BibTeX records: Sumio Watanabe

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@article{DBLP:journals/corr/abs-2303-05731,
  author       = {Naoki Yoshida and
                  Sumio Watanabe},
  title        = {Upper Bound of Real Log Canonical Threshold of Tensor Decomposition
                  and its Application to Bayesian Inference},
  journal      = {CoRR},
  volume       = {abs/2303.05731},
  year         = {2023},
  url          = {https://doi.org/10.48550/arXiv.2303.05731},
  doi          = {10.48550/ARXIV.2303.05731},
  eprinttype    = {arXiv},
  eprint       = {2303.05731},
  timestamp    = {Wed, 15 Mar 2023 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/corr/abs-2303-05731.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2303-15739,
  author       = {Shuya Nagayasu and
                  Sumio Watanabe},
  title        = {Bayesian Free Energy of Deep ReLU Neural Network in Overparametrized
                  Cases},
  journal      = {CoRR},
  volume       = {abs/2303.15739},
  year         = {2023},
  url          = {https://doi.org/10.48550/arXiv.2303.15739},
  doi          = {10.48550/ARXIV.2303.15739},
  eprinttype    = {arXiv},
  eprint       = {2303.15739},
  timestamp    = {Fri, 14 Apr 2023 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/corr/abs-2303-15739.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2307-01417,
  author       = {Shuya Nagayasu and
                  Sumio Watanabe},
  title        = {Free energy of Bayesian Convolutional Neural Network with Skip Connection},
  journal      = {CoRR},
  volume       = {abs/2307.01417},
  year         = {2023},
  url          = {https://doi.org/10.48550/arXiv.2307.01417},
  doi          = {10.48550/ARXIV.2307.01417},
  eprinttype    = {arXiv},
  eprint       = {2307.01417},
  timestamp    = {Mon, 10 Jul 2023 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/corr/abs-2307-01417.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/ijon/NagayasuW22,
  author       = {Shuya Nagayasu and
                  Sumio Watanabe},
  title        = {Asymptotic behavior of free energy when optimal probability distribution
                  is not unique},
  journal      = {Neurocomputing},
  volume       = {500},
  pages        = {528--536},
  year         = {2022},
  url          = {https://doi.org/10.1016/j.neucom.2022.05.071},
  doi          = {10.1016/J.NEUCOM.2022.05.071},
  timestamp    = {Fri, 14 Apr 2023 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/ijon/NagayasuW22.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2203-06884,
  author       = {Takumi Watanabe and
                  Sumio Watanabe},
  title        = {Asymptotic Behavior of Bayesian Generalization Error in Multinomial
                  Mixtures},
  journal      = {CoRR},
  volume       = {abs/2203.06884},
  year         = {2022},
  url          = {https://doi.org/10.48550/arXiv.2203.06884},
  doi          = {10.48550/ARXIV.2203.06884},
  eprinttype    = {arXiv},
  eprint       = {2203.06884},
  timestamp    = {Wed, 16 Mar 2022 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/corr/abs-2203-06884.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2206-05630,
  author       = {Sumio Watanabe},
  title        = {Mathematical Theory of Bayesian Statistics for Unknown Information
                  Source},
  journal      = {CoRR},
  volume       = {abs/2206.05630},
  year         = {2022},
  url          = {https://doi.org/10.48550/arXiv.2206.05630},
  doi          = {10.48550/ARXIV.2206.05630},
  eprinttype    = {arXiv},
  eprint       = {2206.05630},
  timestamp    = {Mon, 20 Jun 2022 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/corr/abs-2206-05630.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2211-10049,
  author       = {Sumio Watanabe},
  title        = {Recent Advances in Algebraic Geometry and Bayesian Statistics},
  journal      = {CoRR},
  volume       = {abs/2211.10049},
  year         = {2022},
  url          = {https://doi.org/10.48550/arXiv.2211.10049},
  doi          = {10.48550/ARXIV.2211.10049},
  eprinttype    = {arXiv},
  eprint       = {2211.10049},
  timestamp    = {Thu, 24 Nov 2022 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/corr/abs-2211-10049.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/ieiceta/KariyaW20,
  author       = {Natsuki Kariya and
                  Sumio Watanabe},
  title        = {Testing Homogeneity for Normal Mixture Models: Variational Bayes Approach},
  journal      = {{IEICE} Trans. Fundam. Electron. Commun. Comput. Sci.},
  volume       = {103-A},
  number       = {11},
  pages        = {1274--1282},
  year         = {2020},
  url          = {https://doi.org/10.1587/transfun.2019EAP1172},
  doi          = {10.1587/TRANSFUN.2019EAP1172},
  timestamp    = {Mon, 18 Jan 2021 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/ieiceta/KariyaW20.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/sncs/HayashiW20,
  author       = {Naoki Hayashi and
                  Sumio Watanabe},
  title        = {Asymptotic Bayesian Generalization Error in Latent Dirichlet Allocation
                  and Stochastic Matrix Factorization},
  journal      = {{SN} Comput. Sci.},
  volume       = {1},
  number       = {2},
  pages        = {69},
  year         = {2020},
  url          = {https://doi.org/10.1007/s42979-020-0071-3},
  doi          = {10.1007/S42979-020-0071-3},
  timestamp    = {Mon, 11 May 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/sncs/HayashiW20.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/ijon/HayashiW17,
  author       = {Naoki Hayashi and
                  Sumio Watanabe},
  title        = {Upper bound of Bayesian generalization error in non-negative matrix
                  factorization},
  journal      = {Neurocomputing},
  volume       = {266},
  pages        = {21--28},
  year         = {2017},
  url          = {https://doi.org/10.1016/j.neucom.2017.04.068},
  doi          = {10.1016/J.NEUCOM.2017.04.068},
  timestamp    = {Mon, 15 Jun 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/ijon/HayashiW17.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/icann/KohjimaW17,
  author       = {Masahiro Kohjima and
                  Sumio Watanabe},
  editor       = {Alessandra Lintas and
                  Stefano Rovetta and
                  Paul F. M. J. Verschure and
                  Alessandro E. P. Villa},
  title        = {Phase Transition Structure of Variational Bayesian Nonnegative Matrix
                  Factorization},
  booktitle    = {Artificial Neural Networks and Machine Learning - {ICANN} 2017 - 26th
                  International Conference on Artificial Neural Networks, Alghero, Italy,
                  September 11-14, 2017, Proceedings, Part {II}},
  series       = {Lecture Notes in Computer Science},
  volume       = {10614},
  pages        = {146--154},
  publisher    = {Springer},
  year         = {2017},
  url          = {https://doi.org/10.1007/978-3-319-68612-7\_17},
  doi          = {10.1007/978-3-319-68612-7\_17},
  timestamp    = {Fri, 27 Mar 2020 08:51:30 +0100},
  biburl       = {https://dblp.org/rec/conf/icann/KohjimaW17.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/ssci/HayashiW17,
  author       = {Naoki Hayashi and
                  Sumio Watanabe},
  title        = {Tighter upper bound of real log canonical threshold of non-negative
                  matrix factorization and its application to Bayesian inference},
  booktitle    = {2017 {IEEE} Symposium Series on Computational Intelligence, {SSCI}
                  2017, Honolulu, HI, USA, November 27 - Dec. 1, 2017},
  pages        = {1--8},
  publisher    = {{IEEE}},
  year         = {2017},
  url          = {https://doi.org/10.1109/SSCI.2017.8280811},
  doi          = {10.1109/SSCI.2017.8280811},
  timestamp    = {Fri, 27 Mar 2020 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/conf/ssci/HayashiW17.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1709-04212,
  author       = {Naoki Hayashi and
                  Sumio Watanabe},
  title        = {Upper Bound of Bayesian Generalization Error in Stochastic Matrix
                  Factorization},
  journal      = {CoRR},
  volume       = {abs/1709.04212},
  year         = {2017},
  url          = {http://arxiv.org/abs/1709.04212},
  eprinttype    = {arXiv},
  eprint       = {1709.04212},
  timestamp    = {Mon, 13 Aug 2018 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/corr/abs-1709-04212.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/icmla/KodaW16,
  author       = {Natsuki Koda and
                  Sumio Watanabe},
  title        = {Interpretation Method of Nonlinear Multilayer Principal Component
                  Analysis by Using Sparsity and Hierarchical Clustering},
  booktitle    = {15th {IEEE} International Conference on Machine Learning and Applications,
                  {ICMLA} 2016, Anaheim, CA, USA, December 18-20, 2016},
  pages        = {1063--1066},
  publisher    = {{IEEE} Computer Society},
  year         = {2016},
  url          = {https://doi.org/10.1109/ICMLA.2016.0193},
  doi          = {10.1109/ICMLA.2016.0193},
  timestamp    = {Fri, 24 Mar 2023 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/conf/icmla/KodaW16.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1612-04112,
  author       = {Naoki Hayashi and
                  Sumio Watanabe},
  title        = {Upper Bound of Bayesian Generalization Error in Non-negative Matrix
                  Factorization},
  journal      = {CoRR},
  volume       = {abs/1612.04112},
  year         = {2016},
  url          = {http://arxiv.org/abs/1612.04112},
  eprinttype    = {arXiv},
  eprint       = {1612.04112},
  timestamp    = {Mon, 13 Aug 2018 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/corr/abs-1612-04112.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/Watanabe15,
  author       = {Sumio Watanabe},
  title        = {Bayesian Cross Validation and {WAIC} for Predictive Prior Design in
                  Regular Asymptotic Theory},
  journal      = {CoRR},
  volume       = {abs/1503.07970},
  year         = {2015},
  url          = {http://arxiv.org/abs/1503.07970},
  eprinttype    = {arXiv},
  eprint       = {1503.07970},
  timestamp    = {Mon, 13 Aug 2018 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/corr/Watanabe15.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/jmlr/Watanabe13,
  author       = {Sumio Watanabe},
  title        = {A widely applicable Bayesian information criterion},
  journal      = {J. Mach. Learn. Res.},
  volume       = {14},
  number       = {1},
  pages        = {867--897},
  year         = {2013},
  url          = {https://dl.acm.org/doi/10.5555/2567709.2502609},
  doi          = {10.5555/2567709.2502609},
  timestamp    = {Thu, 02 Jun 2022 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/jmlr/Watanabe13.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/miwai/OharaYW13,
  author       = {Shigehiro Ohara and
                  Keisuke Yamazaki and
                  Sumio Watanabe},
  editor       = {Sheela Ramanna and
                  Pawan Lingras and
                  Chattrakul Sombattheera and
                  Aneesh Krishna},
  title        = {A Geometric Evaluation of Self-Organizing Map and Application to City
                  Data Analysis},
  booktitle    = {Multi-disciplinary Trends in Artificial Intelligence - 7th International
                  Workshop, {MIWAI} 2013, Krabi, Thailand, December 9-11, 2013. Proceedings},
  series       = {Lecture Notes in Computer Science},
  volume       = {8271},
  pages        = {165--174},
  publisher    = {Springer},
  year         = {2013},
  url          = {https://doi.org/10.1007/978-3-642-44949-9\_16},
  doi          = {10.1007/978-3-642-44949-9\_16},
  timestamp    = {Tue, 14 May 2019 10:00:38 +0200},
  biburl       = {https://dblp.org/rec/conf/miwai/OharaYW13.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/ieicet/YamadaW12,
  author       = {Koshi Yamada and
                  Sumio Watanabe},
  title        = {Statistical Learning Theory of Quasi-Regular Cases},
  journal      = {{IEICE} Trans. Fundam. Electron. Commun. Comput. Sci.},
  volume       = {95-A},
  number       = {12},
  pages        = {2479--2487},
  year         = {2012},
  url          = {https://doi.org/10.1587/transfun.E95.A.2479},
  doi          = {10.1587/TRANSFUN.E95.A.2479},
  timestamp    = {Sat, 11 Apr 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/ieicet/YamadaW12.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/scisisis/YamadaW12,
  author       = {Koshi Yamada and
                  Sumio Watanabe},
  title        = {Information criterion for variational Bayes learning in regular and
                  singular cases},
  booktitle    = {The 6th International Conference on Soft Computing and Intelligent
                  Systems (SCIS), and The 13th International Symposium on Advanced Intelligence
                  Systems (ISIS), Kobe, Japan, November 20-24, 2012},
  pages        = {1551--1555},
  publisher    = {{IEEE}},
  year         = {2012},
  url          = {https://doi.org/10.1109/SCIS-ISIS.2012.6505025},
  doi          = {10.1109/SCIS-ISIS.2012.6505025},
  timestamp    = {Wed, 16 Oct 2019 14:14:48 +0200},
  biburl       = {https://dblp.org/rec/conf/scisisis/YamadaW12.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1208-6338,
  author       = {Sumio Watanabe},
  title        = {A Widely Applicable Bayesian Information Criterion},
  journal      = {CoRR},
  volume       = {abs/1208.6338},
  year         = {2012},
  url          = {http://arxiv.org/abs/1208.6338},
  eprinttype    = {arXiv},
  eprint       = {1208.6338},
  timestamp    = {Mon, 13 Aug 2018 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/corr/abs-1208-6338.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1212-2511,
  author       = {Keisuke Yamazaki and
                  Sumio Watanabe},
  title        = {Stochastic complexity of Bayesian networks},
  journal      = {CoRR},
  volume       = {abs/1212.2511},
  year         = {2012},
  url          = {http://arxiv.org/abs/1212.2511},
  eprinttype    = {arXiv},
  eprint       = {1212.2511},
  timestamp    = {Mon, 13 Aug 2018 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/corr/abs-1212-2511.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/ijon/KajiW11,
  author       = {Daisuke Kaji and
                  Sumio Watanabe},
  title        = {Two design methods of hyperparameters in variational Bayes learning
                  for Bernoulli mixtures},
  journal      = {Neurocomputing},
  volume       = {74},
  number       = {11},
  pages        = {2002--2007},
  year         = {2011},
  url          = {https://doi.org/10.1016/j.neucom.2010.06.027},
  doi          = {10.1016/J.NEUCOM.2010.06.027},
  timestamp    = {Sat, 20 May 2017 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/ijon/KajiW11.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/ajiips/KajiWW10,
  author       = {Daisuke Kaji and
                  Kazuho Watanabe and
                  Sumio Watanabe},
  title        = {Phase Transition of Variational Bayes Learning in Bernoulli Mixture},
  journal      = {Aust. J. Intell. Inf. Process. Syst.},
  volume       = {11},
  number       = {4},
  year         = {2010},
  url          = {http://cs.anu.edu.au/ojs/index.php/ajiips/article/view/1123},
  timestamp    = {Tue, 05 Jan 2021 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/ajiips/KajiWW10.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/ieicet/Watanabe10,
  author       = {Sumio Watanabe},
  title        = {Equations of States in Statistical Learning for an Unrealizable and
                  Regular Case},
  journal      = {{IEICE} Trans. Fundam. Electron. Commun. Comput. Sci.},
  volume       = {93-A},
  number       = {3},
  pages        = {617--626},
  year         = {2010},
  url          = {https://doi.org/10.1587/transfun.E93.A.617},
  doi          = {10.1587/TRANSFUN.E93.A.617},
  timestamp    = {Sat, 11 Apr 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/ieicet/Watanabe10.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/jmlr/Watanabe10,
  author       = {Sumio Watanabe},
  title        = {Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable
                  Information Criterion in Singular Learning Theory},
  journal      = {J. Mach. Learn. Res.},
  volume       = {11},
  pages        = {3571--3594},
  year         = {2010},
  url          = {https://dl.acm.org/doi/10.5555/1756006.1953045},
  doi          = {10.5555/1756006.1953045},
  timestamp    = {Thu, 02 Jun 2022 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/jmlr/Watanabe10.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/nn/Watanabe10,
  author       = {Sumio Watanabe},
  title        = {Equations of states in singular statistical estimation},
  journal      = {Neural Networks},
  volume       = {23},
  number       = {1},
  pages        = {20--34},
  year         = {2010},
  url          = {https://doi.org/10.1016/j.neunet.2009.08.002},
  doi          = {10.1016/J.NEUNET.2009.08.002},
  timestamp    = {Wed, 14 Nov 2018 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/nn/Watanabe10.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/nn/YamazakiAW10,
  author       = {Keisuke Yamazaki and
                  Miki Aoyagi and
                  Sumio Watanabe},
  title        = {Asymptotic analysis of Bayesian generalization error with Newton diagram},
  journal      = {Neural Networks},
  volume       = {23},
  number       = {1},
  pages        = {35--43},
  year         = {2010},
  url          = {https://doi.org/10.1016/j.neunet.2009.07.029},
  doi          = {10.1016/J.NEUNET.2009.07.029},
  timestamp    = {Fri, 30 Nov 2018 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/nn/YamazakiAW10.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/iconip/SaitohW10,
  author       = {Fumiaki Saitoh and
                  Sumio Watanabe},
  editor       = {Kok Wai Wong and
                  B. Sumudu U. Mendis and
                  Abdesselam Bouzerdoum},
  title        = {On Generalization Error of Self-Organizing Map},
  booktitle    = {Neural Information Processing. Models and Applications - 17th International
                  Conference, {ICONIP} 2010, Sydney, Australia, November 22-25, 2010,
                  Proceedings, Part {II}},
  series       = {Lecture Notes in Computer Science},
  volume       = {6444},
  pages        = {399--406},
  publisher    = {Springer},
  year         = {2010},
  url          = {https://doi.org/10.1007/978-3-642-17534-3\_49},
  doi          = {10.1007/978-3-642-17534-3\_49},
  timestamp    = {Tue, 14 May 2019 10:00:42 +0200},
  biburl       = {https://dblp.org/rec/conf/iconip/SaitohW10.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1001-2957,
  author       = {Sumio Watanabe},
  title        = {Asymptotic Learning Curve and Renormalizable Condition in Statistical
                  Learning Theory},
  journal      = {CoRR},
  volume       = {abs/1001.2957},
  year         = {2010},
  url          = {http://arxiv.org/abs/1001.2957},
  eprinttype    = {arXiv},
  eprint       = {1001.2957},
  timestamp    = {Mon, 13 Aug 2018 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/corr/abs-1001-2957.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1004-2316,
  author       = {Sumio Watanabe},
  title        = {Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable
                  Information Criterion in Singular Learning Theory},
  journal      = {CoRR},
  volume       = {abs/1004.2316},
  year         = {2010},
  url          = {http://arxiv.org/abs/1004.2316},
  eprinttype    = {arXiv},
  eprint       = {1004.2316},
  timestamp    = {Mon, 13 Aug 2018 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/corr/abs-1004-2316.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/ml/WatanabeSW09,
  author       = {Kazuho Watanabe and
                  Motoki Shiga and
                  Sumio Watanabe},
  title        = {Upper bound for variational free energy of Bayesian networks},
  journal      = {Mach. Learn.},
  volume       = {75},
  number       = {2},
  pages        = {199--215},
  year         = {2009},
  url          = {https://doi.org/10.1007/s10994-008-5099-x},
  doi          = {10.1007/S10994-008-5099-X},
  timestamp    = {Mon, 02 Mar 2020 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/ml/WatanabeSW09.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/nn/NishiyamaW09,
  author       = {Yu Nishiyama and
                  Sumio Watanabe},
  title        = {Accuracy of Loopy belief propagation in Gaussian models},
  journal      = {Neural Networks},
  volume       = {22},
  number       = {4},
  pages        = {385--394},
  year         = {2009},
  url          = {https://doi.org/10.1016/j.neunet.2009.01.003},
  doi          = {10.1016/J.NEUNET.2009.01.003},
  timestamp    = {Wed, 14 Nov 2018 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/nn/NishiyamaW09.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/iconip/KajiW09a,
  author       = {Daisuke Kaji and
                  Sumio Watanabe},
  editor       = {Chi{-}Sing Leung and
                  Minho Lee and
                  Jonathan Hoyin Chan},
  title        = {Optimal Hyperparameters for Generalized Learning and Knowledge Discovery
                  in Variational Bayes},
  booktitle    = {Neural Information Processing, 16th International Conference, {ICONIP}
                  2009, Bangkok, Thailand, December 1-5, 2009, Proceedings, Part {I}},
  series       = {Lecture Notes in Computer Science},
  volume       = {5863},
  pages        = {476--483},
  publisher    = {Springer},
  year         = {2009},
  url          = {https://doi.org/10.1007/978-3-642-10677-4\_54},
  doi          = {10.1007/978-3-642-10677-4\_54},
  timestamp    = {Tue, 14 May 2019 10:00:42 +0200},
  biburl       = {https://dblp.org/rec/conf/iconip/KajiW09a.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-0901-2376,
  author       = {Sumio Watanabe},
  title        = {A Limit Theorem in Singular Regression Problem},
  journal      = {CoRR},
  volume       = {abs/0901.2376},
  year         = {2009},
  url          = {http://arxiv.org/abs/0901.2376},
  eprinttype    = {arXiv},
  eprint       = {0901.2376},
  timestamp    = {Mon, 13 Aug 2018 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/corr/abs-0901-2376.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-0906-0211,
  author       = {Sumio Watanabe},
  title        = {Equations of States in Statistical Learning for a Nonparametrizable
                  and Regular Case},
  journal      = {CoRR},
  volume       = {abs/0906.0211},
  year         = {2009},
  url          = {http://arxiv.org/abs/0906.0211},
  eprinttype    = {arXiv},
  eprint       = {0906.0211},
  timestamp    = {Mon, 13 Aug 2018 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/corr/abs-0906-0211.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/nn/NagataW08,
  author       = {Kenji Nagata and
                  Sumio Watanabe},
  title        = {Asymptotic behavior of exchange ratio in exchange Monte Carlo method},
  journal      = {Neural Networks},
  volume       = {21},
  number       = {7},
  pages        = {980--988},
  year         = {2008},
  url          = {https://doi.org/10.1016/j.neunet.2007.11.002},
  doi          = {10.1016/J.NEUNET.2007.11.002},
  timestamp    = {Wed, 14 Nov 2018 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/nn/NagataW08.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/tnn/NagataW08,
  author       = {Kenji Nagata and
                  Sumio Watanabe},
  title        = {Exchange Monte Carlo Sampling From Bayesian Posterior for Singular
                  Learning Machines},
  journal      = {{IEEE} Trans. Neural Networks},
  volume       = {19},
  number       = {7},
  pages        = {1253--1266},
  year         = {2008},
  url          = {https://doi.org/10.1109/TNN.2008.2000202},
  doi          = {10.1109/TNN.2008.2000202},
  timestamp    = {Sun, 28 May 2017 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/tnn/NagataW08.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/icaisc/NishiyamaW08,
  author       = {Yu Nishiyama and
                  Sumio Watanabe},
  editor       = {Leszek Rutkowski and
                  Ryszard Tadeusiewicz and
                  Lotfi A. Zadeh and
                  Jacek M. Zurada},
  title        = {On the Minima of Bethe Free Energy in Gaussian Distributions},
  booktitle    = {Artificial Intelligence and Soft Computing - {ICAISC} 2008, 9th International
                  Conference, Zakopane, Poland, June 22-26, 2008, Proceedings},
  series       = {Lecture Notes in Computer Science},
  volume       = {5097},
  pages        = {1075--1086},
  publisher    = {Springer},
  year         = {2008},
  url          = {https://doi.org/10.1007/978-3-540-69731-2\_101},
  doi          = {10.1007/978-3-540-69731-2\_101},
  timestamp    = {Tue, 14 May 2019 10:00:55 +0200},
  biburl       = {https://dblp.org/rec/conf/icaisc/NishiyamaW08.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/icann/NishiyamaW08,
  author       = {Yu Nishiyama and
                  Sumio Watanabe},
  editor       = {Vera Kurkov{\'{a}} and
                  Roman Neruda and
                  Jan Koutn{\'{\i}}k},
  title        = {Generalization of Concave and Convex Decomposition in Kikuchi Free
                  Energy},
  booktitle    = {Artificial Neural Networks - {ICANN} 2008 , 18th International Conference,
                  Prague, Czech Republic, September 3-6, 2008, Proceedings, Part {I}},
  series       = {Lecture Notes in Computer Science},
  volume       = {5163},
  pages        = {51--60},
  publisher    = {Springer},
  year         = {2008},
  url          = {https://doi.org/10.1007/978-3-540-87536-9\_6},
  doi          = {10.1007/978-3-540-87536-9\_6},
  timestamp    = {Tue, 14 May 2019 10:00:49 +0200},
  biburl       = {https://dblp.org/rec/conf/icann/NishiyamaW08.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/iconip/MatsumotoW09,
  author       = {Masashi Matsumoto and
                  Sumio Watanabe},
  editor       = {Mario K{\"{o}}ppen and
                  Nikola K. Kasabov and
                  George G. Coghill},
  title        = {Experimental Study of Ergodic Learning Curve in Hidden Markov Models},
  booktitle    = {Advances in Neuro-Information Processing, 15th International Conference,
                  {ICONIP} 2008, Auckland, New Zealand, November 25-28, 2008, Revised
                  Selected Papers, Part {I}},
  series       = {Lecture Notes in Computer Science},
  volume       = {5506},
  pages        = {688--695},
  publisher    = {Springer},
  year         = {2008},
  url          = {https://doi.org/10.1007/978-3-642-02490-0\_84},
  doi          = {10.1007/978-3-642-02490-0\_84},
  timestamp    = {Tue, 14 May 2019 10:00:42 +0200},
  biburl       = {https://dblp.org/rec/conf/iconip/MatsumotoW09.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/iconip/NagataW09,
  author       = {Kenji Nagata and
                  Sumio Watanabe},
  editor       = {Mario K{\"{o}}ppen and
                  Nikola K. Kasabov and
                  George G. Coghill},
  title        = {Design of Exchange Monte Carlo Method for Bayesian Learning in Normal
                  Mixture Models},
  booktitle    = {Advances in Neuro-Information Processing, 15th International Conference,
                  {ICONIP} 2008, Auckland, New Zealand, November 25-28, 2008, Revised
                  Selected Papers, Part {I}},
  series       = {Lecture Notes in Computer Science},
  volume       = {5506},
  pages        = {696--706},
  publisher    = {Springer},
  year         = {2008},
  url          = {https://doi.org/10.1007/978-3-642-02490-0\_85},
  doi          = {10.1007/978-3-642-02490-0\_85},
  timestamp    = {Wed, 24 May 2017 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/conf/iconip/NagataW09.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/iconip/KajiW09,
  author       = {Daisuke Kaji and
                  Sumio Watanabe},
  editor       = {Mario K{\"{o}}ppen and
                  Nikola K. Kasabov and
                  George G. Coghill},
  title        = {Model Selection Method for AdaBoost Using Formal Information Criteria},
  booktitle    = {Advances in Neuro-Information Processing, 15th International Conference,
                  {ICONIP} 2008, Auckland, New Zealand, November 25-28, 2008, Revised
                  Selected Papers, Part {II}},
  series       = {Lecture Notes in Computer Science},
  volume       = {5507},
  pages        = {903--910},
  publisher    = {Springer},
  year         = {2008},
  url          = {https://doi.org/10.1007/978-3-642-03040-6\_110},
  doi          = {10.1007/978-3-642-03040-6\_110},
  timestamp    = {Tue, 14 May 2019 10:00:42 +0200},
  biburl       = {https://dblp.org/rec/conf/iconip/KajiW09.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/ijcnn/Watanabe08,
  author       = {Sumio Watanabe},
  title        = {A formula of equations of states in singular learning machines},
  booktitle    = {Proceedings of the International Joint Conference on Neural Networks,
                  {IJCNN} 2008, part of the {IEEE} World Congress on Computational Intelligence,
                  {WCCI} 2008, Hong Kong, China, June 1-6, 2008},
  pages        = {2098--2105},
  publisher    = {{IEEE}},
  year         = {2008},
  url          = {https://doi.org/10.1109/IJCNN.2008.4634086},
  doi          = {10.1109/IJCNN.2008.4634086},
  timestamp    = {Wed, 16 Oct 2019 14:14:55 +0200},
  biburl       = {https://dblp.org/rec/conf/ijcnn/Watanabe08.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/neco/NakajimaW07,
  author       = {Shinichi Nakajima and
                  Sumio Watanabe},
  title        = {Variational Bayes Solution of Linear Neural Networks and Its Generalization
                  Performance},
  journal      = {Neural Comput.},
  volume       = {19},
  number       = {4},
  pages        = {1112--1153},
  year         = {2007},
  url          = {https://doi.org/10.1162/neco.2007.19.4.1112},
  doi          = {10.1162/NECO.2007.19.4.1112},
  timestamp    = {Tue, 01 Sep 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/neco/NakajimaW07.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/nn/WatanabeW07,
  author       = {Kazuho Watanabe and
                  Sumio Watanabe},
  title        = {Stochastic complexities of general mixture models in variational Bayesian
                  learning},
  journal      = {Neural Networks},
  volume       = {20},
  number       = {2},
  pages        = {210--219},
  year         = {2007},
  url          = {https://doi.org/10.1016/j.neunet.2006.05.030},
  doi          = {10.1016/J.NEUNET.2006.05.030},
  timestamp    = {Fri, 27 Dec 2019 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/nn/WatanabeW07.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/tcs/WatanabeW07,
  author       = {Kazuho Watanabe and
                  Sumio Watanabe},
  title        = {Stochastic complexity for mixture of exponential families in generalized
                  variational Bayes},
  journal      = {Theor. Comput. Sci.},
  volume       = {387},
  number       = {1},
  pages        = {4--17},
  year         = {2007},
  url          = {https://doi.org/10.1016/j.tcs.2007.07.039},
  doi          = {10.1016/J.TCS.2007.07.039},
  timestamp    = {Wed, 17 Feb 2021 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/tcs/WatanabeW07.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/foci/Watanabe07,
  author       = {Sumio Watanabe},
  title        = {Almost All Learning Machines are Singular},
  booktitle    = {Proceedings of the {IEEE} Symposium on Foundations of Computational
                  Intelligence, {FOCI} 2007, part of the {IEEE} Symposium Series on
                  Computational Intelligence 2007, Honolulu, Hawaii, USA, 1-5 April
                  2007},
  pages        = {383--388},
  publisher    = {{IEEE}},
  year         = {2007},
  url          = {https://doi.org/10.1109/FOCI.2007.371500},
  doi          = {10.1109/FOCI.2007.371500},
  timestamp    = {Wed, 16 Oct 2019 14:14:56 +0200},
  biburl       = {https://dblp.org/rec/conf/foci/Watanabe07.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/foci/NagataW07,
  author       = {Kenji Nagata and
                  Sumio Watanabe},
  title        = {Analysis of Exchange Ratio for Exchange Monte Carlo Method},
  booktitle    = {Proceedings of the {IEEE} Symposium on Foundations of Computational
                  Intelligence, {FOCI} 2007, part of the {IEEE} Symposium Series on
                  Computational Intelligence 2007, Honolulu, Hawaii, USA, 1-5 April
                  2007},
  pages        = {434--439},
  publisher    = {{IEEE}},
  year         = {2007},
  url          = {https://doi.org/10.1109/FOCI.2007.371508},
  doi          = {10.1109/FOCI.2007.371508},
  timestamp    = {Wed, 17 May 2017 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/conf/foci/NagataW07.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/icann/NakajimaW07,
  author       = {Shinichi Nakajima and
                  Sumio Watanabe},
  editor       = {Joaquim Marques de S{\'{a}} and
                  Lu{\'{\i}}s A. Alexandre and
                  Wlodzislaw Duch and
                  Danilo P. Mandic},
  title        = {Generalization Error of Automatic Relevance Determination},
  booktitle    = {Artificial Neural Networks - {ICANN} 2007, 17th International Conference,
                  Porto, Portugal, September 9-13, 2007, Proceedings, Part {I}},
  series       = {Lecture Notes in Computer Science},
  volume       = {4668},
  pages        = {1--10},
  publisher    = {Springer},
  year         = {2007},
  url          = {https://doi.org/10.1007/978-3-540-74690-4\_1},
  doi          = {10.1007/978-3-540-74690-4\_1},
  timestamp    = {Tue, 14 May 2019 10:00:49 +0200},
  biburl       = {https://dblp.org/rec/conf/icann/NakajimaW07.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/icann/MatsudaW07,
  author       = {Takeshi Matsuda and
                  Sumio Watanabe},
  editor       = {Joaquim Marques de S{\'{a}} and
                  Lu{\'{\i}}s A. Alexandre and
                  Wlodzislaw Duch and
                  Danilo P. Mandic},
  title        = {On a Singular Point to Contribute to a Learning Coefficient and Weighted
                  Resolution of Singularities},
  booktitle    = {Artificial Neural Networks - {ICANN} 2007, 17th International Conference,
                  Porto, Portugal, September 9-13, 2007, Proceedings, Part {I}},
  series       = {Lecture Notes in Computer Science},
  volume       = {4668},
  pages        = {11--18},
  publisher    = {Springer},
  year         = {2007},
  url          = {https://doi.org/10.1007/978-3-540-74690-4\_2},
  doi          = {10.1007/978-3-540-74690-4\_2},
  timestamp    = {Fri, 26 May 2017 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/conf/icann/MatsudaW07.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/icann/NishiyamaW07,
  author       = {Yu Nishiyama and
                  Sumio Watanabe},
  editor       = {Joaquim Marques de S{\'{a}} and
                  Lu{\'{\i}}s A. Alexandre and
                  Wlodzislaw Duch and
                  Danilo P. Mandic},
  title        = {Theoretical Analysis of Accuracy of Gaussian Belief Propagation},
  booktitle    = {Artificial Neural Networks - {ICANN} 2007, 17th International Conference,
                  Porto, Portugal, September 9-13, 2007, Proceedings, Part {I}},
  series       = {Lecture Notes in Computer Science},
  volume       = {4668},
  pages        = {29--38},
  publisher    = {Springer},
  year         = {2007},
  url          = {https://doi.org/10.1007/978-3-540-74690-4\_4},
  doi          = {10.1007/978-3-540-74690-4\_4},
  timestamp    = {Fri, 26 May 2017 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/conf/icann/NishiyamaW07.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/icann/IriguchiW07,
  author       = {Ryosuke Iriguchi and
                  Sumio Watanabe},
  editor       = {Joaquim Marques de S{\'{a}} and
                  Lu{\'{\i}}s A. Alexandre and
                  Wlodzislaw Duch and
                  Danilo P. Mandic},
  title        = {Estimation of Poles of Zeta Function in Learning Theory Using Pad{\'{e}}
                  Approximation},
  booktitle    = {Artificial Neural Networks - {ICANN} 2007, 17th International Conference,
                  Porto, Portugal, September 9-13, 2007, Proceedings, Part {I}},
  series       = {Lecture Notes in Computer Science},
  volume       = {4668},
  pages        = {88--97},
  publisher    = {Springer},
  year         = {2007},
  url          = {https://doi.org/10.1007/978-3-540-74690-4\_10},
  doi          = {10.1007/978-3-540-74690-4\_10},
  timestamp    = {Fri, 26 May 2017 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/conf/icann/IriguchiW07.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/icann/NagataW07,
  author       = {Kenji Nagata and
                  Sumio Watanabe},
  editor       = {Joaquim Marques de S{\'{a}} and
                  Lu{\'{\i}}s A. Alexandre and
                  Wlodzislaw Duch and
                  Danilo P. Mandic},
  title        = {Algebraic Geometric Study of Exchange Monte Carlo Method},
  booktitle    = {Artificial Neural Networks - {ICANN} 2007, 17th International Conference,
                  Porto, Portugal, September 9-13, 2007, Proceedings, Part {I}},
  series       = {Lecture Notes in Computer Science},
  volume       = {4668},
  pages        = {687--696},
  publisher    = {Springer},
  year         = {2007},
  url          = {https://doi.org/10.1007/978-3-540-74690-4\_70},
  doi          = {10.1007/978-3-540-74690-4\_70},
  timestamp    = {Fri, 26 May 2017 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/conf/icann/NagataW07.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/icml/YamazakiKWSM07,
  author       = {Keisuke Yamazaki and
                  Motoaki Kawanabe and
                  Sumio Watanabe and
                  Masashi Sugiyama and
                  Klaus{-}Robert M{\"{u}}ller},
  editor       = {Zoubin Ghahramani},
  title        = {Asymptotic Bayesian generalization error when training and test distributions
                  are different},
  booktitle    = {Machine Learning, Proceedings of the Twenty-Fourth International Conference
                  {(ICML} 2007), Corvallis, Oregon, USA, June 20-24, 2007},
  series       = {{ACM} International Conference Proceeding Series},
  volume       = {227},
  pages        = {1079--1086},
  publisher    = {{ACM}},
  year         = {2007},
  url          = {https://doi.org/10.1145/1273496.1273632},
  doi          = {10.1145/1273496.1273632},
  timestamp    = {Wed, 25 Sep 2019 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/conf/icml/YamazakiKWSM07.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/iconip/NagataW07,
  author       = {Kenji Nagata and
                  Sumio Watanabe},
  editor       = {Masumi Ishikawa and
                  Kenji Doya and
                  Hiroyuki Miyamoto and
                  Takeshi Yamakawa},
  title        = {Experimental Analysis of Exchange Ratio in Exchange Monte Carlo Method},
  booktitle    = {Neural Information Processing, 14th International Conference, {ICONIP}
                  2007, Kitakyushu, Japan, November 13-16, 2007, Revised Selected Papers,
                  Part {II}},
  series       = {Lecture Notes in Computer Science},
  volume       = {4985},
  pages        = {67--76},
  publisher    = {Springer},
  year         = {2007},
  url          = {https://doi.org/10.1007/978-3-540-69162-4\_8},
  doi          = {10.1007/978-3-540-69162-4\_8},
  timestamp    = {Tue, 14 May 2019 10:00:42 +0200},
  biburl       = {https://dblp.org/rec/conf/iconip/NagataW07.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/iconip/YamazakiW07,
  author       = {Keisuke Yamazaki and
                  Sumio Watanabe},
  editor       = {Masumi Ishikawa and
                  Kenji Doya and
                  Hiroyuki Miyamoto and
                  Takeshi Yamakawa},
  title        = {Experimental Bayesian Generalization Error of Non-regular Models under
                  Covariate Shift},
  booktitle    = {Neural Information Processing, 14th International Conference, {ICONIP}
                  2007, Kitakyushu, Japan, November 13-16, 2007, Revised Selected Papers,
                  Part {I}},
  series       = {Lecture Notes in Computer Science},
  volume       = {4984},
  pages        = {466--476},
  publisher    = {Springer},
  year         = {2007},
  url          = {https://doi.org/10.1007/978-3-540-69158-7\_49},
  doi          = {10.1007/978-3-540-69158-7\_49},
  timestamp    = {Tue, 14 May 2019 10:00:42 +0200},
  biburl       = {https://dblp.org/rec/conf/iconip/YamazakiW07.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/mdai/AoyagiW07,
  author       = {Miki Aoyagi and
                  Sumio Watanabe},
  editor       = {Vicen{\c{c}} Torra and
                  Yasuo Narukawa and
                  Yuji Yoshida},
  title        = {Resolution of Singularities and Stochastic Complexity of Complete
                  Bipartite Graph-Type Spin Model in Bayesian Estimation},
  booktitle    = {Modeling Decisions for Artificial Intelligence, 4th International
                  Conference, {MDAI} 2007, Kitakyushu, Japan, August 16-18, 2007, Proceedings},
  series       = {Lecture Notes in Computer Science},
  volume       = {4617},
  pages        = {443--454},
  publisher    = {Springer},
  year         = {2007},
  url          = {https://doi.org/10.1007/978-3-540-73729-2\_42},
  doi          = {10.1007/978-3-540-73729-2\_42},
  timestamp    = {Tue, 14 May 2019 10:00:52 +0200},
  biburl       = {https://dblp.org/rec/conf/mdai/AoyagiW07.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/mlmta/MatsudaW07,
  author       = {Takeshi Matsuda and
                  Sumio Watanabe},
  editor       = {Hamid R. Arabnia and
                  Matthias Dehmer and
                  Frank Emmert{-}Streib and
                  Mary Qu Yang},
  title        = {The Calculation Method of Learning Coefficients by Weighted Resolution
                  of Singularities},
  booktitle    = {Proceedings of the 2007 International Conference on Machine Learning;
                  Models, Technologies {\&} Applications, {MLMTA} 2007, June 25-28,
                  2007, Las Vegas Nevada, {USA}},
  pages        = {177--181},
  publisher    = {{CSREA} Press},
  year         = {2007},
  timestamp    = {Fri, 04 Jan 2008 11:07:18 +0100},
  biburl       = {https://dblp.org/rec/conf/mlmta/MatsudaW07.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-0712-0653,
  author       = {Sumio Watanabe},
  title        = {Equations of States in Singular Statistical Estimation},
  journal      = {CoRR},
  volume       = {abs/0712.0653},
  year         = {2007},
  url          = {http://arxiv.org/abs/0712.0653},
  eprinttype    = {arXiv},
  eprint       = {0712.0653},
  timestamp    = {Mon, 13 Aug 2018 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/corr/abs-0712-0653.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/ieicet/NakajimaW06,
  author       = {Shinichi Nakajima and
                  Sumio Watanabe},
  title        = {Generalization Performance of Subspace Bayes Approach in Linear Neural
                  Networks},
  journal      = {{IEICE} Trans. Inf. Syst.},
  volume       = {89-D},
  number       = {3},
  pages        = {1128--1138},
  year         = {2006},
  url          = {https://doi.org/10.1093/ietisy/e89-d.3.1128},
  doi          = {10.1093/IETISY/E89-D.3.1128},
  timestamp    = {Sat, 11 Apr 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/ieicet/NakajimaW06.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/jmlr/WatanabeW06,
  author       = {Kazuho Watanabe and
                  Sumio Watanabe},
  title        = {Stochastic Complexities of Gaussian Mixtures in Variational Bayesian
                  Approximation},
  journal      = {J. Mach. Learn. Res.},
  volume       = {7},
  pages        = {625--644},
  year         = {2006},
  url          = {http://jmlr.org/papers/v7/watanabe06a.html},
  timestamp    = {Wed, 10 Jul 2019 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/jmlr/WatanabeW06.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/iastedCI/AoyagiW06,
  author       = {Miki Aoyagi and
                  Sumio Watanabe},
  editor       = {Boris Kovalerchuk},
  title        = {Generalization error of three layered learning model in bayesian estimation},
  booktitle    = {Proceedings of the Second {IASTED} International Conference on Computational
                  Intelligence, San Francisco, California, USA, November 20-22, 2006},
  pages        = {295--300},
  publisher    = {{IASTED/ACTA} Press},
  year         = {2006},
  timestamp    = {Mon, 30 Nov 2009 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/conf/iastedCI/AoyagiW06.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/icann/MatsudaW06,
  author       = {Takeshi Matsuda and
                  Sumio Watanabe},
  editor       = {Stefanos D. Kollias and
                  Andreas Stafylopatis and
                  Wlodzislaw Duch and
                  Erkki Oja},
  title        = {Analytic Equivalence of Bayes a Posteriori Distributions},
  booktitle    = {Artificial Neural Networks - {ICANN} 2006, 16th International Conference,
                  Athens, Greece, September 10-14, 2006. Proceedings, Part {I}},
  series       = {Lecture Notes in Computer Science},
  volume       = {4131},
  pages        = {113--121},
  publisher    = {Springer},
  year         = {2006},
  url          = {https://doi.org/10.1007/11840817\_12},
  doi          = {10.1007/11840817\_12},
  timestamp    = {Tue, 14 May 2019 10:00:49 +0200},
  biburl       = {https://dblp.org/rec/conf/icann/MatsudaW06.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/icann/NakajimaW06,
  author       = {Shinichi Nakajima and
                  Sumio Watanabe},
  editor       = {Stefanos D. Kollias and
                  Andreas Stafylopatis and
                  Wlodzislaw Duch and
                  Erkki Oja},
  title        = {Analytic Solution of Hierarchical Variational Bayes in Linear Inverse
                  Problem},
  booktitle    = {Artificial Neural Networks - {ICANN} 2006, 16th International Conference,
                  Athens, Greece, September 10-14, 2006. Proceedings, Part {II}},
  series       = {Lecture Notes in Computer Science},
  volume       = {4132},
  pages        = {240--249},
  publisher    = {Springer},
  year         = {2006},
  url          = {https://doi.org/10.1007/11840930\_25},
  doi          = {10.1007/11840930\_25},
  timestamp    = {Tue, 14 May 2019 10:00:49 +0200},
  biburl       = {https://dblp.org/rec/conf/icann/NakajimaW06.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/icann/YamazakiNWM06,
  author       = {Keisuke Yamazaki and
                  Kenji Nagata and
                  Sumio Watanabe and
                  Klaus{-}Robert M{\"{u}}ller},
  editor       = {Stefanos D. Kollias and
                  Andreas Stafylopatis and
                  Wlodzislaw Duch and
                  Erkki Oja},
  title        = {A Model Selection Method Based on Bound of Learning Coefficient},
  booktitle    = {Artificial Neural Networks - {ICANN} 2006, 16th International Conference,
                  Athens, Greece, September 10-14, 2006. Proceedings, Part {II}},
  series       = {Lecture Notes in Computer Science},
  volume       = {4132},
  pages        = {371--380},
  publisher    = {Springer},
  year         = {2006},
  url          = {https://doi.org/10.1007/11840930\_38},
  doi          = {10.1007/11840930\_38},
  timestamp    = {Tue, 21 Mar 2023 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/conf/icann/YamazakiNWM06.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/iconip/HosinoWW06,
  author       = {Tikara Hosino and
                  Kazuho Watanabe and
                  Sumio Watanabe},
  editor       = {Irwin King and
                  Jun Wang and
                  Laiwan Chan and
                  DeLiang L. Wang},
  title        = {Free Energy of Stochastic Context Free Grammar on Variational Bayes},
  booktitle    = {Neural Information Processing, 13th International Conference, {ICONIP}
                  2006, Hong Kong, China, October 3-6, 2006, Proceedings, Part {I}},
  series       = {Lecture Notes in Computer Science},
  volume       = {4232},
  pages        = {407--416},
  publisher    = {Springer},
  year         = {2006},
  url          = {https://doi.org/10.1007/11893028\_46},
  doi          = {10.1007/11893028\_46},
  timestamp    = {Tue, 14 May 2019 10:00:42 +0200},
  biburl       = {https://dblp.org/rec/conf/iconip/HosinoWW06.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/iconip/NishiyamaW06,
  author       = {Yu Nishiyama and
                  Sumio Watanabe},
  editor       = {Irwin King and
                  Jun Wang and
                  Laiwan Chan and
                  DeLiang L. Wang},
  title        = {Asymptotic Behavior of Stochastic Complexity of Complete Bipartite
                  Graph-Type Boltzmann Machines},
  booktitle    = {Neural Information Processing, 13th International Conference, {ICONIP}
                  2006, Hong Kong, China, October 3-6, 2006, Proceedings, Part {I}},
  series       = {Lecture Notes in Computer Science},
  volume       = {4232},
  pages        = {417--426},
  publisher    = {Springer},
  year         = {2006},
  url          = {https://doi.org/10.1007/11893028\_47},
  doi          = {10.1007/11893028\_47},
  timestamp    = {Wed, 24 May 2017 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/conf/iconip/NishiyamaW06.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/iconip/TakamatsuNW06,
  author       = {Shingo Takamatsu and
                  Shinichi Nakajima and
                  Sumio Watanabe},
  editor       = {Irwin King and
                  Jun Wang and
                  Laiwan Chan and
                  DeLiang L. Wang},
  title        = {Localized Bayes Estimation for Non-identifiable Models},
  booktitle    = {Neural Information Processing, 13th International Conference, {ICONIP}
                  2006, Hong Kong, China, October 3-6, 2006, Proceedings, Part {I}},
  series       = {Lecture Notes in Computer Science},
  volume       = {4232},
  pages        = {650--659},
  publisher    = {Springer},
  year         = {2006},
  url          = {https://doi.org/10.1007/11893028\_73},
  doi          = {10.1007/11893028\_73},
  timestamp    = {Wed, 24 May 2017 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/conf/iconip/TakamatsuNW06.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/ideal/NagataW06,
  author       = {Kenji Nagata and
                  Sumio Watanabe},
  editor       = {Emilio Corchado and
                  Hujun Yin and
                  Vicente J. Botti and
                  Colin Fyfe},
  title        = {Generalization Performance of Exchange Monte Carlo Method for Normal
                  Mixture Models},
  booktitle    = {Intelligent Data Engineering and Automated Learning - {IDEAL} 2006,
                  7th International Conference, Burgos, Spain, September 20-23, 2006,
                  Proceedings},
  series       = {Lecture Notes in Computer Science},
  volume       = {4224},
  pages        = {125--132},
  publisher    = {Springer},
  year         = {2006},
  url          = {https://doi.org/10.1007/11875581\_15},
  doi          = {10.1007/11875581\_15},
  timestamp    = {Tue, 14 May 2019 10:00:45 +0200},
  biburl       = {https://dblp.org/rec/conf/ideal/NagataW06.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/ideal/WatanabeSW06,
  author       = {Kazuho Watanabe and
                  Motoki Shiga and
                  Sumio Watanabe},
  editor       = {Emilio Corchado and
                  Hujun Yin and
                  Vicente J. Botti and
                  Colin Fyfe},
  title        = {Upper Bounds for Variational Stochastic Complexities of Bayesian Networks},
  booktitle    = {Intelligent Data Engineering and Automated Learning - {IDEAL} 2006,
                  7th International Conference, Burgos, Spain, September 20-23, 2006,
                  Proceedings},
  series       = {Lecture Notes in Computer Science},
  volume       = {4224},
  pages        = {139--146},
  publisher    = {Springer},
  year         = {2006},
  url          = {https://doi.org/10.1007/11875581\_17},
  doi          = {10.1007/11875581\_17},
  timestamp    = {Fri, 26 May 2017 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/conf/ideal/WatanabeSW06.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/ijcnn/NagataW06,
  author       = {Kenji Nagata and
                  Sumio Watanabe},
  title        = {The Exchange Monte Carlo Method for Bayesian Learning in Singular
                  Learning Machines},
  booktitle    = {Proceedings of the International Joint Conference on Neural Networks,
                  {IJCNN} 2006, part of the {IEEE} World Congress on Computational Intelligence,
                  {WCCI} 2006, Vancouver, BC, Canada, 16-21 July 2006},
  pages        = {3351--3357},
  publisher    = {{IEEE}},
  year         = {2006},
  url          = {https://doi.org/10.1109/IJCNN.2006.247334},
  doi          = {10.1109/IJCNN.2006.247334},
  timestamp    = {Tue, 10 Aug 2021 14:29:47 +0200},
  biburl       = {https://dblp.org/rec/conf/ijcnn/NagataW06.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/ijon/Watanabe05,
  author       = {Sumio Watanabe},
  title        = {Algebraic geometry of singular learning machines and symmetry of generalization
                  and training errors},
  journal      = {Neurocomputing},
  volume       = {67},
  pages        = {198--213},
  year         = {2005},
  url          = {https://doi.org/10.1016/j.neucom.2004.11.037},
  doi          = {10.1016/J.NEUCOM.2004.11.037},
  timestamp    = {Sat, 20 May 2017 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/ijon/Watanabe05.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/ijon/YamazakiW05,
  author       = {Keisuke Yamazaki and
                  Sumio Watanabe},
  title        = {Algebraic geometry and stochastic complexity of hidden Markov models},
  journal      = {Neurocomputing},
  volume       = {69},
  number       = {1-3},
  pages        = {62--84},
  year         = {2005},
  url          = {https://doi.org/10.1016/j.neucom.2005.02.014},
  doi          = {10.1016/J.NEUCOM.2005.02.014},
  timestamp    = {Fri, 30 Nov 2018 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/ijon/YamazakiW05.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/nn/AoyagiW05,
  author       = {Miki Aoyagi and
                  Sumio Watanabe},
  title        = {Stochastic complexities of reduced rank regression in Bayesian estimation},
  journal      = {Neural Networks},
  volume       = {18},
  number       = {7},
  pages        = {924--933},
  year         = {2005},
  url          = {https://doi.org/10.1016/j.neunet.2005.03.014},
  doi          = {10.1016/J.NEUNET.2005.03.014},
  timestamp    = {Wed, 14 Nov 2018 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/nn/AoyagiW05.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/tnn/YamazakiW05,
  author       = {Keisuke Yamazaki and
                  Sumio Watanabe},
  title        = {Singularities in complete bipartite graph-type Boltzmann machines
                  and upper bounds of stochastic complexities},
  journal      = {{IEEE} Trans. Neural Networks},
  volume       = {16},
  number       = {2},
  pages        = {312--324},
  year         = {2005},
  url          = {https://doi.org/10.1109/TNN.2004.841792},
  doi          = {10.1109/TNN.2004.841792},
  timestamp    = {Fri, 02 Nov 2018 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/tnn/YamazakiW05.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/alt/WatanabeW05,
  author       = {Kazuho Watanabe and
                  Sumio Watanabe},
  editor       = {Sanjay Jain and
                  Hans Ulrich Simon and
                  Etsuji Tomita},
  title        = {Stochastic Complexity for Mixture of Exponential Families in Variational
                  Bayes},
  booktitle    = {Algorithmic Learning Theory, 16th International Conference, {ALT}
                  2005, Singapore, October 8-11, 2005, Proceedings},
  series       = {Lecture Notes in Computer Science},
  volume       = {3734},
  pages        = {107--121},
  publisher    = {Springer},
  year         = {2005},
  url          = {https://doi.org/10.1007/11564089\_10},
  doi          = {10.1007/11564089\_10},
  timestamp    = {Fri, 08 Sep 2023 21:18:15 +0200},
  biburl       = {https://dblp.org/rec/conf/alt/WatanabeW05.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/ijcai/NakajimaW05,
  author       = {Shinichi Nakajima and
                  Sumio Watanabe},
  editor       = {Leslie Pack Kaelbling and
                  Alessandro Saffiotti},
  title        = {Generalization Error of Linear Neural Networks in an Empirical Bayes
                  Approach},
  booktitle    = {IJCAI-05, Proceedings of the Nineteenth International Joint Conference
                  on Artificial Intelligence, Edinburgh, Scotland, UK, July 30 - August
                  5, 2005},
  pages        = {804--810},
  publisher    = {Professional Book Center},
  year         = {2005},
  url          = {http://ijcai.org/Proceedings/05/Papers/0770.pdf},
  timestamp    = {Tue, 20 Aug 2019 16:16:29 +0200},
  biburl       = {https://dblp.org/rec/conf/ijcai/NakajimaW05.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/nips/WatanabeW05,
  author       = {Kazuho Watanabe and
                  Sumio Watanabe},
  title        = {Variational Bayesian Stochastic Complexity of Mixture Models},
  booktitle    = {Advances in Neural Information Processing Systems 18 [Neural Information
                  Processing Systems, {NIPS} 2005, December 5-8, 2005, Vancouver, British
                  Columbia, Canada]},
  pages        = {1465--1472},
  year         = {2005},
  url          = {https://proceedings.neurips.cc/paper/2005/hash/b6617980ce90f637e68c3ebe8b9be745-Abstract.html},
  timestamp    = {Mon, 16 May 2022 15:41:51 +0200},
  biburl       = {https://dblp.org/rec/conf/nips/WatanabeW05.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/alt/WatanabeW04,
  author       = {Kazuho Watanabe and
                  Sumio Watanabe},
  editor       = {Shai Ben{-}David and
                  John Case and
                  Akira Maruoka},
  title        = {Estimation of the Data Region Using Extreme-Value Distributions},
  booktitle    = {Algorithmic Learning Theory, 15th International Conference, {ALT}
                  2004, Padova, Italy, October 2-5, 2004, Proceedings},
  series       = {Lecture Notes in Computer Science},
  volume       = {3244},
  pages        = {206--220},
  publisher    = {Springer},
  year         = {2004},
  url          = {https://doi.org/10.1007/978-3-540-30215-5\_17},
  doi          = {10.1007/978-3-540-30215-5\_17},
  timestamp    = {Tue, 14 May 2019 10:00:51 +0200},
  biburl       = {https://dblp.org/rec/conf/alt/WatanabeW04.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/alt/YamazakiW04,
  author       = {Keisuke Yamazaki and
                  Sumio Watanabe},
  editor       = {Shai Ben{-}David and
                  John Case and
                  Akira Maruoka},
  title        = {Newton Diagram and Stochastic Complexity in Mixture of Binomial Distributions},
  booktitle    = {Algorithmic Learning Theory, 15th International Conference, {ALT}
                  2004, Padova, Italy, October 2-5, 2004, Proceedings},
  series       = {Lecture Notes in Computer Science},
  volume       = {3244},
  pages        = {350--364},
  publisher    = {Springer},
  year         = {2004},
  url          = {https://doi.org/10.1007/978-3-540-30215-5\_27},
  doi          = {10.1007/978-3-540-30215-5\_27},
  timestamp    = {Fri, 26 May 2017 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/conf/alt/YamazakiW04.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/neco/WatanabeA03,
  author       = {Sumio Watanabe and
                  Shun{-}ichi Amari},
  title        = {Learning Coefficients of Layered Models When the True Distribution
                  Mismatches the Singularities},
  journal      = {Neural Comput.},
  volume       = {15},
  number       = {5},
  pages        = {1013--1033},
  year         = {2003},
  url          = {https://doi.org/10.1162/089976603765202640},
  doi          = {10.1162/089976603765202640},
  timestamp    = {Tue, 01 Sep 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/neco/WatanabeA03.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/nn/YamazakiW03,
  author       = {Keisuke Yamazaki and
                  Sumio Watanabe},
  title        = {Singularities in mixture models and upper bounds of stochastic complexity},
  journal      = {Neural Networks},
  volume       = {16},
  number       = {7},
  pages        = {1029--1038},
  year         = {2003},
  url          = {https://doi.org/10.1016/S0893-6080(03)00005-4},
  doi          = {10.1016/S0893-6080(03)00005-4},
  timestamp    = {Wed, 14 Nov 2018 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/nn/YamazakiW03.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/nnsp/YamazakiW03,
  author       = {Keisuke Yamazaki and
                  Sumio Watanabe},
  title        = {Stochastic complexities of hidden Markov models},
  booktitle    = {{NNSP} 2003, {IEEE} {XIII} Workshop on Neural Networks for Signal
                  Processing, Toulouse, France, September 17-19, 2003},
  pages        = {179--188},
  publisher    = {{IEEE}},
  year         = {2003},
  url          = {https://doi.org/10.1109/NNSP.2003.1318017},
  doi          = {10.1109/NNSP.2003.1318017},
  timestamp    = {Wed, 16 Oct 2019 14:14:54 +0200},
  biburl       = {https://dblp.org/rec/conf/nnsp/YamazakiW03.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/uai/YamazakiW03,
  author       = {Keisuke Yamazaki and
                  Sumio Watanabe},
  editor       = {Christopher Meek and
                  Uffe Kj{\ae}rulff},
  title        = {Stochastic Complexity of Bayesian Networks},
  booktitle    = {{UAI} '03, Proceedings of the 19th Conference in Uncertainty in Artificial
                  Intelligence, Acapulco, Mexico, August 7-10 2003},
  pages        = {592--599},
  publisher    = {Morgan Kaufmann},
  year         = {2003},
  url          = {https://dslpitt.org/uai/displayArticleDetails.jsp?mmnu=1\&\#38;smnu=2\&\#38;article\_id=978\&\#38;proceeding\_id=19},
  timestamp    = {Wed, 03 Feb 2021 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/conf/uai/YamazakiW03.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/tnn/Watanabe02,
  author       = {Sumio Watanabe},
  title        = {Errata to "learning efficiency of redundant neural networks in
                  bayesian estimation"},
  journal      = {{IEEE} Trans. Neural Networks},
  volume       = {13},
  number       = {1},
  pages        = {254},
  year         = {2002},
  url          = {https://doi.org/10.1109/TNN.2002.977325},
  doi          = {10.1109/TNN.2002.977325},
  timestamp    = {Wed, 14 Nov 2018 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/tnn/Watanabe02.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/nips/WatanabeA02,
  author       = {Sumio Watanabe and
                  Shun{-}ichi Amari},
  editor       = {Suzanna Becker and
                  Sebastian Thrun and
                  Klaus Obermayer},
  title        = {The Effect of Singularities in a Learning Machine when the True Parameters
                  Do Not Lie on such Singularities},
  booktitle    = {Advances in Neural Information Processing Systems 15 [Neural Information
                  Processing Systems, {NIPS} 2002, December 9-14, 2002, Vancouver, British
                  Columbia, Canada]},
  pages        = {391--398},
  publisher    = {{MIT} Press},
  year         = {2002},
  url          = {https://proceedings.neurips.cc/paper/2002/hash/c2ba1bc54b239208cb37b901c0d3b363-Abstract.html},
  timestamp    = {Mon, 16 May 2022 15:41:51 +0200},
  biburl       = {https://dblp.org/rec/conf/nips/WatanabeA02.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/neco/Watanabe01,
  author       = {Sumio Watanabe},
  title        = {Algebraic Analysis for Nonidentifiable Learning Machines},
  journal      = {Neural Comput.},
  volume       = {13},
  number       = {4},
  pages        = {899--933},
  year         = {2001},
  url          = {https://doi.org/10.1162/089976601300014402},
  doi          = {10.1162/089976601300014402},
  timestamp    = {Tue, 01 Sep 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/neco/Watanabe01.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/nn/Watanabe01,
  author       = {Sumio Watanabe},
  title        = {Algebraic geometrical methods for hierarchical learning machines},
  journal      = {Neural Networks},
  volume       = {14},
  number       = {8},
  pages        = {1049--1060},
  year         = {2001},
  url          = {https://doi.org/10.1016/S0893-6080(01)00069-7},
  doi          = {10.1016/S0893-6080(01)00069-7},
  timestamp    = {Wed, 14 Nov 2018 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/nn/Watanabe01.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/tnn/Watanabe01,
  author       = {Sumio Watanabe},
  title        = {Learning efficiency of redundant neural networks in Bayesian estimation},
  journal      = {{IEEE} Trans. Neural Networks},
  volume       = {12},
  number       = {6},
  pages        = {1475--1486},
  year         = {2001},
  url          = {https://doi.org/10.1109/72.963783},
  doi          = {10.1109/72.963783},
  timestamp    = {Wed, 14 Nov 2018 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/journals/tnn/Watanabe01.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/nips/Watanabe00,
  author       = {Sumio Watanabe},
  editor       = {Todd K. Leen and
                  Thomas G. Dietterich and
                  Volker Tresp},
  title        = {Algebraic Information Geometry for Learning Machines with Singularities},
  booktitle    = {Advances in Neural Information Processing Systems 13, Papers from
                  Neural Information Processing Systems {(NIPS)} 2000, Denver, CO, {USA}},
  pages        = {329--335},
  publisher    = {{MIT} Press},
  year         = {2000},
  url          = {https://proceedings.neurips.cc/paper/2000/hash/f442d33fa06832082290ad8544a8da27-Abstract.html},
  timestamp    = {Mon, 16 May 2022 15:41:51 +0200},
  biburl       = {https://dblp.org/rec/conf/nips/Watanabe00.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/alt/Watanabe98,
  author       = {Sumio Watanabe},
  editor       = {Osamu Watanabe and
                  Takashi Yokomori},
  title        = {Algebraic Analysis for Singular Statistical Estimation},
  booktitle    = {Algorithmic Learning Theory, 10th International Conference, {ALT}
                  '99, Tokyo, Japan, December 6-8, 1999, Proceedings},
  series       = {Lecture Notes in Computer Science},
  volume       = {1720},
  pages        = {39--50},
  publisher    = {Springer},
  year         = {1999},
  url          = {https://doi.org/10.1007/3-540-46769-6\_4},
  doi          = {10.1007/3-540-46769-6\_4},
  timestamp    = {Tue, 14 May 2019 10:00:51 +0200},
  biburl       = {https://dblp.org/rec/conf/alt/Watanabe98.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/nips/Watanabe99,
  author       = {Sumio Watanabe},
  editor       = {Sara A. Solla and
                  Todd K. Leen and
                  Klaus{-}Robert M{\"{u}}ller},
  title        = {Algebraic Analysis for Non-regular Learning Machines},
  booktitle    = {Advances in Neural Information Processing Systems 12, {[NIPS} Conference,
                  Denver, Colorado, USA, November 29 - December 4, 1999]},
  pages        = {356--362},
  publisher    = {The {MIT} Press},
  year         = {1999},
  url          = {http://papers.nips.cc/paper/1739-algebraic-analysis-for-non-regular-learning-machines},
  timestamp    = {Mon, 16 May 2022 15:41:51 +0200},
  biburl       = {https://dblp.org/rec/conf/nips/Watanabe99.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/iconip/Watanabe98,
  author       = {Sumio Watanabe},
  editor       = {Shiro Usui and
                  Takashi Omori},
  title        = {Inequalities of Generalization Errors for Layered Neural Networks
                  in Bayesian Learning},
  booktitle    = {The Fifth International Conference on Neural Information Processing,
                  ICONIP'R98, Kitakyushu, Japan, October 21-23, 1998, Proceedings},
  pages        = {59--62},
  publisher    = {{IOA} Press},
  year         = {1998},
  timestamp    = {Tue, 10 May 2005 13:22:06 +0200},
  biburl       = {https://dblp.org/rec/conf/iconip/Watanabe98.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@incollection{DBLP:books/mk/98/WatanabeF98,
  author       = {Sumio Watanabe and
                  Kenji Fukumizu},
  editor       = {Cornelius T. Leondes},
  title        = {Probabilistic design},
  booktitle    = {Algorithms and Architectures},
  series       = {Neural network systems techniques and applications},
  volume       = {1},
  pages        = {181--229},
  publisher    = {Morgan Kaufmann},
  year         = {1998},
  url          = {https://doi.org/10.1016/s1874-5946(98)80071-0},
  doi          = {10.1016/S1874-5946(98)80071-0},
  timestamp    = {Thu, 14 May 2020 16:10:09 +0200},
  biburl       = {https://dblp.org/rec/books/mk/98/WatanabeF98.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/adcm/Watanabe96,
  author       = {Sumio Watanabe},
  title        = {Solvable models of layered neural networks based on their differential
                  structure},
  journal      = {Adv. Comput. Math.},
  volume       = {5},
  number       = {1},
  pages        = {205--231},
  year         = {1996},
  url          = {https://doi.org/10.1007/BF02124744},
  doi          = {10.1007/BF02124744},
  timestamp    = {Sun, 28 May 2017 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/adcm/Watanabe96.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/nn/IshiFW96,
  author       = {Shin Ishii and
                  Kenji Fukumizu and
                  Sumio Watanabe},
  title        = {A network of chaotic elements for information processing},
  journal      = {Neural Networks},
  volume       = {9},
  number       = {1},
  pages        = {25--40},
  year         = {1996},
  url          = {https://doi.org/10.1016/0893-6080(95)00100-X},
  doi          = {10.1016/0893-6080(95)00100-X},
  timestamp    = {Thu, 23 Jun 2022 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/nn/IshiFW96.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/ieicet/Watanabe95,
  author       = {Sumio Watanabe},
  title        = {A Modified Information Criterion for Automatic Model and Parameter
                  Selection in Neural Network Learning},
  journal      = {{IEICE} Trans. Inf. Syst.},
  volume       = {78-D},
  number       = {4},
  pages        = {490--499},
  year         = {1995},
  url          = {http://search.ieice.org/bin/summary.php?id=e78-d\_4\_490},
  timestamp    = {Sat, 11 Apr 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/ieicet/Watanabe95.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/scjapan/TakatsuSWY95,
  author       = {Kazunori Takatsu and
                  Hidefumi Sawai and
                  Sumio Watanabe and
                  Masahide Yoneyama},
  title        = {Genetic algorithms applied to bayesian image restoration},
  journal      = {Syst. Comput. Jpn.},
  volume       = {26},
  number       = {5},
  pages        = {89--98},
  year         = {1995},
  url          = {https://doi.org/10.1002/scj.4690260508},
  doi          = {10.1002/SCJ.4690260508},
  timestamp    = {Wed, 13 Sep 2023 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/scjapan/TakatsuSWY95.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/tnn/WatanabeF95,
  author       = {Sumio Watanabe and
                  Kenji Fukumizu},
  title        = {Probabilistic design of layered neural networks based on their unified
                  framework},
  journal      = {{IEEE} Trans. Neural Networks},
  volume       = {6},
  number       = {3},
  pages        = {691--702},
  year         = {1995},
  url          = {https://doi.org/10.1109/72.377974},
  doi          = {10.1109/72.377974},
  timestamp    = {Thu, 23 Jun 2022 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/tnn/WatanabeF95.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/nips/Watanabe93,
  author       = {Sumio Watanabe},
  editor       = {Jack D. Cowan and
                  Gerald Tesauro and
                  Joshua Alspector},
  title        = {An Optimization Method of Layered Neural Networks based on the Modified
                  Information Criterion},
  booktitle    = {Advances in Neural Information Processing Systems 6, [7th {NIPS} Conference,
                  Denver, Colorado, USA, 1993]},
  pages        = {293--302},
  publisher    = {Morgan Kaufmann},
  year         = {1993},
  url          = {http://papers.nips.cc/paper/747-an-optimization-method-of-layered-neural-networks-based-on-the-modified-information-criterion},
  timestamp    = {Mon, 16 May 2022 15:41:51 +0200},
  biburl       = {https://dblp.org/rec/conf/nips/Watanabe93.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/nips/Watanabe93a,
  author       = {Sumio Watanabe},
  editor       = {Jack D. Cowan and
                  Gerald Tesauro and
                  Joshua Alspector},
  title        = {Solvable Models of Artificial Neural Networks},
  booktitle    = {Advances in Neural Information Processing Systems 6, [7th {NIPS} Conference,
                  Denver, Colorado, USA, 1993]},
  pages        = {423--430},
  publisher    = {Morgan Kaufmann},
  year         = {1993},
  url          = {http://papers.nips.cc/paper/786-solvable-models-of-artificial-neural-networks},
  timestamp    = {Fri, 06 Mar 2020 00:00:00 +0100},
  biburl       = {https://dblp.org/rec/conf/nips/Watanabe93a.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/trob/WatanabeY92,
  author       = {Sumio Watanabe and
                  Masahide Yoneyama},
  title        = {An ultrasonic visual sensor for three-dimensional object recognition
                  using neural networks},
  journal      = {{IEEE} Trans. Robotics Autom.},
  volume       = {8},
  number       = {2},
  pages        = {240--249},
  year         = {1992},
  url          = {https://doi.org/10.1109/70.134277},
  doi          = {10.1109/70.134277},
  timestamp    = {Tue, 19 May 2020 01:00:00 +0200},
  biburl       = {https://dblp.org/rec/journals/trob/WatanabeY92.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
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