-
1
-
-
0016355478
-
A new look at the statistical model identification
-
Akaike, H. (1974). A new look at the statistical model identification. IEEE Trans. on Automatic Control, 19, 716-723.
-
(1974)
IEEE Trans. on Automatic Control
, vol.19
, pp. 716-723
-
-
Akaike, H.1
-
2
-
-
51849177370
-
Likelihood and Bayes procedure
-
J. M. Bernald (Ed.), Valencia, Spain: University Press
-
Akaike, H. (1980). Likelihood and Bayes procedure. In J. M. Bernald (Ed.), Bayesian statistics (pp. 143-166), Valencia, Spain: University Press.
-
(1980)
Bayesian Statistics
, pp. 143-166
-
-
Akaike, H.1
-
4
-
-
0027257001
-
A universal theorem on learning curves
-
Amari, S. (1993). A universal theorem on learning curves. Neural Networks, 6, 161-166.
-
(1993)
Neural Networks
, vol.6
, pp. 161-166
-
-
Amari, S.1
-
5
-
-
0000660569
-
Four types of learning curves
-
Amari, S., Fujita, N., & Shinomoto, S. (1992). Four types of learning curves. Neural Computation, 4(4), 608-618.
-
(1992)
Neural Computation
, vol.4
, Issue.4
, pp. 608-618
-
-
Amari, S.1
Fujita, N.2
Shinomoto, S.3
-
6
-
-
0000729504
-
Statistical theory of learning curves under entropic loss
-
Amari, S., & Murata, N. (1993). Statistical theory of learning curves under entropic loss. Neural Computation, 5, 140-153.
-
(1993)
Neural Computation
, vol.5
, pp. 140-153
-
-
Amari, S.1
Murata, N.2
-
7
-
-
84980186498
-
Resolution of singularities and division of distributions
-
Atiyah, M. F. (1970). Resolution of singularities and division of distributions. Comm. Pure and Appl. Math., 13, 145-150.
-
(1970)
Comm. Pure and Appl. Math.
, vol.13
, pp. 145-150
-
-
Atiyah, M.F.1
-
8
-
-
0001325515
-
Approximation and estimation bounds for artificial neural networks
-
Barron, A. R. (1994). Approximation and estimation bounds for artificial neural networks. Machine Learning, 14(1), 115-133.
-
(1994)
Machine Learning
, vol.14
, Issue.1
, pp. 115-133
-
-
Barron, A.R.1
-
9
-
-
0001620260
-
The analytic continuation of generalized functions with respect to a parameter
-
Bernstein, I. N. (1972). The analytic continuation of generalized functions with respect to a parameter. Functional Anal. Appl., 6, 26-40.
-
(1972)
Functional Anal. Appl.
, vol.6
, pp. 26-40
-
-
Bernstein, I.N.1
-
13
-
-
84996128633
-
Testing in locally conic models, and application to mixture models
-
Dacunha-Castelle, D., & Gassiat, E. (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, E.2
-
14
-
-
0030198493
-
A regularity condition of information matrix of a multilayer perceptron network
-
Fukumizu, K. (1996). A regularity condition of information matrix of a multilayer perceptron network. Neural Networks, 9, 871-879.
-
(1996)
Neural Networks
, vol.9
, pp. 871-879
-
-
Fukumizu, K.1
-
15
-
-
84957085126
-
Generalization error of linear neural networks in unidentifiable cases
-
Fukumizu, K. (1999). Generalization error of linear neural networks in unidentifiable cases. In Lecture Notes on Computer Science, 1720, 51-62.
-
(1999)
Lecture Notes on Computer Science
, vol.1720
, pp. 51-62
-
-
Fukumizu, K.1
-
17
-
-
0033698411
-
On the problem in model selection of neural network regression in overrealizable scenario
-
Italy, Como.
-
Hagiwara, K., Kuno, K., & Usui, S. (2000). On the problem in model selection of neural network regression in overrealizable scenario. In Proc. of Int. Joint Conf. on Neural Netork, Italy, Como.
-
(2000)
Proc. of Int. Joint Conf. on Neural Netork
-
-
Hagiwara, K.1
Kuno, K.2
Usui, S.3
-
18
-
-
0027884625
-
On the problem of applying AIC to determine the structure of a layered feed-forward neural network
-
Hagiwara, K., Toda, N., & Usui, S. (1993). On the problem of applying AIC to determine the structure of a layered feed-forward neural network. Proc. of IJCNN Nagoya Japan, 3, 2263-2266.
-
(1993)
Proc. of IJCNN Nagoya Japan
, vol.3
, pp. 2263-2266
-
-
Hagiwara, K.1
Toda, N.2
Usui, S.3
-
19
-
-
0000554923
-
Resolution of singularities of an algebraic variety over a field of characteristic zero
-
Hironaka, H. (1964). Resolution of singularities of an algebraic variety over a field of characteristic zero. Annals of Mathematics, 79, 109-326.
-
(1964)
Annals of Mathematics
, vol.79
, pp. 109-326
-
-
Hironaka, H.1
-
20
-
-
0003015630
-
B-functions and holonomic systems
-
Kashiwara, M. (1976). B-functions and holonomic systems. Inventions Math., 38, 33-53.
-
(1976)
Inventions Math.
, vol.38
, pp. 33-53
-
-
Kashiwara, M.1
-
21
-
-
0001000930
-
On Hotelling's approach to testing for a nonlinear parameter in regression
-
Knowles, M., & Siegmund, D. (1989). On Hotelling's approach to testing for a nonlinear parameter in regression. International Statistical Review, 57, 205-220.
-
(1989)
International Statistical Review
, vol.57
, pp. 205-220
-
-
Knowles, M.1
Siegmund, D.2
-
22
-
-
0025508916
-
A statistical approaches to learning and generalization in layered neural networks
-
Levin, E., Tishby, N., & Solla, S. A. (1990). A statistical approaches to learning and generalization in layered neural networks. Proc. of IEEE, 78(10), 1568-1674.
-
(1990)
Proc. of IEEE
, vol.78
, Issue.10
, pp. 1568-1674
-
-
Levin, E.1
Tishby, N.2
Solla, S.A.3
-
23
-
-
0001025418
-
Bayesian interpolation
-
Mackay, D. J. (1992). Bayesian interpolation. Neural Computation, 4(2), 415-447.
-
(1992)
Neural Computation
, vol.4
, Issue.2
, pp. 415-447
-
-
Mackay, D.J.1
-
24
-
-
0000041417
-
Neural networks for optimal approximation of smooth and analytic functions
-
Mhaskar, H. N. (1996). Neural networks for optimal approximation of smooth and analytic functions. Neural Computation, 8, 164-177.
-
(1996)
Neural Computation
, vol.8
, pp. 164-177
-
-
Mhaskar, H.N.1
-
25
-
-
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), 797-807.
-
(1994)
IEEE Transactions on Neural Networks
, vol.5
, Issue.6
, pp. 797-807
-
-
Murata, N.1
Yoshizawa, S.2
Amari, S.3
-
26
-
-
0031145751
-
Algorithms for the b-function and D-modules associated with a polynomial
-
Oaku, T. (1997). Algorithms for the b-function and D-modules associated with a polynomial. Journal of Pure and Applied Algebra, 117, 495-518.
-
(1997)
Journal of Pure and Applied Algebra
, vol.117
, pp. 495-518
-
-
Oaku, T.1
-
28
-
-
0000285881
-
Bounds for predictive errors in the statistical mechanics of supervised learning
-
Opper, M., & Haussler, D. (1995). Bounds for predictive errors in the statistical mechanics of supervised learning. Physical Review letters, 75(20), 3772-3775.
-
(1995)
Physical Review Letters
, vol.75
, Issue.20
, pp. 3772-3775
-
-
Opper, M.1
Haussler, D.2
-
29
-
-
0000318553
-
Stochastic complexity and modeling
-
Rissanen, J. (1986). Stochastic complexity and modeling. Annals of Statistics, 14, 1080-1100.
-
(1986)
Annals of Statistics
, vol.14
, pp. 1080-1100
-
-
Rissanen, J.1
-
30
-
-
0000557192
-
On zeta functions associated with prehomogeneous vector space
-
Sato, M., & Shintani, T. (1974). On zeta functions associated with prehomogeneous vector space. Annals of Mathematics, 100, 131-170.
-
(1974)
Annals of Mathematics
, vol.100
, pp. 131-170
-
-
Sato, M.1
Shintani, T.2
-
31
-
-
0000120766
-
Estimating the dimension of a model
-
Schwarz, G. (1974). Estimating the dimension of a model. Annals of Statistics, 6(2), 461-464.
-
(1974)
Annals of Statistics
, vol.6
, Issue.2
, pp. 461-464
-
-
Schwarz, G.1
-
32
-
-
77956887130
-
An optimal model selection of regression variables
-
Shibata, R. (1981). An optimal model selection of regression variables. Biometrika, 68, 45-54.
-
(1981)
Biometrika
, vol.68
, pp. 45-54
-
-
Shibata, R.1
-
33
-
-
0040567317
-
Inequalities of generalization errors for layered neural networks in Bayesian learning
-
Watanabe, S. (1998a). Inequalities of generalization errors for layered neural networks in Bayesian learning. Proc. of Int. Conf. on Neural. Inform. Process, 1, 59-62.
-
(1998)
Proc. of Int. Conf. on Neural. Inform. Process
, vol.1
, pp. 59-62
-
-
Watanabe, S.1
-
34
-
-
0000839087
-
On the generalization error by a layered statistical model with Bayesian estimation
-
Watanabe, S. (1998b). On the generalization error by a layered statistical model with Bayesian estimation. IEICE Trans., J81-A, 1442-1452. (English version is in Elect. and Comm. in Japan, (2000), 95-104.)
-
(1998)
IEICE Trans.
, vol.J81-A
, pp. 1442-1452
-
-
Watanabe, S.1
-
35
-
-
0041161467
-
-
Watanabe, S. (1998b). On the generalization error by a layered statistical model with Bayesian estimation. IEICE Trans., J81-A, 1442-1452. (English version is in Elect. and Comm. in Japan, (2000), 95-104.)
-
(2000)
Elect. and Comm. in Japan
, pp. 95-104
-
-
-
36
-
-
0002550762
-
Algebraic analysis for singular statistical estimation
-
Watanabe, S. (1999). Algebraic analysis for singular statistical estimation. Lecture Notes in Computer Science, 1720, 39-50.
-
(1999)
Lecture Notes in Computer Science
, vol.1720
, pp. 39-50
-
-
Watanabe, S.1
-
37
-
-
0000213888
-
Algebraic analysis for non-regular learning machines
-
Watanabe, S. (2000a). Algebraic analysis for non-regular learning machines. Advances in Neural Information Processing, 12, 356-362.
-
(2000)
Advances in Neural Information Processing
, vol.12
, pp. 356-362
-
-
Watanabe, S.1
-
39
-
-
0029306567
-
Probabilistic design of layered neural networks based on their unified framework
-
Watanabe, S., & Fukumizu, K. (1995). Probabilistic design of layered neural networks based on their unified framework. IEEE Trans. on Neural Networks, 6(3), 691-702.
-
(1995)
IEEE Trans. on Neural Networks
, vol.6
, Issue.3
, pp. 691-702
-
-
Watanabe, S.1
Fukumizu, K.2
-
40
-
-
0032121805
-
A decision-theoretic extension of stochastic complexity and its applications to learning
-
Yamanishi, K. (1998). A decision-theoretic extension of stochastic complexity and its applications to learning. IEEE Trans. on Information Theory, 44(4), 1424-1439.
-
(1998)
IEEE Trans. on Information Theory
, vol.44
, Issue.4
, pp. 1424-1439
-
-
Yamanishi, K.1
|