-
1
-
-
33646407804
-
Singularities affect dynamics of learning in neuromanifolds
-
Amari S., Park H., and Ozeki T. Singularities affect dynamics of learning in neuromanifolds. Neural Computation 18 5 (2006) 1007-1065
-
(2006)
Neural Computation
, vol.18
, Issue.5
, pp. 1007-1065
-
-
Amari, S.1
Park, H.2
Ozeki, T.3
-
2
-
-
24344502351
-
Stochastic complexities of reduced rank regression in Bayesian estimation
-
Aoyagi M., and Watanabe S. Stochastic complexities of reduced rank regression in Bayesian estimation. Neural Networks 18 7 (2005) 924-933
-
(2005)
Neural Networks
, vol.18
, Issue.7
, pp. 924-933
-
-
Aoyagi, M.1
Watanabe, S.2
-
3
-
-
33749822350
-
Resolution of singularities and generalization error with Bayesian estimation for layered neural network
-
Aoyagi M., and Watanabe S. Resolution of singularities and generalization error with Bayesian estimation for layered neural network. IEICE Transactions J88-D-II 10 (2005) 2112-2124
-
(2005)
IEICE Transactions
, vol.J88-D-II
, Issue.10
, pp. 2112-2124
-
-
Aoyagi, M.1
Watanabe, S.2
-
4
-
-
84980186498
-
Resolution of singularities and division of distributions
-
Atiyah M.F. Resolution of singularities and division of distributions. Communications in Pure and Applied Mathematics 13 (1970) 145-150
-
(1970)
Communications in Pure and Applied Mathematics
, vol.13
, pp. 145-150
-
-
Atiyah, M.F.1
-
5
-
-
0040079861
-
On the problem in model selection of neural network regression in overrealizable scenario
-
Hagiwara K. On the problem in model selection of neural network regression in overrealizable scenario. Neural Computation 14 8 (2002) 1979-2002
-
(2002)
Neural Computation
, vol.14
, Issue.8
, pp. 1979-2002
-
-
Hagiwara, K.1
-
7
-
-
0347526308
-
On the asymptotic distribution of the least-squares estimators in unidentifiable models
-
Hayasaka T., Kitahara M., and Usui S. On the asymptotic distribution of the least-squares estimators in unidentifiable models. Neural Computation 16 1 (2004) 99-114
-
(2004)
Neural Computation
, 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
-
Hironaka H. Resolution of singularities of an algebraic variety over a field of characteristic zero. Annals of Mathematics 79 (1964) 109-326
-
(1964)
Annals of Mathematics
, vol.79
, pp. 109-326
-
-
Hironaka, H.1
-
9
-
-
0003015630
-
B-functions and holonomic systems
-
Kashiwara M. B-functions and holonomic systems. Inventions Mathematicae 38 (1976) 33-53
-
(1976)
Inventions Mathematicae
, vol.38
, pp. 33-53
-
-
Kashiwara, M.1
-
11
-
-
47549090314
-
Exchange Monte Carlo sampling from Bayesian Posterior for singular learning machines
-
Nagata K., and Watanabe S. Exchange Monte Carlo sampling from Bayesian Posterior for singular learning machines. IEEE Transactions on Neural Networks 19 7 (2008) 1253-1266
-
(2008)
IEEE Transactions on Neural Networks
, vol.19
, Issue.7
, pp. 1253-1266
-
-
Nagata, K.1
Watanabe, S.2
-
14
-
-
0002550762
-
Algebraic analysis for singular statistical estimation
-
Proc. of international journal of algorithmic learning theory
-
Watanabe S. Algebraic analysis for singular statistical estimation. Proc. of international journal of algorithmic learning theory. Lecture Notes on Computer Sciences 1720 (1999) 39-50
-
(1999)
Lecture Notes on Computer Sciences
, vol.1720
, pp. 39-50
-
-
Watanabe, S.1
-
15
-
-
0006698283
-
Algebraic information geometry for learning machines with singularities
-
Watanabe S. Algebraic information geometry for learning machines with singularities. Advances in Neural Information Processing Systems (2000) 329-336
-
(2000)
Advances in Neural Information Processing Systems
, pp. 329-336
-
-
Watanabe, S.1
-
16
-
-
0035316373
-
Algebraic analysis for nonidentifiable learning machines
-
Watanabe S. Algebraic analysis for nonidentifiable learning machines. Neural Computation 13 4 (2001) 899-933
-
(2001)
Neural Computation
, vol.13
, Issue.4
, pp. 899-933
-
-
Watanabe, S.1
-
17
-
-
0034842476
-
Algebraic geometrical methods for hierarchical learning machines
-
Watanabe S. Algebraic geometrical methods for hierarchical learning machines. Neural Networks 14 8 (2001) 1049-1060
-
(2001)
Neural Networks
, vol.14
, Issue.8
, pp. 1049-1060
-
-
Watanabe, S.1
-
18
-
-
0035506030
-
Learning efficiency of redundant neural networks in Bayesian estimation
-
Watanabe S. Learning efficiency of redundant neural networks in Bayesian estimation. IEEE Transactions on Neural Networks 12 6 (2001) 1475-1486
-
(2001)
IEEE Transactions on Neural Networks
, vol.12
, Issue.6
, pp. 1475-1486
-
-
Watanabe, S.1
-
19
-
-
0042879444
-
Learning coefficients of layered models when the true distribution mismatches the singularities
-
Watanabe S., and Amari S. Learning coefficients of layered models when the true distribution mismatches the singularities. Neural Computation 15 5 (2003) 1013-1033
-
(2003)
Neural Computation
, vol.15
, Issue.5
, pp. 1013-1033
-
-
Watanabe, S.1
Amari, S.2
-
20
-
-
21744459329
-
Algebraic geometry of singular learning machines and symmetry of generalization and training errors
-
Watanabe S. Algebraic geometry of singular learning machines and symmetry of generalization and training errors. Neurocomputing 67 (2005) 198-213
-
(2005)
Neurocomputing
, vol.67
, pp. 198-213
-
-
Watanabe, S.1
-
22
-
-
77950802088
-
Generalization and training errors in Bayes and Gibbs estimations in singular learning machines
-
NC2007-75 pp
-
Watanabe, S. (2007). Generalization and training errors in Bayes and Gibbs estimations in singular learning machines. IEICE Technical Report, NC2007-75 (pp. 25-30)
-
(2007)
IEICE Technical Report
, pp. 25-30
-
-
Watanabe, S.1
-
23
-
-
70649083526
-
On a relation between a limit theorem in learning theory and singular fluctuation
-
NC2008-111 pp
-
Watanabe, S. (2009). On a relation between a limit theorem in learning theory and singular fluctuation, IEICE Technical Report, NC2008-111 (pp. 45-50)
-
(2009)
IEICE Technical Report
, pp. 45-50
-
-
Watanabe, S.1
-
24
-
-
0742324924
-
Singularities in mixture models and upper bounds of stochastic complexity
-
Yamazaki K., and Watanabe S. Singularities in mixture models and upper bounds of stochastic complexity. Neural Networks 16 7 (2003) 1029-1038
-
(2003)
Neural Networks
, vol.16
, Issue.7
, pp. 1029-1038
-
-
Yamazaki, K.1
Watanabe, S.2
-
25
-
-
15344345868
-
Singularities in complete bipartite graph-type Boltzmann machines and upper bounds of stochastic complexities
-
Yamazaki K., and Watanabe S. Singularities in complete bipartite graph-type Boltzmann machines and upper bounds of stochastic complexities. IEEE Transactions on Neural Networks 16 2 (2005) 312-324
-
(2005)
IEEE Transactions on Neural Networks
, vol.16
, Issue.2
, pp. 312-324
-
-
Yamazaki, K.1
Watanabe, S.2
-
26
-
-
27844446553
-
Algebraic geometry and stochastic complexity of hidden Markov models
-
Yamazaki K., and Watanabe S. Algebraic geometry and stochastic complexity of hidden Markov models. Neurocomputing 69 (2005) 62-84
-
(2005)
Neurocomputing
, vol.69
, pp. 62-84
-
-
Yamazaki, K.1
Watanabe, S.2
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