-
1
-
-
33646407804
-
Singularities Affect Dynamics of Learning in Neuromanifolds
-
S.-i. Amari, H. Park, and T. Ozeki, "Singularities Affect Dynamics of Learning in Neuromanifolds," Neural Comput., 18(5),pp.1007-1065, 2006.
-
(2006)
Neural Comput
, vol.18
, Issue.5
, pp. 1007-1065
-
-
Amari, S.-I.1
Park, H.2
Ozeki, T.3
-
2
-
-
34548816357
-
-
M.Aoyagi,S.Watanabe,Resolution of singularities and generalization error with Bayesian estimation for layered neural network, J88-D-II, No.10, pp.2112-2124, 2005.
-
M.Aoyagi,S.Watanabe,"Resolution of singularities and generalization error with Bayesian estimation for layered neural network," Vol.J88-D-II, No.10, pp.2112-2124, 2005.
-
-
-
-
3
-
-
24344502351
-
Stochastic complexities of reduced rank regression in Bayesian estimation
-
M.Aoyagi, S.Watanabe/'Stochastic complexities of reduced rank regression in Bayesian estimation," Neural Networks, Vol.18,No.7, pp.924-933, 2005.
-
(2005)
Neural Networks
, vol.18
, Issue.7
, pp. 924-933
-
-
Aoyagi, M.1
Watanabe, S.2
-
4
-
-
84980186498
-
Resolution of singularities and division of distributions
-
M.F.Atiyah,"Resolution of singularities and division of distributions," Comm. Pure Appl. Math., Vol.13,pp. 145-150, 1970.
-
(1970)
Comm. Pure Appl. Math
, vol.13
, pp. 145-150
-
-
Atiyah, M.F.1
-
5
-
-
0040079861
-
On the Problem in Model Selection of Neural Network Regression in Overrealizable Scenario,
-
8, pp
-
K. Hagiwara, "On the Problem in Model Selection of Neural Network Regression in Overrealizable Scenario, " Neural Comput., Vol.14,Vol.8, pp.1979-2002, 2002.
-
(2002)
Neural Comput
, vol.14
, pp. 1979-2002
-
-
Hagiwara, K.1
-
7
-
-
0347526308
-
On the Asymptotic Distribution of the Least-Squares Estimators in Unidentifiable Models
-
T. Hayasaka, M. Kitahara, and S. Usui, "On the Asymptotic Distribution of the Least-Squares Estimators in Unidentifiable Models," Neural Comput., Vol.16 ,No.1, pp.99 - 114, 2004.
-
(2004)
Neural Comput
, vol.16
, Issue.1
, pp. 99-114
-
-
Hayasaka, T.1
Kitahara, M.2
Usui, S.3
-
8
-
-
0000554923
-
Resolution of singularities of an algebraic variety over a field of characteristic zero
-
H. Hironaka, "Resolution of singularities of an algebraic variety over a field of characteristic zero," Ann. of Math., Vol.79, 109-326,1964.
-
(1964)
Ann. of Math
, vol.79
, pp. 109-326
-
-
Hironaka, H.1
-
9
-
-
34548842673
-
Stochastic complexity of Hidden Markov Models on the Variational Bayesian Learning
-
D-II, to appear in
-
T.Hosino, K.Watanabe,S.Watanabe,"Stochastic complexity of Hidden Markov Models on the Variational Bayesian Learning," to appear in IEICE Transactions (D-II).
-
IEICE Transactions
-
-
Hosino, T.1
Watanabe, K.2
Watanabe, S.3
-
10
-
-
33750588021
-
Free Energy of Stochastic Context Free Grammar on Variational Bayes.
-
pp
-
T.Hosino, K.Watanabe, S.Watanabe,"Free Energy of Stochastic Context Free Grammar on Variational Bayes. " pp.407-416, Proc. of ICONIP,2006.
-
(2006)
Proc. of ICONIP
, pp. 407-416
-
-
Hosino, T.1
Watanabe, K.2
Watanabe, S.3
-
11
-
-
0003015630
-
B-functions and holonomic systems
-
M. Kashiwara, "B-functions and holonomic systems," Inventions Math., 38, 33-53,1976.
-
(1976)
Inventions Math
, vol.38
, pp. 33-53
-
-
Kashiwara, M.1
-
12
-
-
34548863827
-
The Exchange Monte Carlo Method for Bayesian Learning in Singular Learning Machines
-
K.Nagata, S.Watanabe, "The Exchange Monte Carlo Method for Bayesian Learning in Singular Learning Machines," Proc. of WCCI2006,(Canada, Cancouver), 2006.
-
(2006)
Proc. of WCCI2006,(Canada, Cancouver)
-
-
Nagata, K.1
Watanabe, S.2
-
13
-
-
34247210751
-
Variational Bayes Solution of Linear Neural Networks and its Generalization Performance
-
to appear
-
S. Nakajima, S. Watanabe, "Variational Bayes Solution of Linear Neural Networks and its Generalization Performance," Neural Computation, to appear.
-
Neural Computation
-
-
Nakajima, S.1
Watanabe, S.2
-
14
-
-
34548823684
-
Asymptotic Behavior of Stochastic Complexity of Complete Bipartite Graph-type Boltzmann Machines
-
Chaina,HongKong to appear
-
Y. Nishiyama, S.Watanabe, "Asymptotic Behavior of Stochastic Complexity of Complete Bipartite Graph-type Boltzmann Machines," Proc. of ICONIP2006, (Chaina,HongKong) to appear, 2006.
-
(2006)
Proc. of ICONIP2006
-
-
Nishiyama, Y.1
Watanabe, S.2
-
15
-
-
33646348720
-
Stochastic Complexities of Gaussian Mixtures in Variational Bayesian Approximation
-
Apr,pp
-
K.Watanabe, S.Watanabe, "Stochastic Complexities of Gaussian Mixtures in Variational Bayesian Approximation," Journal of Machine Learning Research, Vol.7, (Apr),pp. 625-644, 2006.
-
(2006)
Journal of Machine Learning Research
, vol.7
, pp. 625-644
-
-
Watanabe, K.1
Watanabe, S.2
-
16
-
-
33847097822
-
Stochastic complexities of general mixture models in variational Bayesian leaning
-
to appear
-
K.Watanabe, S.Watanabe, "Stochastic complexities of general mixture models in variational Bayesian leaning," Neural Networks, to appear.
-
Neural Networks
-
-
Watanabe, K.1
Watanabe, S.2
-
17
-
-
0042777587
-
Generalized Bayesian framework for neural networks with singular Fisher information matrices
-
Las Vegas, pp
-
S.Watanabe, "Generalized Bayesian framework for neural networks with singular Fisher information matrices," Proc. of International Symposium on Nonlinear Theory and Its applications, (Las Vegas), pp.207-210, 1995.
-
(1995)
Proc. of International Symposium on Nonlinear Theory and Its applications
, pp. 207-210
-
-
Watanabe, S.1
-
18
-
-
0002550762
-
Algebraic analysis for singular statistical estimation
-
Proc. of International Journal of Algorithmic Learning Theory
-
S.Watanabe, "Algebraic analysis for singular statistical estimation," Proc. of International Journal of Algorithmic Learning Theory, Lecture Notes on Computer Sciences, 1720, pp.39-50, 1999.
-
(1999)
Lecture Notes on Computer Sciences
, vol.1720
, pp. 39-50
-
-
Watanabe, S.1
-
19
-
-
0003937573
-
-
Advances in Neural Information Processing Systems, Denver, USA, pp
-
S. Watanabe, "Algebraic information geometry for learning machines with singularities," Advances in Neural Information Processing Systems, (Denver, USA), pp.329-336. 2001.
-
(2001)
Algebraic information geometry for learning machines with singularities
, pp. 329-336
-
-
Watanabe, S.1
-
20
-
-
0035316373
-
Algebraic Analysis for Nonidentifiable Learning Machines
-
S.Watanabe, "Algebraic Analysis for Nonidentifiable Learning Machines," Neural Computation, Vol.13, No.4, pp.899-933, 2001.
-
(2001)
Neural Computation
, vol.13
, Issue.4
, pp. 899-933
-
-
Watanabe, S.1
-
21
-
-
0034842476
-
Algebraic geometrical methods for hierarchical learning machines
-
S. Watanabe, "Algebraic geometrical methods for hierarchical learning machines," Neural Networks, Vol.14, No.8,pp.1049-1060, 2001.
-
(2001)
Neural Networks
, vol.14
, Issue.8
, pp. 1049-1060
-
-
Watanabe, S.1
-
22
-
-
0035506030
-
Learning efficiency of redundant neural networks in Bayesian estimation
-
S. Watanabe, "Learning efficiency of redundant neural networks in Bayesian estimation," IEEE Transactions on Neural Networks, Vol.12, No.6, 1475-1486,2001.
-
(2001)
IEEE Transactions on Neural Networks
, vol.12
, Issue.6
, pp. 1475-1486
-
-
Watanabe, S.1
-
23
-
-
0042879444
-
Leaming coefficients of layered models when the true distribution mismatches the singularities
-
S.Watanabe, S.-I.Amari,"Leaming coefficients of layered models when the true distribution mismatches the singularities", Neural Computation, Vol.15,No.5,1013-1033, 2003.
-
(2003)
Neural Computation
, vol.15
, Issue.5
, pp. 1013-1033
-
-
Watanabe, S.1
Amari, S.I.2
-
24
-
-
21744459329
-
Algebraic geometry of singular learning machines and symmetry of generalization and training errors
-
S.Watanabe,"Algebraic geometry of singular learning machines and symmetry of generalization and training errors," Neurocomputing, Vol.67,pp. 198-213,2005.
-
(2005)
Neurocomputing
, vol.67
, pp. 198-213
-
-
Watanabe, S.1
-
25
-
-
0742324924
-
Singularities in mixture models and upper bounds of stochastic complexity
-
K.Yamazaki, S.Watanabe,"Singularities in mixture models and upper bounds of stochastic complexity." International Journal of Neural Networks, Vol.16, No.7, pp.1029-1038,2003.
-
(2003)
International Journal of Neural Networks
, vol.16
, Issue.7
, pp. 1029-1038
-
-
Yamazaki, K.1
Watanabe, S.2
-
26
-
-
15344345868
-
Singularities in Complete bipartite graph-type Boltzmann machines and upper bounds of stochastic complexities
-
K.Yamazaki, S.Watanabe," Singularities in Complete bipartite graph-type Boltzmann machines and upper bounds of stochastic complexities", IEEE Trans. on Neural Networks, Vol. 16 (2), pp.312-324, 2005.
-
(2005)
IEEE Trans. on Neural Networks
, vol.16
, Issue.2
, pp. 312-324
-
-
Yamazaki, K.1
Watanabe, S.2
-
27
-
-
27844446553
-
Algebraic geometry and stochastic complexity of hidden Markov models
-
K. Yamazaki and S. Watanabe, "Algebraic geometry and stochastic complexity of hidden Markov models", Neurocomputing, Vol.69, pp.62-84, 2005.
-
(2005)
Neurocomputing
, vol.69
, pp. 62-84
-
-
Yamazaki, K.1
Watanabe, S.2
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