-
1
-
-
0034202524
-
Nonmonotonic generalization bias of gaussian mixture models
-
Akaho, S., & Kappen, H. J. (2000). Nonmonotonic generalization bias of gaussian mixture models. Neural Computation, 12, 6, 1411-1428.
-
(2000)
Neural Computation
, vol.12
, Issue.6
, pp. 1411-1428
-
-
Akaho, S.1
Kappen, H.J.2
-
2
-
-
0016355478
-
A new look at the statistical model identification
-
Akaike, H. (1974). A new look at the statistical model identification. IEEE Trans. Appl. Comp., AC-19, 716-723.
-
(1974)
IEEE Trans. Appl. Comp.
, vol.AC-19
, pp. 716-723
-
-
Akaike, H.1
-
3
-
-
0000920843
-
Theory of adaptive pattern classifiers
-
Amari, S. (1967). Theory of adaptive pattern classifiers. IEEE Trans., EC-16(3), 299-307.
-
(1967)
IEEE Trans.
, vol.EC-16
, Issue.3
, pp. 299-307
-
-
Amari, S.1
-
4
-
-
0017713690
-
Dynamics of pattern formation in lateral-inhibition type neural fields
-
Amari, S. (1977). Dynamics of pattern formation in lateral-inhibition type neural fields. Biological Cybernetics. 27, 77-87.
-
(1977)
Biological Cybernetics
, vol.27
, pp. 77-87
-
-
Amari, S.1
-
5
-
-
0002975366
-
Differential geometry of a parametric family of invertible linear systems - Riemannian metric, dual affine connections and divergence
-
Amari, S. (1987). Differential geometry of a parametric family of invertible linear systems - Riemannian metric, dual affine connections and divergence. Mathematical Systems Theory, 20, 53-82.
-
(1987)
Mathematical Systems Theory
, vol.20
, pp. 53-82
-
-
Amari, S.1
-
6
-
-
0000396062
-
Natural gradient works efficiently in learning
-
Amari, S. (1998). Natural gradient works efficiently in learning. Neural Computation, 10, 251-276.
-
(1998)
Neural Computation
, vol.10
, pp. 251-276
-
-
Amari, S.1
-
9
-
-
0000729504
-
Statistical theory of learning curves under entropic loss criterion
-
Amari, S., & Murata, N. (1993). Statistical theory of learning curves under entropic loss criterion. Neural Computation, 5, 140-154.
-
(1993)
Neural Computation
, vol.5
, pp. 140-154
-
-
Amari, S.1
Murata, N.2
-
11
-
-
17144406556
-
Difficulty of singularity in population coding
-
Amari, S., & Nakahara, H. (2005). Difficulty of singularity in population coding. Neural Computation, 17, 839-858.
-
(2005)
Neural Computation
, vol.17
, pp. 839-858
-
-
Amari, S.1
Nakahara, H.2
-
12
-
-
0035125794
-
Differential and algebraic geometry of multilayer perceptrons
-
Amari, S., & Ozeki, T. (2001). Differential and algebraic geometry of multilayer perceptrons. IEICE Trans., E84-A, 31-38.
-
(2001)
IEICE Trans.
, vol.E84-A
, pp. 31-38
-
-
Amari, S.1
Ozeki, T.2
-
13
-
-
0038030649
-
Learning and inference in hierarchical models with singularities
-
Amari, S., Ozeki, T., & Park, H. (2003). Learning and inference in hierarchical models with singularities. Systems and Computers in Japan, 34, 34-42.
-
(2003)
Systems and Computers in Japan
, vol.34
, pp. 34-42
-
-
Amari, S.1
Ozeki, T.2
Park, H.3
-
14
-
-
0034201611
-
Adaptive method of realizing natural gradient learning for multilayer perceptrons
-
Amari, S., Park, H., & Fukumizu, K. (2000). Adaptive method of realizing natural gradient learning for multilayer perceptrons. Neural Computation, 12, 1399-1409.
-
(2000)
Neural Computation
, vol.12
, pp. 1399-1409
-
-
Amari, S.1
Park, H.2
Fukumizu, K.3
-
15
-
-
33646435394
-
Statistical inference in nonidentifiable and singular statistical models
-
Amari, S., Park, H., & Ozeki, T. (2001). Statistical inference in nonidentifiable and singular statistical models. J. of the Korean Statistical Society, 30(2), 179-192.
-
(2001)
J. of the Korean Statistical Society
, vol.30
, Issue.2
, pp. 179-192
-
-
Amari, S.1
Park, H.2
Ozeki, T.3
-
16
-
-
84898934178
-
Geometrical singularities in the neuromanifold of multilayer perceptrons
-
T. G. Dietterich, S. Becker, & Z. Ghahramani (Eds.). Cambridge, MA: MIT Press
-
Amari, S., Park, H., & Ozeki, T. (2002). Geometrical singularities in the neuromanifold of multilayer perceptrons. In T. G. Dietterich, S. Becker, & Z. Ghahramani (Eds.), Advances in neural information processing systems, 14 (pp. 343-350). Cambridge, MA: MIT Press.
-
(2002)
Advances in Neural Information Processing Systems
, vol.14
, pp. 343-350
-
-
Amari, S.1
Park, H.2
Ozeki, T.3
-
17
-
-
0016991025
-
Some geometric questions in the theory of linear systems
-
Brockett, R. W. (1976). Some geometric questions in the theory of linear systems. IEEE Trans. on Automatic Control, 21, 449-455.
-
(1976)
IEEE Trans. on Automatic Control
, vol.21
, pp. 449-455
-
-
Brockett, R.W.1
-
18
-
-
0001199897
-
On the geometry of feedforward neural network error surfaces
-
Chen, A. M., Lu, H., & Hecht-Nielsen, R. (1993). On the geometry of feedforward neural network error surfaces. Neural Computation, 5, 910-927.
-
(1993)
Neural Computation
, vol.5
, pp. 910-927
-
-
Chen, A.M.1
Lu, H.2
Hecht-Nielsen, R.3
-
19
-
-
84996128633
-
Testing in locally conic models, and application to mixture models
-
Dacunha-Castelle, D., & Gassiat, É. (1997). Testing in locally conic models, and application to mixture models. Probability and Statistics, 1, 285-317.
-
(1997)
Probability and Statistics
, vol.1
, pp. 285-317
-
-
Dacunha-Castelle, D.1
Gassiat, É.2
-
21
-
-
0042311289
-
Likelihood ratio of unidentifiable models and multilayer neural networks
-
Fukumizu, K. (2003). Likelihood ratio of unidentifiable models and multilayer neural networks. Annals of Statistics, 32(3), 833-851.
-
(2003)
Annals of Statistics
, vol.32
, Issue.3
, pp. 833-851
-
-
Fukumizu, K.1
-
22
-
-
0034018074
-
Local minima and plateaus in hierarchical structures of multilayer perceptrons
-
Fukumizu, K., & Amari, S. (2000), Local minima and plateaus in hierarchical structures of multilayer perceptrons. Neural Networks, 13, 317-327.
-
(2000)
Neural Networks
, vol.13
, pp. 317-327
-
-
Fukumizu, K.1
Amari, S.2
-
23
-
-
0040079861
-
On the problem in model selection of neural network regression in overrealizable scenario
-
Hagiwara, K. (2002a). On the problem in model selection of neural network regression in overrealizable scenario. Neural Computation, 14, 1979-2002.
-
(2002)
Neural Computation
, vol.14
, pp. 1979-2002
-
-
Hagiwara, K.1
-
24
-
-
0036826115
-
Regularization learning, early stopping and biased estimator
-
Hagiwara, K. (2002b). Regularization learning, early stopping and biased estimator. Neurocomputing, 48, 937-955.
-
(2002)
Neurocomputing
, vol.48
, pp. 937-955
-
-
Hagiwara, K.1
-
25
-
-
0035200563
-
Upper bound of the expected training error of neural network regression for a gaussian noise sequence
-
Hagiwara, K., Hayasaka, T., Toda, N., Usui, S., & Kuno, K. (2001). Upper bound of the expected training error of neural network regression for a gaussian noise sequence. Neural Networks, 14, 1419-1429.
-
(2001)
Neural Networks
, vol.14
, pp. 1419-1429
-
-
Hagiwara, K.1
Hayasaka, T.2
Toda, N.3
Usui, S.4
Kuno, K.5
-
26
-
-
0027884625
-
On the problem of applying AIC to determine the structure of a layered feed-forward neural network
-
Nagoya, Japan
-
Hagiwara, K., Toda, N., & Usui, S. (1993). On the problem of applying AIC to determine the structure of a layered feed-forward neural network. Proceedings of IJCNN (Vol. 3, pp. 2263-2266). Nagoya, Japan.
-
(1993)
Proceedings of IJCNN
, vol.3
, pp. 2263-2266
-
-
Hagiwara, K.1
Toda, N.2
Usui, S.3
-
28
-
-
0001070336
-
Tubes and spheres in n-spaces, and a class of statistical problems
-
Hotelling, H. (1939). Tubes and spheres in n-spaces, and a class of statistical problems. Amer. J. Math., 61, 440-460.
-
(1939)
Amer. J. Math.
, vol.61
, pp. 440-460
-
-
Hotelling, H.1
-
29
-
-
0038323312
-
On-line learning theory of soft committee machines with correlated hidden units - Steepest gradient descent and natural gradient descent
-
Inoue, M., Park, H., & Okada, M. (2003). On-line learning theory of soft committee machines with correlated hidden units - Steepest gradient descent and natural gradient descent. J. Phys. Soc. Jpn., 72(4), 805-810.
-
(2003)
J. Phys. Soc. Jpn.
, vol.72
, Issue.4
, pp. 805-810
-
-
Inoue, M.1
Park, H.2
Okada, M.3
-
30
-
-
0040899705
-
Generalization in a two-layer neural networks
-
Kang, K., Oh, J.-H., Kwon, S., & Park, Y. (1993). Generalization in a two-layer neural networks. Phys. Rev. E, 48(6), 4805-4809.
-
(1993)
Phys. Rev. E
, vol.48
, Issue.6
, pp. 4805-4809
-
-
Kang, K.1
Oh, J.-H.2
Kwon, S.3
Park, Y.4
-
31
-
-
20344383126
-
On the statistical properties of least squares estimators of layered neural networks (in Japanese)
-
Kitahara, M., Hayasaka, T., Toda, N., & Usui, S. (2000). On the statistical properties of least squares estimators of layered neural networks (in Japanese). IEICE Transactions, J86-D-II, 563-570.
-
(2000)
IEICE Transactions, J86-D-II
, pp. 563-570
-
-
Kitahara, M.1
Hayasaka, T.2
Toda, N.3
Usui, S.4
-
32
-
-
0000720909
-
Functionally equivalent feedforward neural networks
-
Kůrková, V., & Kainen, P. C. (1994). Functionally equivalent feedforward neural networks. Neural Computation, 6, 543-558.
-
(1994)
Neural Computation
, vol.6
, pp. 543-558
-
-
Kůrková, V.1
Kainen, P.C.2
-
33
-
-
0041810454
-
Asymptotics for likelihood ratio tests under loss of identifiability
-
Liu, X., & Shao, Y. (2003). Asymptotics for likelihood ratio tests under loss of identifiability. Annals of Statistics, 32(3), 807-832.
-
(2003)
Annals of Statistics
, vol.32
, Issue.3
, pp. 807-832
-
-
Liu, X.1
Shao, Y.2
-
35
-
-
0028544395
-
Network information criterion -determining the number of hidden units for an artificial neural network model
-
Murata, N., Yoshizawa, S., & Amari, S. (1994). Network information criterion -determining the number of hidden units for an artificial neural network model. IEEE Transactions on Neural Networks, 5(6), 865-872.
-
(1994)
IEEE Transactions on Neural Networks
, vol.5
, Issue.6
, pp. 865-872
-
-
Murata, N.1
Yoshizawa, S.2
Amari, S.3
-
36
-
-
0034266869
-
Adaptive natural gradient learning algorithms for various stochastic models
-
Park, H., Amari, S., & Fukumizu, K. (2000). Adaptive natural gradient learning algorithms for various stochastic models. Neural Networks, 13, 755-764.
-
(2000)
Neural Networks
, vol.13
, pp. 755-764
-
-
Park, H.1
Amari, S.2
Fukumizu, K.3
-
37
-
-
0345581643
-
On-line learning dynamics of multilayer perceptrons with unidentifiable parameters
-
Submitted to
-
Park, H., Inoue, M., & Okada, M. (2003). On-line learning dynamics of multilayer perceptrons with unidentifiable parameters. Submitted to J. Phys. A: Math. Gen., 36, 11753-11764.
-
(2003)
J. Phys. A: Math. Gen.
, vol.36
, pp. 11753-11764
-
-
Park, H.1
Inoue, M.2
Okada, M.3
-
38
-
-
0032613639
-
Analysis of natural gradient descent for multilayer neural networks
-
Rattray, M., & Saad, D. (1999). Analysis of natural gradient descent for multilayer neural networks. Physical Review E, 59, 4523-4532.
-
(1999)
Physical Review E
, vol.59
, pp. 4523-4532
-
-
Rattray, M.1
Saad, D.2
-
39
-
-
0000198852
-
Natural gradient descent for on-line learning
-
Rattray, M., Saad, D., & Amari, S. (1998). Natural gradient descent for on-line learning. Physical Review Letters, 81, 5461-5464.
-
(1998)
Physical Review Letters
, vol.81
, pp. 5461-5464
-
-
Rattray, M.1
Saad, D.2
Amari, S.3
-
40
-
-
21844501969
-
On-line backpropagation in two-layered neural networks
-
Riegler, P., & Biehl, M. (1995). On-line backpropagation in two-layered neural networks. J. Phys. A; Math. Gen., 28, L507-L513.
-
(1995)
J. Phys. A; Math. Gen.
, vol.28
-
-
Riegler, P.1
Biehl, M.2
-
41
-
-
0000318553
-
Stochastic complexity and modeling
-
Risssanen, J. (1986). Stochastic complexity and modeling. Ann. Statist. 14, 1080-1100.
-
(1986)
Ann. Statist.
, vol.14
, pp. 1080-1100
-
-
Risssanen, J.1
-
44
-
-
0000646059
-
Learning internal representations by error backpropagation
-
D. Rumelhart & J. L. McClelland (Eds.). Cambridge, MA: MIT Press
-
Rumelhart, D., Hinton, G. E., & Williams, R. J. (1986). Learning internal representations by error backpropagation. In D. Rumelhart & J. L. McClelland (Eds.), Parallel distributed processing: Explorations in the microstructure of cognition (Vol. 1). Cambridge, MA: MIT Press.
-
(1986)
Parallel Distributed Processing: Explorations in the Microstructure of Cognition
, vol.1
-
-
Rumelhart, D.1
Hinton, G.E.2
Williams, R.J.3
-
45
-
-
4243234689
-
On-line learning in soft committee machines
-
Saad, D., & Solla, A. (1995). On-line learning in soft committee machines. Phys. Rev. E, 52, 4225-4243.
-
(1995)
Phys. Rev. E
, vol.52
, pp. 4225-4243
-
-
Saad, D.1
Solla, A.2
-
46
-
-
0000120766
-
Estimating the dimension of a model
-
Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461-164.
-
(1978)
Annals of Statistics
, vol.6
, pp. 461-1164
-
-
Schwarz, G.1
-
47
-
-
0026897370
-
Uniqueness of the weights for minimal feedforward nets with a given input-output map
-
Sussmann, H. J. (1992). Uniqueness of the weights for minimal feedforward nets with a given input-output map. Neural Networks. 5, 589-593.
-
(1992)
Neural Networks.
, vol.5
, pp. 589-593
-
-
Sussmann, H.J.1
-
48
-
-
0035316373
-
Algebraic analysis for non-identifiable learning machines
-
Watanabe, S. (2001a). Algebraic analysis for non-identifiable learning machines. Neural Computation, 23, 899-933.
-
(2001)
Neural Computation
, vol.23
, pp. 899-933
-
-
Watanabe, S.1
-
49
-
-
0034842476
-
Algebraic geometrical methods for hierarchical learning machines
-
Watanabe, S. (2001b). Algebraic geometrical methods for hierarchical learning machines. Neural Networks, 24(8), 1409-1060.
-
(2001)
Neural Networks
, vol.24
, Issue.8
, pp. 1409-11060
-
-
Watanabe, S.1
-
50
-
-
0003937573
-
Algebraic information geometry for learning machines with singularities
-
T. K. Leen, T. G. Dietterich, & V. Tresp (Eds.). Cambridge, MA: MIT Press
-
Watanabe, S. (2001c). Algebraic information geometry for learning machines with singularities. In T. K. Leen, T. G. Dietterich, & V. Tresp (Eds.), Advances in neural information processing systems, 13 (pp. 329-336). Cambridge, MA: MIT Press.
-
(2001)
Advances in Neural Information Processing Systems
, vol.13
, pp. 329-336
-
-
Watanabe, S.1
-
51
-
-
0042879444
-
Learning coefficients of layered models when the true distribution mismatches the singularities
-
Watanabe, S., & Amari, S. (2003). Learning coefficients of layered models when the true distribution mismatches the singularities. Neural Computation, 15(5), 1013-1033.
-
(2003)
Neural Computation
, vol.15
, Issue.5
, pp. 1013-1033
-
-
Watanabe, S.1
Amari, S.2
-
52
-
-
0000045032
-
On the volume of tubes
-
Weyl, H. (1939). On the volume of tubes. Amer. J. Math., 61, 461-472.
-
(1939)
Amer. J. Math.
, vol.61
, pp. 461-472
-
-
Weyl, H.1
-
53
-
-
0036583146
-
Population coding and decoding in a neural field: A computational study
-
Wu, S., Amari, S., & Nakahara, H. (2002). Population coding and decoding in a neural field: A computational study. Neural Computation, 14, 999-1026.
-
(2002)
Neural Computation
, vol.14
, pp. 999-1026
-
-
Wu, S.1
Amari, S.2
Nakahara, H.3
-
54
-
-
0035319119
-
Population coding with correlation and an unfaithful model
-
Wu, S., Nakahara, H., & Amari, S. (2001). Population coding with correlation and an unfaithful model. Neural Computation, 23, 775-797.
-
(2001)
Neural Computation
, vol.23
, pp. 775-797
-
-
Wu, S.1
Nakahara, H.2
Amari, S.3
-
55
-
-
0742318729
-
A probabilistic algorithm to calculate the learning curves of hierarchical learning machines with singularities
-
Yamazaki, K., & Watanabe, S. (2002). A probabilistic algorithm to calculate the learning curves of hierarchical learning machines with singularities. Trans. on IEICE, J85-D-II(3), 363-372.
-
(2002)
Trans. on IEICE, J85-D-II
, Issue.3
, pp. 363-372
-
-
Yamazaki, K.1
Watanabe, S.2
-
56
-
-
0742324924
-
Singularities in mixture models and upper bounds of stochastic complexity
-
Yamazaki, K., & Watanabe, S. (2003). Singularities in mixture models and upper bounds of stochastic complexity. International Journal of Neural Networks, 16(7), 1029-1038.
-
(2003)
International Journal of Neural Networks
, vol.16
, Issue.7
, pp. 1029-1038
-
-
Yamazaki, K.1
Watanabe, S.2
|