@article{CTT100848638,
  author = {Naoki Hayashi},
  title = {The exact asymptotic form of Bayesian generalization error in latent Dirichlet allocation},
  journal = {Neural Networks},
  year = 2021,
}

@article{CTT100821826,
  author = {Naoki Hayashi},
  title = {Variational approximation error in non-negative matrix factorization},
  journal = {Neural Networks},
  year = 2020,
}

@article{CTT100821827,
  author = {Keita Harada and Naoki Hayashi and Katsushi Kagaya},
  title = {Individual behavioral type captured by a Bayesian model comparison in cap making by sponge crab},
  journal = {PeerJ},
  year = 2020,
}

@article{CTT100818855,
  author = {Naoki Hayashi and Sumio Watanabe},
  title = {Asymptotic Bayesian Generalization Error in Latent Dirichlet Allocation  and Stochastic Matrix Factorization},
  journal = {Springer Nature Computer Science},
  year = 2020,
}

@article{CTT100780881,
  author = {Naoki Hayashi and SUMIO WATANABE},
  title = {Upper Bound of Bayesian Generalization Error in Non-Negative Matrix Factorization},
  journal = {NEUROCOMPUTING},
  year = 2017,
}

@inproceedings{CTT100780891,
  author = {林 直輝 and 渡邊澄夫},
  title = {ハミルトニアンモンテカルロ法を用いた確率行列分解における実対数閾値の実験的考察},
  booktitle = {},
  year = 2018,
}

@inproceedings{CTT100780888,
  author = {林 直輝 and 渡邊澄夫},
  title = {確率行列分解の実対数閾値とBayes学習への応用},
  booktitle = {},
  year = 2017,
}

@inproceedings{CTT100780885,
  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 = {},
  year = 2017,
}

@misc{CTT100875381,
  author = {Naoki Hayashi},
  title = {Statistical Learning Theory of Parameter-Restricted Singular Models},
  year = 2021,
}

@misc{CTT100848643,
  author = {Naoki Hayashi},
  title = {Statistical Learning Theory of Parameter-Restricted Singular Models},
  year = 2021,
}

@misc{CTT100848642,
  author = {Naoki Hayashi},
  title = {Statistical Learning Theory of Parameter-Restricted Singular Models},
  year = 2021,
}



@phdthesis{CTT100875381,
  author = {Naoki Hayashi},
  title = {Statistical Learning Theory of Parameter-Restricted Singular Models},
  school = {東京工業大学},
  year = 2021,
}

@phdthesis{CTT100848643,
  author = {Naoki Hayashi},
  title = {Statistical Learning Theory of Parameter-Restricted Singular Models},
  school = {東京工業大学},
  year = 2021,
}

@phdthesis{CTT100848642,
  author = {Naoki Hayashi},
  title = {Statistical Learning Theory of Parameter-Restricted Singular Models},
  school = {東京工業大学},
  year = 2021,
}