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

@book{CTT100780898,
  author = {SUMIO WATANABE},
  title = {Mathematical theory of Bayesian statistics},
  publisher = {CRC Press},
  year = 2018,
}

@book{CTT100780894,
  author = {渡邊澄夫},
  title = {学習の代数的理論（人工知能学大辞典）},
  publisher = {共立出版},
  year = 2017,
}

@book{CTT100715451,
  author = {渡邊澄夫 and 永尾 太郎 and 樺島祥介 and 田中利幸 and 中島伸一},
  title = {ランダム行列の数理と科学},
  publisher = {森北出版},
  year = 2014,
}

@book{CTT100658079,
  author = {渡邊澄夫},
  title = {ベイズ統計の理論と方法},
  publisher = {コロナ社},
  year = 2012,
}

@book{CTT100614523,
  author = {渡邊澄夫},
  title = {特異モデルの学習理論},
  publisher = {},
  year = 2010,
}

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

@book{CTT100508080,
  author = {渡邊澄夫},
  title = {代数幾何と学習理論},
  publisher = {森北出版},
  year = 2006,
}

@book{CTT100404925,
  author = {渡辺澄夫　萩原克幸　赤穂昭太郎　本村陽一　福水健次　岡田真人　青柳美輝},
  title = {学習システムの理論と実現},
  publisher = {森北出版},
  year = 2005,
}

@book{CTT100404921,
  author = {渡辺澄夫　村田昇},
  title = {確率と統計－情報学への架橋－},
  publisher = {コロナ社},
  year = 2005,
}

@book{CTT100504722,
  author = {渡邊澄夫},
  title = {学習理論と数学的自然},
  publisher = {数学のたのしみ　日本評論社},
  year = 2004,
}

@book{CTT100504724,
  author = {渡邊澄夫},
  title = {数学と統計科学},
  publisher = {統計科学のフロンティア　岩波書店},
  year = 2004,
}

@book{CTT100504705,
  author = {Kazuho Watanabe Sumio Watanabe},
  title = {Estimation of the Data region using Extreme-value distributions},
  publisher = {Lecture Notes in Computer Science},
  year = 2004,
}

@book{CTT100489059,
  author = {渡辺澄夫},
  title = {脳情報数理科学の発展},
  publisher = {サイエンス社},
  year = 2002,
}

@book{CTT100450693,
  author = {渡邊澄夫},
  title = {データ学習アルゴリズム},
  publisher = {共立出版},
  year = 2001,
}

@book{CTT100419494,
  author = {Sumio Watanabe Kenji Fukumizu},
  title = {Algorithms and Architectures.},
  publisher = {Academic Press},
  year = 1998,
}

@book{CTT100419495,
  author = {SUMIO WATANABE},
  title = {Neural Networks for Robotic Control-Theory and Applications.},
  publisher = {Ellis Horwood},
  year = 1996,
}

@article{CTT100589311,
  author = {SUMIO WATANABE},
  title = {Equations of states in singular statistical estimation},
  journal = {Neural Networks},
  year = 2010,
}

@article{CTT100504693,
  author = {Sumio Watanabe},
  title = {Algebraic geometry of singular learning machines and  symmetry of generalization and training errors},
  journal = {Neurocomputing},
  year = 2005,
}

@article{CTT100404930,
  author = {Miki Aoyagi Sumio Watanabe},
  title = {Stochastic complexities of reduced rank regression in Bayesian estimation},
  journal = {International Journal of Neural Networks},
  year = 2005,
}

@article{CTT100504696,
  author = {渡邊澄夫 福水健次 萩原克幸 甘利俊一},
  title = {特異モデルの学習理論},
  journal = {IEICE Transactions},
  year = 2005,
}

@article{CTT100404940,
  author = {Keisuke Yamazaki Sumio Watanabe},
  title = {Algebraic geometry and stochastic complexity of hidden Markov models},
  journal = {Neurocomputing},
  year = 2005,
}

@article{CTT100504692,
  author = {Keisuke Yamazaki Sumio Watanabe},
  title = {Singularities in complete bipartite graph-type Boltzmann machines and upper bounds of stochastic complexities},
  journal = {IEEE Transactions on Neural Networks},
  year = 2005,
}

@article{CTT100404039,
  author = {中野修弘　高橋克之　渡辺澄夫},
  title = {特異モデルにおけるマルコフ連鎖モンテカルロ法の評価法},
  journal = {電子情報通信学会誌},
  year = 2005,
}

@article{CTT100404037,
  author = {青柳美輝　渡辺澄夫},
  title = {特異点解消とニューラルネットワークのベイズ推定における汎化誤差},
  journal = {電子情報通信学会誌},
  year = 2005,
}

@article{CTT100504719,
  author = {渡邊澄夫},
  title = {人工知能と特異な学習モデル},
  journal = {人工知能学会誌},
  year = 2004,
}

@article{CTT100591352,
  author = {SUMIO WATANABE},
  title = {A limit theorem in singular regression problem},
  journal = {Advanced Studies in Pure Mathematics},
  year = 2010,
}

@article{CTT100891717,
  author = {SUMIO WATANABE},
  title = {Mathematical Theory of Bayesian Statistics for Unknown Information Source},
  journal = {Philosophical Transactions of the Royal Society A},
  year = 2023,
}

@article{CTT100891718,
  author = {SUMIO WATANABE},
  title = {Recent Advances in Algebraic Geometry and Bayesian Statistics},
  journal = {Information Geometry},
  year = 2022,
}

@article{CTT100882654,
  author = {SUMIO WATANABE},
  title = {Mathematical Theory of Bayesian Statistics where All Models are Wrong},
  journal = {Handbook of Statistics},
  year = 2022,
}

@article{CTT100891735,
  author = {Shuya Nagayasu and SUMIO WATANABE},
  title = {Asymptotic behavior of free energy when optimal probability distribution is not unique},
  journal = {Neurocomputing},
  year = 2022,
}

@article{CTT100875636,
  author = {渡邊澄夫},
  title = {代数幾何と統計理論},
  journal = {応用数理},
  year = 2021,
}

@article{CTT100849018,
  author = {SUMIO WATANABE},
  title = {Information criteria and cross validation for Bayesian inference in regular and singular cases},
  journal = {Japanese Journal of Statistics and Data Science},
  year = 2021,
}

@article{CTT100849017,
  author = {SUMIO WATANABE},
  title = {WAIC and WBIC for mixture models.},
  journal = {Behaviormetrika},
  year = 2021,
}

@article{CTT100838131,
  author = {Natsuki Kariya and Sumio Watanabe},
  title = {Testing Homogeneity for Normal Mixture Models: Variational Bayes Approach},
  journal = {IEICE Transactions on Fundamentals of Electronics,Communications and Computer Sciences},
  year = 2020,
}

@article{CTT100838132,
  author = {Natsuki Kariya and Sumio Watanabe},
  title = {Asymptotic analysis of singular likelihood ratio of normal mixture by Bayesian learning theory for testing homogeneity},
  journal = {Communications in Statistics - Theory and Methods},
  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{CTT100780897,
  author = {SUMIO WATANABE},
  title = {Higher Order Equivalence of Bayes Cross Validation and  WAIC},
  journal = {Springer Proceedings in Mathematics and Statistics,  Information Geometry and Its Applications},
  year = 2018,
}

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

@article{CTT100801535,
  author = {Koda, N. and SUMIO WATANABE},
  title = {Interpretation method of nonlinear multilayer principal component analysis by using sparsity and hierarchical clustering},
  journal = {Proceedings - 2016 15th IEEE International Conference on Machine Learning and Applications, ICMLA 2016},
  year = 2017,
}

@article{CTT100714729,
  author = {中村文士 and 渡辺澄夫},
  title = {一般ディリクレ分布を用いた混合正規分布の変分自由エネルギーの漸近挙動について},
  journal = {電子情報通信学会論文誌. D, 情報・システム},
  year = 2014,
}

@article{CTT100658080,
  author = {SUMIO WATANABE},
  title = {A Widely Applicable Bayesian Information Criterion},
  journal = {Journal of Machine Learning Research},
  year = 2013,
}

@article{CTT100801108,
  author = {Ohara, S. and Yamazaki, K. and SUMIO WATANABE},
  title = {A geometric evaluation of self-organizing map and application to city data analysis},
  journal = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
  year = 2013,
}

@article{CTT100801516,
  author = {Yamada, K. and SUMIO WATANABE},
  title = {Statistical learning theory of quasi-regular cases},
  journal = {IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences},
  year = 2012,
}

@article{CTT100801088,
  author = {Yamada, K. and SUMIO WATANABE},
  title = {Information criterion for variational Bayes learning in regular and singular cases},
  journal = {6th International Conference on Soft Computing and Intelligent Systems, and 13th International Symposium on Advanced Intelligence Systems, SCIS/ISIS 2012},
  year = 2012,
}

@article{CTT100633544,
  author = {Daisuke Kaji and SUMIO WATANABE},
  title = {Two Design Methods of Hyperparameters in Variational Bayes Learning for Bernoulli Mixtures},
  journal = {Neurocomputing},
  year = 2011,
}

@article{CTT100619293,
  author = {SUMIO WATANABE},
  title = {Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory},
  journal = {Journal of Machine Learning Research},
  year = 2010,
}

@article{CTT100614516,
  author = {松田健 and 渡邊澄夫},
  title = {重みつきブローアップの混合正規分布への応用},
  journal = {電子情報通信学会誌},
  year = 2010,
}

@article{CTT100599955,
  author = {SUMIO WATANABE},
  title = {Equations of states in statistical learning for an unrealizable and regular case},
  journal = {IEICE Transactions},
  year = 2010,
}

@article{CTT100599972,
  author = {Keisuke Yamazaki and Miki Aoyagi and Sumio Watanabe},
  title = {Asymptotic Analysis of Bayesian Generalization Error with Newton Diagram},
  journal = {Neural Networks},
  year = 2010,
}

@article{CTT100801080,
  author = {Saitoh F. and SUMIO WATANABE},
  title = {On generalization error of self-organizing map},
  journal = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
  year = 2010,
}

@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,
}

@article{CTT100566505,
  author = {藤原香織 and 渡邊澄夫},
  title = {特異モデルにおけるベイズ検定と時系列解析への応用},
  journal = {電子情報通信学会論文誌D},
  year = 2008,
}

@article{CTT100566502,
  author = {Kenji Nagata and SUMIO WATANABE},
  title = {Asymptotic Behavior of Exchange Ratio in Exchange Monte Carlo Method},
  journal = {},
  year = 2008,
}

@article{CTT100566503,
  author = {Kenji Nagata and SUMIO WATANABE},
  title = {Exchange Monte Carlo Sampling From Bayesian Posterior for Singular Learning Machines},
  journal = {IEEE Transactions on Neural Networks},
  year = 2008,
}

@article{CTT100566504,
  author = {Kenji Nagata and SUMIO WATANABE},
  title = {Theory and Experiments of Exchange Ratio for Exchange Monte Carlo Method},
  journal = {Neural Information Processing - Letters and Reviews},
  year = 2008,
}

@article{CTT100566518,
  author = {SUMIO WATANABE},
  title = {Algebraic geometrical method in singular statistical estimation},
  journal = {Quantum Bio-Informatics},
  year = 2008,
}

@article{CTT100549962,
  author = {KAZUHO WATANABE and SUMIO WATANABE},
  title = {Stochastic complexities of general mixture models in variational Bayesian learning},
  journal = {Neural Networks},
  year = 2007,
}

@article{CTT100544378,
  author = {SHINICHI NAKAJIMA and SUMIO WATANABE},
  title = {Variational Bayes Solution of Linear Neural Networks and its Generalization Performance},
  journal = {Neural Computation},
  year = 2007,
}

@article{CTT100544379,
  author = {KAZUHO WATANABE and SUMIO WATANABE},
  title = {Estimating the Data Region Using Minimum and Maximum Values},
  journal = {Interdisciplinary Information Sciences},
  year = 2007,
}

@article{CTT100508085,
  author = {高松 慎吾 and 中島伸一 and 渡邊澄夫},
  title = {局所化ベイズ学習法},
  journal = {電子情報通信学会論文誌},
  year = 2006,
}

@article{CTT100507192,
  author = {西山 悠 and 渡辺澄夫},
  title = {完全2部グラフ型ボルツマンマシンの平均場近似による確率的複雑さについて},
  journal = {電子情報通信学会論文誌},
  year = 2006,
}

@article{CTT100507191,
  author = {星野力 and 渡辺一帆 and 渡辺澄夫},
  title = {隠れマルコフモデルの変分ベイズ学習における確率的複雑さについて},
  journal = {電子情報通信学会論文誌},
  year = 2006,
}

@article{CTT100508083,
  author = {SHINICHI NAKAJIMA and SUMIO WATANABE},
  title = {Generalization Performance of Subspace Bayes Approach in Linear Neural Networks},
  journal = {IEICE Transactions},
  year = 2006,
}

@article{CTT100508082,
  author = {KAZUHO WATANABE and SUMIO WATANABE},
  title = {Stochastic complexities of gaussian mixtures in variational bayesian approximation},
  journal = {Journal of Machine Learning Research},
  year = 2006,
}

@article{CTT100504714,
  author = {Shin-ichi Nakajima Sumio Watanabe},
  title = {Simulation Data Generation from Extended EGA Model and Optimization of Alignment Strategy for Lithography},
  journal = {Proceedings of International Symposium on Information Theory and its Applications,},
  year = 2004,
}

@article{CTT100504713,
  author = {Keisuke Yamazaki Sumio Watanabe},
  title = {Stochastic Complexity and Newton Diagram},
  journal = {International Symposium on Information Theory and its Applications},
  year = 2004,
}

@article{CTT100504710,
  author = {Kazuho Watanabe Sumio Watanabe},
  title = {Learning method of the data region based on extreme-value theory},
  journal = {Proceedings of International Symposium on Information Theory and its Applications},
  year = 2004,
}

@article{CTT100504708,
  author = {Kazuho Watanabe Sumio Watanabe},
  title = {Lower bounds of stochastic complexities in variational bayes learning of gaussian mixture models},
  journal = {Proceedings of IEEE International Conference on Cybernetics and Intelligent Systems},
  year = 2004,
}

@article{CTT100504701,
  author = {Miki Aoyagi Sumio Watanabe},
  title = {The generalization error of reduced rank regression in Bayesian estimation},
  journal = {International Symposium on Information Theory and its Applications},
  year = 2004,
}

@article{CTT100489053,
  author = {Keisuke Yamazaki Sumio Watanabe},
  title = {Stochastic complexities of hidden Markov models},
  journal = {Proceedings of IEEE Neural Networks and Signal Processing},
  year = 2003,
}

@article{CTT100489043,
  author = {西上功一郎　渡辺澄夫},
  title = {特異な学習モデルの選択における事前分布の影響について},
  journal = {電子情報通信学会誌},
  year = 2003,
}

@article{CTT100504721,
  author = {渡邊澄夫},
  title = {特異モデルとベイズ学習},
  journal = {日本神経回路学会誌},
  year = 2003,
}

@article{CTT100489040,
  author = {Sumio Watanabe Shun-ichi Amari},
  title = {Learning coefficients of layered models when the true distribution mismatches the singularities},
  journal = {Neural Computation},
  year = 2003,
}

@article{CTT100489044,
  author = {渡辺一帆　渡辺澄夫},
  title = {縮小ランク回帰モデルのベイズ汎化誤差について},
  journal = {電子情報通信学会誌},
  year = 2003,
}

@article{CTT100489051,
  author = {Keisuke Yamazaki Sumio Watanabe},
  title = {Stochastic complexity of Bayesian networks},
  journal = {Proceedings of Uncertainty in Artificial Intelligence},
  year = 2003,
}

@article{CTT100467467,
  author = {Keisuke Yamazaki and Sumio Watanabe},
  title = {Resolution of Singularities in Mixture Models and its Stochastic Complexity},
  journal = {Proceedings of International Conference on Neural Information Processing},
  year = 2002,
}

@article{CTT100467456,
  author = {Sumio Watanabe and Shunichi Amari},
  title = {The effect of singularities when the true parameters do not lie on such singularities},
  journal = {Advances in Neural Information Processing Systems},
  year = 2002,
}

@article{CTT100467474,
  author = {Sumio Watanabe and Shunichi Amari},
  title = {Singularities in neural networks make Bayes generalization erros smaller even if they do not contain the true},
  journal = {Proceedings of International Conference on Neural Information Processing},
  year = 2002,
}

@article{CTT100438233,
  author = {SUMIO WATANABE},
  title = {Algebraic Analysis for nonidentifiable learning machines},
  journal = {Neural Computation},
  year = 2001,
}

@article{CTT100438235,
  author = {渡邊澄夫},
  title = {特異点を持つ学習モデルと事前分布の代数幾何},
  journal = {人工知能学会誌},
  year = 2001,
}

@article{CTT100450691,
  author = {SUMIO WATANABE},
  title = {Algebraic geometrical methods for hierarchical learning machines},
  journal = {Neural Networks},
  year = 2001,
}

@article{CTT100438234,
  author = {渡邊澄夫},
  title = {代数的な特異点を持つ学習モデルの学習誤差と汎化誤差},
  journal = {電子情報通信学会誌(A)},
  year = 2001,
}

@article{CTT100450700,
  author = {SUMIO WATANABE},
  title = {Algebraic information geometry for learning machines with singularities},
  journal = {Advances in neural information processing systems},
  year = 2001,
}

@article{CTT100450692,
  author = {SUMIO WATANABE},
  title = {Learning efficiency of redundant neural networks in Bayesian estimation},
  journal = {IEEE Transactions on Neural Networks},
  year = 2001,
}

@article{CTT100419508,
  author = {SUMIO WATANABE},
  title = {Algebraic Analysis for Non-regular Learning Machines},
  journal = {Advances in Neural Information Processing Systems},
  year = 2000,
}

@article{CTT100422660,
  author = {SUMIO WATANABE},
  title = {Algebraic Analysis for Singular Statistical Estimation},
  journal = {Algorithmic Learning Theory, Lecture Notes in Computer Science.},
  year = 1999,
}

@article{CTT100422661,
  author = {SUMIO WATANABE},
  title = {Mathematical foundation for Redundant Statistical Estimation},
  journal = {Proceedings of Stochastic Systems Symposium},
  year = 1999,
}

@article{CTT100419509,
  author = {渡邊澄夫},
  title = {ベイズ法による階層型統計モデルの推定誤差について},
  journal = {電子情報通信学会誌},
  year = 1998,
}

@article{CTT100419507,
  author = {渡邊澄夫},
  title = {有限ウェーブレット展開の一手法},
  journal = {電子情報通信学会誌},
  year = 1996,
}

@article{CTT100419506,
  author = {福水健次　渡辺澄夫},
  title = {多項式近似における学習データの最適設計と予測誤差},
  journal = {電子情報通信学会誌},
  year = 1996,
}

@article{CTT100419505,
  author = {SUMIO WATANABE},
  title = {Solvable models of layered neural networks based on their differential structure.},
  journal = {Advances in Computational Mathematics},
  year = 1996,
}

@article{CTT100419504,
  author = {S.Ishii and K.Fukumizu and S.Watanabe},
  title = {A Network of Chaotic Elements for Information Processing.},
  journal = {Neural Networks},
  year = 1996,
}

@article{CTT100419503,
  author = {SUMIO WATANABE},
  title = {A modified information criterion for automatic model and parameter selection in neural network learning.},
  journal = {IEICE Transactions},
  year = 1995,
}

@article{CTT100419496,
  author = {Sumio Watanabe Kenji Fukumizu},
  title = {Probabilistic design of layered neural networks based on their unified framework.},
  journal = {IEEE Transactions on Neural Networks},
  year = 1995,
}

@article{CTT100419502,
  author = {K Takatsu and H. Sawai and S. Watanabe and M.Yoneyama},
  title = {遺伝的アルゴリズムによる画像のベイズ復元},
  journal = {電子情報通信学会誌},
  year = 1994,
}

@article{CTT100419499,
  author = {SUMIO WATANABE},
  title = {An Ultrasonic 3-D visual Sensor Using Neural Networks.},
  journal = {IEEE Transactions on Robotics and Automation},
  year = 1992,
}

@article{CTT100419501,
  author = {渡邊澄夫},
  title = {平行移動と回転に不変な特徴量を用いたニューロ超音波視覚センサによる3次元物体の識別法},
  journal = {日本音響学会誌},
  year = 1992,
}

@article{CTT100419500,
  author = {渡邊澄夫},
  title = {ニューラルネットワークを用いた超音波画像の一復元法},
  journal = {日本音響学会誌},
  year = 1992,
}

@article{CTT100419498,
  author = {渡邊澄夫},
  title = {超音波映像法とニューラルネットワークを用いた3次元物体認識法},
  journal = {日本音響学会誌},
  year = 1991,
}

@article{CTT100419497,
  author = {SUMIO WATANABE},
  title = {Ultrasonic Robot Eyes Using Neural Networks.},
  journal = {IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control},
  year = 1990,
}

@inproceedings{CTT100891736,
  author = {槇望 and 渡邊澄夫},
  title = {データ生成分布が学習モデルの特異点の近傍にあるときの事前分布の影響について},
  booktitle = {},
  year = 2022,
}

@inproceedings{CTT100891719,
  author = {SUMIO WATANABE},
  title = {Singularity Theory in Statistical Science},
  booktitle = {},
  year = 2022,
}

@inproceedings{CTT100875638,
  author = {広瀬青 and 渡邊澄夫},
  title = {入力分布が低次元超平面上にあるときの縮小ランク回帰の実対数閾値},
  booktitle = {},
  year = 2022,
}

@inproceedings{CTT100838133,
  author = {Sumio Watanabe},
  title = {Singular Learning Theory and Information Criteria},
  booktitle = {},
  year = 2020,
}

@inproceedings{CTT100838134,
  author = {渡邊澄夫},
  title = {ベイズ統計における情報量規準とクロスバリデーション},
  booktitle = {},
  year = 2020,
}

@inproceedings{CTT100819593,
  author = {永安修也 and 渡邊澄夫},
  title = {最適な確率分布が一意でないときのベイズ学習曲線},
  booktitle = {信学技報},
  year = 2020,
}

@inproceedings{CTT100818862,
  author = {田中来輝 and 渡邊澄夫},
  title = {Swish 関数を用いた階層型神経回路網の実対数閾値},
  booktitle = {信学技報},
  year = 2020,
}

@inproceedings{CTT100818861,
  author = {渡邉匠 and 渡邊澄夫},
  title = {混合多項分布のベイズ汎化誤差の漸近挙動},
  booktitle = {信学技報},
  year = 2020,
}

@inproceedings{CTT100780901,
  author = {渡邊澄夫},
  title = {構造学習理論と代数幾何学},
  booktitle = {},
  year = 2018,
}

@inproceedings{CTT100780902,
  author = {仮屋 夏樹 and 渡邊澄夫},
  title = {混合正規分布の均一性検定におけるベイズ検定統計量の漸近挙動},
  booktitle = {},
  year = 2018,
}

@inproceedings{CTT100780900,
  author = {渡邊澄夫},
  title = {ベイズ事後分布の相転移について},
  booktitle = {},
  year = 2018,
}

@inproceedings{CTT100780893,
  author = {渡邊澄夫},
  title = {統計力学と統計学の形式的な相違点を考えることに物理学の課題があるだろうか},
  booktitle = {},
  year = 2018,
}

@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{CTT100780890,
  author = {佐藤 件一郎 and 渡邊澄夫},
  title = {混合ポアソン分布の実対数閾値とベイズ汎化誤差について},
  booktitle = {},
  year = 2018,
}

@inproceedings{CTT100780887,
  author = {SUMIO WATANABE},
  title = {Cross Validation and WAIC in layered neural networks},
  booktitle = {},
  year = 2018,
}

@inproceedings{CTT100780889,
  author = {大橋 耕也 and 渡邊澄夫},
  title = {変化点検出問題におけるベイズ検定統計量の導出と検出力の実験的考察},
  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,
}

@inproceedings{CTT100780892,
  author = {渡邊澄夫},
  title = {学習理論よ何処へ},
  booktitle = {},
  year = 2017,
}

@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{CTT100780884,
  author = {Masahiro Koujima and SUMIO WATANABE},
  title = {Phase Transition Structure of Variational Bayesian Nonnegative Matrix Factorization.},
  booktitle = {},
  year = 2017,
}

@inproceedings{CTT100780886,
  author = {SUMIO WATANABE},
  title = {Difference between Bayes Cross Validation and WAIC for Conditional Independent Samples},
  booktitle = {},
  year = 2017,
}

@inproceedings{CTT100780895,
  author = {渡邊澄夫},
  title = {情報量規準とクロスバリデーションの同じ点と異なる点},
  booktitle = {},
  year = 2017,
}

@inproceedings{CTT100714643,
  author = {Sumio Watanabe},
  title = {Higher Order Analysis of Bayesian Cross Validation  in Regular Asymptotic Theory},
  booktitle = {Information Geometry and its Applications IV},
  year = 2016,
}

@inproceedings{CTT100714345,
  author = {須貝将士 and 渡邊澄夫},
  title = {非ガウス可解モデルを用いたレプリカモンテカルロ法 による自由エネルギーの計算精度の評価},
  booktitle = {信学技報},
  year = 2016,
}

@inproceedings{CTT100714342,
  author = {中村文士 and 渡邊澄夫},
  title = {ハミルトニアンモンテカルロ法を用いた神経回路網の学習と汎化誤差の推定について},
  booktitle = {信学技報},
  year = 2016,
}

@inproceedings{CTT100714341,
  author = {SUMIO WATANABE},
  title = {Cross validation and WAIC in statistical model evaluation},
  booktitle = {},
  year = 2016,
}

@inproceedings{CTT100714311,
  author = {渡邊澄夫},
  title = {潜在変数を持つモデルの評価について},
  booktitle = {欠測データ解析とモデル選択},
  year = 2016,
}

@inproceedings{CTT100714321,
  author = {香田夏輝 and 渡邊澄夫},
  title = {スパース表現を用いた非線形多層主成分分析における 学習結果の分類法について},
  booktitle = {信学技報},
  year = 2015,
}

@inproceedings{CTT100714885,
  author = {宮崎 大 and 渡邊澄夫},
  title = {情報量規準WAICによるLASSO学習の最適化と都市データ解析への応用},
  booktitle = {},
  year = 2015,
}

@inproceedings{CTT100715447,
  author = {渡邊澄夫},
  title = {尤度関数がガウス近似できないときの統計的学習の評価指標について},
  booktitle = {},
  year = 2014,
}

@inproceedings{CTT100715445,
  author = {SUMIO WATANABE},
  title = {Birational Invariants in Marginal Likelihood Computation},
  booktitle = {},
  year = 2014,
}

@inproceedings{CTT100715443,
  author = {SUMIO WATANABE},
  title = {Discovery Phenomenon and Information Criteria},
  booktitle = {},
  year = 2014,
}

@inproceedings{CTT100715461,
  author = {SUMIO WATANABE},
  title = {WAIC and WBIC are Information Criteria for Singular Statistical Model Evaluation},
  booktitle = {},
  year = 2013,
}

@inproceedings{CTT100715460,
  author = {SUMIO WATANABE},
  title = {Model Selection for Non-Regular Statistical Models},
  booktitle = {JSM 2013 Program book,},
  year = 2013,
}

@inproceedings{CTT100715453,
  author = {SUMIO WATANABE},
  title = {Resolution of Singularities and Statistical Model Evaluation},
  booktitle = {},
  year = 2013,
}

@inproceedings{CTT100633545,
  author = {Sumio Watanabe},
  title = {Algebraic geometry and model selection},
  booktitle = {},
  year = 2011,
}

@inproceedings{CTT100614518,
  author = {SUMIO WATANABE},
  title = {Asymptotic learning curve and renormalizable condition in statistical learning theory},
  booktitle = {Journal of Physics Conference Series},
  year = 2010,
}

@inproceedings{CTT100614521,
  author = {渡邊澄夫},
  title = {確率論における極限定理と双有理不変量},
  booktitle = {日本数学会２０１０年春季大会},
  year = 2010,
}

@inproceedings{CTT100600523,
  author = {Kaori Fujiwara and SUMIO WATANABE},
  title = {Determining the Number of the Components of Gaussian Mixture Models},
  booktitle = {Proc. of IASTED},
  year = 2010,
}

@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,
}

@inproceedings{CTT100591354,
  author = {SUMIO WATANABE},
  title = {Algebraic geometrical method in singular statistical estimation},
  booktitle = {},
  year = 2008,
}

@inproceedings{CTT100566508,
  author = {Kenji Nagata and SUMIO WATANABE},
  title = {Design of Exchange Monte Carlo Method for Bayesian Learning in Normal Mixture Models},
  booktitle = {},
  year = 2008,
}

@inproceedings{CTT100566512,
  author = {Masashi Matsumoto and SUMIO WATANABE},
  title = {Experimental Study of Ergodic Learning Curve in Hidden Markov Models},
  booktitle = {},
  year = 2008,
}

@inproceedings{CTT100566509,
  author = {Daisuke Kaji and SUMIO WATANABE},
  title = {Model Selection Method for AdaBoost Using Formal Information Criteria},
  booktitle = {},
  year = 2008,
}

@inproceedings{CTT100566517,
  author = {SUMIO WATANABE},
  title = {Algebraic Geometry, Empirical Process, and Singular Model Evaluation},
  booktitle = {},
  year = 2008,
}

@inproceedings{CTT100550002,
  author = {Kenji Nagata and SUMIO WATANABE},
  title = {A Method to Approximate the Baysian Posterior Distribution in Singular Learning Machines},
  booktitle = {Proc. of ICONIP2005},
  year = 2008,
}

@inproceedings{CTT100550004,
  author = {KAZUHO WATANABE and SUMIO WATANABE},
  title = {Variational Bayesian Algorithm and Stochastic Complexity for Mixture Models},
  booktitle = {Proc. of ICONIP2005},
  year = 2008,
}

@inproceedings{CTT100566513,
  author = {TAKESHI MATSUDA and SUMIO WATANABE},
  title = {Weighted Blowups of Kullback Information and Application to Multinomial Distributions},
  booktitle = {},
  year = 2008,
}

@inproceedings{CTT100566514,
  author = {Yu Nishiyama and SUMIO WATANABE},
  title = {Generalization of Concave and Convex Decomposition in Kikuchi Free Energy},
  booktitle = {},
  year = 2008,
}

@inproceedings{CTT100566515,
  author = {SUMIO WATANABE},
  title = {A foumula of equations of states in singular learning machines},
  booktitle = {},
  year = 2008,
}

@inproceedings{CTT100566516,
  author = {SUMIO WATANABE},
  title = {What we can estimate about singularity from random samples},
  booktitle = {},
  year = 2008,
}

@inproceedings{CTT100549960,
  author = {Keisuke Yamazaki and Sumio Watanabe},
  title = {Experimental Bayesian Generalization Error of Non-Regular Models under  Covariate Shift},
  booktitle = {Proc. of ICONIP 2007},
  year = 2007,
}

@inproceedings{CTT100575851,
  author = {Keisuke Yamazaki and Motoaki Kawanabe and Sumio Watanabe and Masashi Sugiyama and Klaus-Robert Mueller},
  title = {Asymptotic Bayesian generalization error when training and test distributions are different},
  booktitle = {Proceedings of 24th International Conference on Machine Learning (ICML2007)},
  year = 2007,
}

@inproceedings{CTT100544384,
  author = {Keisuke Yamazaki and SUMIO WATANABE and Masashi Sugiyama},
  title = {Asymptotic Bayesian Generalization Error When Training and Test Distributions Are Different},
  booktitle = {Proc. of ICML},
  year = 2007,
}

@inproceedings{CTT100544381,
  author = {Kenji Nagata and SUMIO WATANABE},
  title = {Analysis of Exchange Ratio for Exchange Monte Carlo Method},
  booktitle = {Proc. of FOCI2007},
  year = 2007,
}

@inproceedings{CTT100544392,
  author = {miki aoyagi and SUMIO WATANABE},
  title = {Resolution of Singularities and Stochastic Complexity of Complete Bipartite Graph-Type Spin Model in Bayesian Estimation},
  booktitle = {Proc. of MDAI},
  year = 2007,
}

@inproceedings{CTT100544391,
  author = {Ryosuke Iriguchi and SUMIO WATANABE},
  title = {Estimation of Poles of Zeta Function in Learning Theory Using Pade Approximation},
  booktitle = {Proc.of  ICANN},
  year = 2007,
}

@inproceedings{CTT100544390,
  author = {Kenji Nagata and SUMIO WATANABE},
  title = {Algebraic Geometric Study of Exchange Monte Carlo Method},
  booktitle = {Proc. of ICANN},
  year = 2007,
}

@inproceedings{CTT100544389,
  author = {YU NISHIYAMA and SUMIO WATANABE},
  title = {Theoretical Analysis of Accuracy of Gaussian Belief Propagation},
  booktitle = {Proc. of ICANN},
  year = 2007,
}

@inproceedings{CTT100544386,
  author = {TAKESHI MATSUDA and SUMIO WATANABE},
  title = {On a Singular Point to Contribute to a Learning Coefficient and Weighted Resolution of Singularities},
  booktitle = {Proc. of ICANN},
  year = 2007,
}

@inproceedings{CTT100544385,
  author = {SHINICHI NAKAJIMA and SUMIO WATANABE},
  title = {Generalization Error of Automatic Relevance Determination},
  booktitle = {Proc. of ICANN},
  year = 2007,
}

@inproceedings{CTT100544382,
  author = {SUMIO WATANABE},
  title = {Almost All Learning Machines are Singular},
  booktitle = {Proc. of FOCI},
  year = 2007,
}

@inproceedings{CTT100549965,
  author = {SUMIO WATANABE and KAZUHO WATANABE},
  title = {Stochastic complexity for mixture of exponential families in generalized variational Bayes},
  booktitle = {Theoretical Computer Science},
  year = 2007,
}

@inproceedings{CTT100508098,
  author = {Yu  Nishiyama and SUMIO WATANABE},
  title = {Asymptotic Behavior of Stochastic Complexity of Complete Bipartite Graph-Type Boltzmann Machines},
  booktitle = {Proc. of ICONIP},
  year = 2006,
}

@inproceedings{CTT100508090,
  author = {Tikara  Hosino and KAZUHO WATANABE and SUMIO WATANABE},
  title = {Free Energy of Stochastic Context Free Grammar on Variational Bayes},
  booktitle = {Proc. of  ICONIP},
  year = 2006,
}

@inproceedings{CTT100508087,
  author = {KAZUHO WATANABE and Motoki  Shiga and SUMIO WATANABE},
  title = {Upper bounds for variational stochastic complexities of Bayesian networks},
  booktitle = {Proc. of International Conference on Intelligent Data Engineering and Automated Learning},
  year = 2006,
}

@inproceedings{CTT100508089,
  author = {KAZUHO WATANABE and SUMIO WATANABE},
  title = {Variational bayesian stochastic complexity of mixture models},
  booktitle = {Proc. of Advances in Neural Information Processing Systems},
  year = 2006,
}

@inproceedings{CTT100508099,
  author = {Miki  Aoyagi and SUMIO WATANABE},
  title = {Generalization Error of Three Layered Learning Model in Bayesian Estimation},
  booktitle = {Proc. of the 2nd IASTED International Conference on Computational Intelligence},
  year = 2006,
}

@inproceedings{CTT100508096,
  author = {Shingo Takamatsu and SHINICHI NAKAJIMA and SUMIO WATANABE},
  title = {Localized Bayes Estimation for Non-identifiable Models},
  booktitle = {Proc. of International Conference on Neural Information Processing},
  year = 2006,
}

@inproceedings{CTT100507840,
  author = {YU NISHIYAMA and SUMIO WATANABE},
  title = {Asymptotic Behavior of Stochastic Complexity of Complete Bipartite Graph-type Boltzmann Machines},
  booktitle = {LNCS 4232},
  year = 2006,
}

@inproceedings{CTT100508094,
  author = {Keisuke Yamazaki and Kenji  Nagata and SUMIO WATANABE and Klaus-Robert  Mueller},
  title = {A Model Selection Method Based on Bound of Learning Coefficient},
  booktitle = {Proc. of International Conference on Artificial Neural Networks},
  year = 2006,
}

@inproceedings{CTT100508093,
  author = {Kenji  Nagata and SUMIO WATANABE},
  title = {Generalization Performance of Exchange Monte Carlo Method for Normal Mixture Models},
  booktitle = {Proc. of 7th International Conference on Intelligent Data Engineering and Automated Learning},
  year = 2006,
}

@inproceedings{CTT100508097,
  author = {SHINICHI NAKAJIMA and SUMIO WATANABE},
  title = {Analytic Solution of Hierarchical Variational Bayes in Linear Inverse Problem},
  booktitle = {Proc. of International Conference on Artificial Neural Networks},
  year = 2006,
}

@inproceedings{CTT100508095,
  author = {Kenji  Nagata and SUMIO WATANABE},
  title = {The Exchange Monte Carlo Method for Bayesian Learning in Singular Learning Machines},
  booktitle = {Proc. of IEEE World Congress on Computational Intelligence},
  year = 2006,
}

@inproceedings{CTT100507124,
  author = {渡辺澄夫},
  title = {代数幾何と学習理論の関係について},
  booktitle = {},
  year = 2006,
}

@inproceedings{CTT100550012,
  author = {KAZUHO WATANABE and SUMIO WATANABE},
  title = {Variational Bayesian Stochastic Complexity of Mixture Models},
  booktitle = {Proc. of Advances in Neural Information Processing Systems},
  year = 2006,
}

@inproceedings{CTT100549995,
  author = {Keisuke Yamazaki and Kenji Nagata and SUMIO WATANABE},
  title = {A New Method of Model Selection Based on Learning Coefficient},
  booktitle = {Proc. of International Symposium on Nonlinear Theory and its Applications},
  year = 2005,
}

@inproceedings{CTT100549999,
  author = {SHINICHI NAKAJIMA and SUMIO WATANABE},
  title = {Generalization Error of Linear Neural Networks in an Empirical Bayes Approach},
  booktitle = {Proc. of IJCAI2005},
  year = 2005,
}

@inproceedings{CTT100550000,
  author = {SHINICHI NAKAJIMA and SUMIO WATANABE},
  title = {Generalization Error and Free Energy of Linear Neural Networks in Variational Bayes Approach},
  booktitle = {Proc. of ICONIP2005},
  year = 2005,
}

@inproceedings{CTT100550009,
  author = {KAZUHO WATANABE and SUMIO WATANABE},
  title = {On Variational Bayes Algorithms for Exponential Family Mixtures},
  booktitle = {Proc. of International Symposium on Nonlinear Theory and its Applications},
  year = 2005,
}

@inproceedings{CTT100549983,
  author = {TIKARA HOSHINO and KAZUHO WATANABE and SUMIO WATANABE},
  title = {Stochastic Complexity of Variational Bayesian Hidden Markov Models},
  booktitle = {Proc. of IJCNN},
  year = 2005,
}

@inproceedings{CTT100550005,
  author = {KAZUHO WATANABE and SUMIO WATANABE},
  title = {Stochastic complexity for mixture of exponential families in variational bayes},
  booktitle = {Proc. of ALT2005},
  year = 2005,
}

@inproceedings{CTT100549989,
  author = {Keisuke Yamazaki and SUMIO WATANABE},
  title = {Generalization Errors in Estimation of Stochastic Context-Free Grammar},
  booktitle = {The IASTED International Conference on Artificial Intelligence and Soft Computing},
  year = 2005,
}

@inproceedings{CTT100550014,
  author = {miki aoyagi and SUMIO WATANABE},
  title = {The zeta function for learning theory and resolution of singularities},
  booktitle = {Proc. of ISAAC},
  year = 2005,
}

@misc{CTT100785189,
  author = {金森敬文 and 樺島祥介 and 高安美佐子 and 中野 張 and 福田光浩 and 三好直人 and 山下  真 and 渡邊澄夫},
  title = {東京工業大学情報理工学院数理・計算科学系―情報の未来を作り出す数理的アプローチを探究する―},
  year = 2019,
}

@misc{CTT100780899,
  author = {渡邊澄夫},
  title = {機械学習の数学入門},
  year = 2018,
}

@misc{CTT100715449,
  author = {渡邊澄夫},
  title = {ラプラスとフィッシャーから荒野へ},
  year = 2014,
}

@misc{CTT100614520,
  author = {渡邊澄夫},
  title = {学習理論に現れる数学},
  year = 2010,
}

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

@misc{CTT100558973,
  author = {桑子敏雄 and 渡邊澄夫 and 他},
  title = {大学授業がやってきた！ 知の冒険},
  year = 2008,
}

@misc{CTT100544393,
  author = {渡邊澄夫},
  title = {物理学者でない人にとって平衡統計力学とは},
  year = 2007,
}

@misc{CTT100507834,
  author = {西山悠 and 渡邊澄夫},
  title = {一般ボルツマンマシンにおける平均場近似自由エネルギーの漸近的挙動},
  year = 2006,
}

@misc{CTT100507831,
  author = {西山悠 and 渡邊澄夫},
  title = {完全2部グラフ型ボルツマンマシンにおける平均場近似自由エネルギーの漸近的挙動},
  year = 2006,
}

@misc{CTT100595359,
  author = {SUMIO WATANABE},
  title = {神経回路網援用超音波影像法による３次元物体認識},
  year = 1993,
}

@misc{CTT100594548,
  author = {SUMIO WATANABE},
  title = {Spectral analysis for multipole ghost},
  year = 1984,
}



@phdthesis{CTT100595359,
  author = {SUMIO WATANABE},
  title = {神経回路網援用超音波影像法による３次元物体認識},
  school = {東京工業大学大学院総合理工研究科電子システム専攻},
  year = 1993,
}

@mastersthesis{CTT100594548,
  author = {SUMIO WATANABE},
  title = {Spectral analysis for multipole ghost},
  school = {京都大学大学院理学系研究科数理解析専攻},
  year = 1984,
}
@misc{CTT100806761,
  author = {SUMIO WATANABE},
  title = {Highly Cited Paper: A widely applicable Bayesian information criterion},
  year = 2019,
  note = {2019-2019},
}

@misc{CTT100748585,
  author = {SUMIO WATANABE},
  title = {Highly Cited Paper: Asymptotic equivalence of Bayes Cross Validation and WAIC},
  year = 2017,
  note = {2017-},
}

@misc{CTT100780896,
  author = {Masahiro Koujima and SUMIO WATANABE},
  title = {ICANN Best Paper Award},
  year = 2017,
  note = {2017-2017},
}

@misc{CTT100715469,
  author = {渡邊澄夫},
  title = {情報量規準 WAIC と WBIC},
  year = 2010,
  note = {2010-2016},
}

@misc{CTT100714654,
  author = {渡邊澄夫},
  title = {代数幾何と学習理論},
  year = 2002,
  note = {2002-2017},
}