stochastic complexity and modeling," Annals of Statistics, vol.14, no.3, pp. 1080-1100, 1986.
    • (1986) Annals of Statistics , vol.14 , Issue.3 , pp. 1080-1100
    • Rissanen, J.1
  • 10
    • 0031318748 scopus 로고    scopus 로고
    • Weights of chi-bar-square distribution for smooth or piecewise smooth cone alternatives
    • A. Takemura and S. Kuriki, "Weights of chi-bar-square distribution for smooth or piecewise smooth cone alternatives," Annals of Statistics, vol.25, no.6, pp.2368-2387, 1997.
    • (1997) Annals of Statistics , vol.25 , Issue.6 , pp. 2368-2387
    • Takemura, A.1    Kuriki, S.2
  • 11
    • 0035599160 scopus 로고    scopus 로고
    • Tail probabilities of the maxima of multilinear forms and their applications
    • S. Kuriki and A. Takemura, "Tail probabilities of the maxima of multilinear forms and their applications," Annals of Statistics, vol.29, no.2, pp.328-371, 2001.
    • (2001) Annals of Statistics , vol.29 , Issue.2 , pp. 328-371
    • Kuriki, S.1    Takemura, A.2
  • 12
    • 0042311289 scopus 로고    scopus 로고
    • Likelihood ratio of unidentifiable models and multilayer neural networks
    • K. Fukumizu, "Likelihood ratio of unidentifiable models and multilayer neural networks," Annals of Statistics, vol.31, no.3, pp.833-851, 2003.
    • (2003) Annals of Statistics , vol.31 , Issue.3 , pp. 833-851
    • Fukumizu, K.1
  • 13
    • 84996128633 scopus 로고    scopus 로고
    • Testing in locally conic models, and application to mixture models
    • D. Dacunha-Castelle and E. Gassiat, "Testing in locally conic models, and application to mixture models," Probability and Statistics, vol.1, pp.285-317, 1997.
    • (1997) Probability and Statistics , vol.1 , pp. 285-317
    • Dacunha-Castelle, D.1    Gassiat, E.2
  • 14
    • 84957085126 scopus 로고    scopus 로고
    • Generalization error of linear neural networks in unidentifiable cases
    • Springer
    • K. Fukumizu, "Generalization error of linear neural networks in unidentifiable cases," Proc. ALT, pp.51-62, Springer, 1999.
    • (1999) Proc. ALT , pp. 51-62
    • Fukumizu, K.1
  • 15
    • 0029343566 scopus 로고
    • Learning in linear neural networks: A survey
    • F.F. Baldi and K. Hornik, "Learning in linear neural networks: A survey," IEEE Trans. Neural Netw., vol.6, no.4, pp.837-858, 1995.
    • (1995) IEEE Trans. Neural Netw. , vol.6 , Issue.4 , pp. 837-858
    • Baldi, F.F.1    Hornik, K.2
  • 16
    • 0035316373 scopus 로고    scopus 로고
    • Algebraic analysis for nonidentifiable learning machines
    • S. Watanabe, "Algebraic analysis for nonidentifiable learning machines," Neural Comput., vol.13, no.4, pp.899-933, 2001.
    • (2001) Neural Comput. , vol.13 , Issue.4 , pp. 899-933
    • Watanabe, S.1
  • 17
    • 84968585977 scopus 로고    scopus 로고
    • Resolution of singularities in mixture models and its stochastic complexity
    • Singapore
    • K. Yamazaki and S. Watanabe, "Resolution of singularities in mixture models and its stochastic complexity," Proc. ICONIP, pp.1355-1359, Singapore, 2002.
    • (2002) Proc. ICONIP , pp. 1355-1359
    • Yamazaki, K.1    Watanabe, S.2
  • 18
    • 8344233612 scopus 로고    scopus 로고
    • Asymptotic model selection for naive bayesian networks
    • Alberta, Canada
    • D. Rusakov and D. Geiger, "Asymptotic model selection for naive Bayesian networks," Proc. UAI, pp.438-445, Alberta, Canada, 2002.
    • (2002) Proc. UAI , pp. 438-445
    • Rusakov, D.1    Geiger, D.2
  • 20
    • 22944471325 scopus 로고    scopus 로고
    • Stochastic complexity of Bayesian networks
    • Acapulco, Mexico
    • K. Yamazaki and S. Watanabe, "Stochastic complexity of Bayesian networks," Proc. UAI, pp.592-599, Acapulco, Mexico, 2003.
    • (2003) Proc. UAI , pp. 592-599
    • Yamazaki, K.1    Watanabe, S.2
  • 21
    • 33645797360 scopus 로고    scopus 로고
    • The generalization error of reduced rank regression in bayesian estimation
    • Parma, Italy
    • M. Aoyagi and S. Watanabe, "The generalization error of reduced rank regression in Bayesian estimation," Proc. ISITA, pp. 1068-1073, Parma, Italy, 2004.
    • (2004) Proc. ISITA , pp. 1068-1073
    • Aoyagi, M.1    Watanabe, S.2
  • 22
    • 0003937573 scopus 로고    scopus 로고
    • Algebraic information geometry for learning machines with singularities
    • S. Watanabe, "Algebraic information geometry for learning machines with singularities," Advances in NIPS, vol.13, pp.329-336, 2001.
    • (2001) Advances in NIPS , vol.13 , pp. 329-336
    • Watanabe, S.1
  • 23
    • 0027803368 scopus 로고
    • Keeping neural networks simple by minimizing the description length of the weights
    • G.E. Hinton and D. van Camp, "Keeping neural networks simple by minimizing the description length of the weights," Proc. COLT, pp.5-13, 1993.
    • (1993) Proc. COLT , pp. 5-13
    • Hinton, G.E.1    Van Camp, D.2
  • 24
    • 0038765941 scopus 로고
    • Developments in probabilistic modeling with neural networks - Ensemble learning
    • D.J.C. MacKay, "Developments in probabilistic modeling with neural networks - Ensemble learning," Proc. 3rd Ann. Symp. on Neural Networks, pp. 191-198, 1995.
    • (1995) Proc. 3rd Ann. Symp. on Neural Networks , pp. 191-198
    • MacKay, D.J.C.1
  • 25
    • 0003278032 scopus 로고    scopus 로고
    • Inferring parameters and structure of latent variable models by variational Bayes
    • H. Attias, "Inferring parameters and structure of latent variable models by variational Bayes," Proc. UAI, 1999.
    • (1999) Proc. UAI
    • Attias, H.1
  • 26
    • 1542559558 scopus 로고    scopus 로고
    • Graphical models and variational methods
    • MIT Press
    • Z. Ghahramani and M.J. Beal, "Graphical models and variational methods," in Advanced Mean Field Methods, pp. 161-177, MIT Press, 2001.
    • (2001) Advanced Mean Field Methods , pp. 161-177
    • Ghahramani, Z.1    Beal, M.J.2
  • 27
    • 33645790065 scopus 로고    scopus 로고
    • Generalization error and free energy of variational bayes approach of linear neural networks
    • Taipei, Taiwan
    • S. Nakajima and S. Watanabe, "Generalization error and free energy of variational Bayes approach of linear neural networks," Proc. ICONIP, pp.55-60, Taipei, Taiwan, 2005.
    • (2005) Proc. ICONIP , pp. 55-60
    • Nakajima, S.1    Watanabe, S.2
  • 29
    • 0042879444 scopus 로고    scopus 로고
    • Learning coefficients of layered models when the true distribution mismatches the singularities
    • S. Watanabe and S. Amari, "Learning coefficients of layered models when the true distribution mismatches the singularities," Neural Comput., vol.15, pp. 1013-1033, 2003.
    • (2003) Neural Comput. , vol.15 , pp. 1013-1033
    • Watanabe, S.1    Amari, S.2
  • 31
    • 84949161149 scopus 로고
    • Stein's estimation rule and its competitors - An empirical bayes approach
    • B. Efron and C. Morris, "Stein's estimation rule and its competitors - An empirical Bayes approach," J. Am. Stat. Assoc., vol.68, pp.117-130, 1973.
    • (1973) J. Am. Stat. Assoc. , vol.68 , pp. 117-130
    • Efron, B.1    Morris, C.2
  • 32
    • 51849177370 scopus 로고
    • Likelihood and bayes procedure
    • ed. J.M. Bemald, University Press
    • H. Akaike, "Likelihood and Bayes Procedure," in Bayesian Statistics, ed. J.M. Bemald, pp. 143-166, University Press, 1980.
    • (1980) Bayesian Statistics , pp. 143-166
    • Akaike, H.1
  • 33
    • 80052029170 scopus 로고
    • Approximate Bayesian inference in conditionally independent hierarchical models (Parametric empirical Bayes models)
    • R.E. Kass and D. Steffey, "Approximate Bayesian inference in conditionally independent hierarchical models (Parametric empirical Bayes models)," J. Am. Stat. Assoc., vol.84, pp.717-726, 1989.
    • (1989) J. Am. Stat. Assoc. , vol.84 , pp. 717-726
    • Kass, R.E.1    Steffey, D.2
  • 34
    • 0002247902 scopus 로고
    • The strong limits of random matrix spectra for sample matrices of independent elements
    • K. W. Watcher, "The strong limits of random matrix spectra for sample matrices of independent elements," Ann. Prob., vol.6, pp. 1-18, 1978.
    • (1978) Ann. Prob. , vol.6 , pp. 1-18
    • Watcher, K.W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.