@book{CTT100589310,
  author = {SUMIO WATANABE},
  title = {Algebraic geometry and statistical learning theory},
  publisher = {Cambridge University Press},
  year = 2009,
}

@book{CTT100600525,
  author = {Miki Aoyagi and SUMIO WATANABE},
  title = {The zeta function for learning theory and resolution of singularities},
  publisher = {World Scientific},
  year = 2009,
}

@article{CTT100599974,
  author = {梶大介 and 渡邊澄夫},
  title = {形式的情報量規準による決定株を用いた AdaBoost のモデル選択},
  journal = {電子情報通信学会誌},
  year = 2009,
}

@article{CTT100599973,
  author = {Yu Nishiyama and Sumio Watanabe},
  title = {Accuracy of Loopy Belief Propagation in Gaussian Models},
  journal = {Neural Networks},
  year = 2009,
}

@article{CTT100591351,
  author = {Kazuho Watanabe and Shiga Motoki and SUMIO WATANABE},
  title = {Upper bound for variational free energy of Bayesian networks},
  journal = {Machine Learning},
  year = 2009,
}

@inproceedings{CTT100600522,
  author = {Daisuke Kaji and SUMIO WATANABE},
  title = {Optimal Hyperparameters for Generalized Learning and Knowledge Discovery in Variational Bayes},
  booktitle = {Proc. of ICONIP},
  year = 2009,
}

@inproceedings{CTT100600524,
  author = {SUMIO WATANABE},
  title = {A Singular limit theorem in statistical learning theory},
  booktitle = {Proc. of Mathematical Quantum Field Theory and Renormalization Theory},
  year = 2009,
}

@inproceedings{CTT100600520,
  author = {Taruhi Iwagaki and SUMIO WATANABE},
  title = {Generalization Error by Langevin Equation in Singular Learning Machines},
  booktitle = {Proc. of ISITA},
  year = 2009,
}

@inproceedings{CTT100600521,
  author = {Shinji Oyama and SUMIO WATANABE},
  title = {Phase Transition of Generalization Errors in Variational Bayes Learning},
  booktitle = {Proc. of ISITA},
  year = 2009,
}

@inproceedings{CTT100591353,
  author = {SUMIO WATANABE},
  title = {Two birational invariants in statistical learning theory},
  booktitle = {},
  year = 2009,
}

@misc{CTT100600526,
  author = {渡邊澄夫},
  title = {有理型関数と学習理論},
  year = 2009,
}