-
1
-
-
33645770499
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
19
-
-
22944464295
-
Stochastic complexities of hidden markov models
-
Toulouse, France
-
K. Yamazaki and S. Watanabe, "Stochastic complexities of hidden Markov models," Proc. Neural Networks for Signal Processing XIII (NNSP), pp. 179-188, Toulouse, France, 2003.
-
(2003)
Proc. Neural Networks for Signal Processing XIII (NNSP)
, pp. 179-188
-
-
Yamazaki, K.1
Watanabe, S.2
-
20
-
-
22944471325
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
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