"SUMIO WATANABE","Mathematical Theory of Bayesian Statistics for Unknown Information Source",,"Philosophical Transactions of the Royal Society A",,,,,2023,Mar.
"Nozomi Maki,SUMIO WATANABE","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","情報論的学習理論と機械学習研究会",,,,,,2022,Dec.
"SUMIO WATANABE","Recent Advances in Algebraic Geometry and Bayesian Statistics",,"Information Geometry",,,,,2022,Dec.
"SUMIO WATANABE","Singularity Theory in Statistical Science","Deepening and Evolution of Applied Singularity Theory",,,,,,2022,Nov.
"SUMIO WATANABE","Mathematical Theory of Bayesian Statistics where All Models are Wrong",,"Handbook of Statistics","Elsevior","Vol. 47",,"pp. 209-238",2022,Sept.
"Shuya Nagayasu,SUMIO WATANABE","Asymptotic behavior of free energy when optimal probability distribution is not unique",,"Neurocomputing",,"Vol. 500",,"pp. 528-536",2022,Aug.
"Joe Hirose,SUMIO WATANABE","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","情報論的学習理論と機械学習研究会",,,,,,2022,Mar.
"SUMIO WATANABE","代数幾何と統計理論",,"応用数理",,"Vol. 31","No. 3","pp. 7-14",2021,Sept.
"SUMIO WATANABE","Information criteria and cross validation for Bayesian inference in regular and singular cases",,"Japanese Journal of Statistics and Data Science",,,,,2021,May
"SUMIO WATANABE","WAIC and WBIC for mixture models.",,"Behaviormetrika",,"Vol. 48",,"pp. 5-21",2021,Feb.
"Natsuki Kariya,Sumio Watanabe","Testing Homogeneity for Normal Mixture Models: Variational Bayes Approach",,"IEICE Transactions on Fundamentals of Electronics,Communications and Computer Sciences",,"Vol. 103A","No. 11","pp. 1274-1282",2020,Nov.
"Natsuki Kariya,Sumio Watanabe","Asymptotic analysis of singular likelihood ratio of normal mixture by Bayesian learning theory for testing homogeneity",,"Communications in Statistics - Theory and Methods",,"Vol. 42",,,2020,Nov.
"Sumio Watanabe","Singular Learning Theory and Information Criteria","統計連合大会",,,,,,2020,Sept.
"SUMIO WATANABE","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","行動計量学会",,,,,,2020,Sept.
"Shuya Nagayasu,SUMIO WATANABE","最適な確率分布が一意でないときのベイズ学習曲線",,"信学技報",,"vol. 119","no. 453","pp. 107-112",2020,Mar.
"Naoki Hayashi,Sumio Watanabe","Asymptotic Bayesian Generalization Error in Latent Dirichlet Allocation  and Stochastic Matrix Factorization",,"Springer Nature Computer Science","Springer Nature","vol. 1","no. 2","pp. 1-22",2020,Feb.
"Raiki Tanaka,SUMIO WATANABE","Swish 関数を用いた階層型神経回路網の実対数閾値",,"信学技報",,"vol. 119","no. 360","pp. 9-15",2020,Jan.
"Takumi Watanabe,SUMIO WATANABE","混合多項分布のベイズ汎化誤差の漸近挙動",,"信学技報",,"vol. 119","no. 360","pp. 1-8",2020,Jan.
"takafumi kanamori,YOSHIYUKI KABASHIMA,Misako Takayasu,Yumiharu Nakano,Mituhiro Fukuda,Naoto Miyoshi,Makoto Yamashita,SUMIO WATANABE","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―",,"オペレーションズ・リサーチ",,"Vol. 64","No. 1","pp. 31-32",2019,Jan.
"SUMIO WATANABE","Higher Order Equivalence of Bayes Cross Validation and  WAIC",,"Springer Proceedings in Mathematics and Statistics,  Information Geometry and Its Applications",,,,"pp. 47-73",2018,Nov.
"SUMIO WATANABE","構造学習理論と代数幾何学",,,,,,,2018,Sept.
"Natsuki Kariya,SUMIO WATANABE","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","2018年度統計関連連合大会",,,,,,2018,Sept.
"SUMIO WATANABE","機械学習の数学入門",,"数理科学 2018年8月号",,"vol. 662",,"pp. 5-13",2018,Aug.
"SUMIO WATANABE","ベイズ事後分布の相転移について","産総研AIセミナー",,,,,,2018,July
"SUMIO WATANABE","Mathematical theory of Bayesian statistics",,,"CRC Press",,,,2018,May
"Kenji Sato,SUMIO WATANABE","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","情報論的学習理論と機械学習研究会",,,,,,2018,Mar.
"SUMIO WATANABE","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","統計物理学懇談会（第 6 回）",,,,,,2018,Mar.
"Naoki Hayashi,SUMIO WATANABE","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","NC研究会",,,,,,2018,Mar.
"SUMIO WATANABE","Cross Validation and WAIC in layered neural networks","Deep Learning: Theory, Algorithms, and Applications",,,,,,2018,Mar.
"Kouya Ohashi,SUMIO WATANABE","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","第116回数理モデル化と問題解決(MPS)研究会",,,,,,2017,Dec.
"Naoki Hayashi,SUMIO WATANABE","Upper Bound of Bayesian Generalization Error in Non-Negative Matrix Factorization",,"NEUROCOMPUTING","Elsevier Science Publishers","Vol. 266",,"pp. 21-28",2017,Nov.
"Naoki Hayashi,SUMIO WATANABE","確率行列分解の実対数閾値とBayes学習への応用","情報論的学習理論と機械学習研究会",,,,,,2017,Nov.
"SUMIO WATANABE","学習理論よ何処へ","情報論的学習理論と機械学習研究会",,,,,,2017,Nov.
"Naoki Hayashi,SUMIO WATANABE","Tighter Upper Bound of Real Log Canonical Threshold of Non-negative Matrix Factorization and its Application to Bayesian Inference","2017 IEEE Symposium Series on Computational Intelligence",,,,,,2017,Nov.
"SUMIO WATANABE","Difference between Bayes Cross Validation and WAIC for Conditional Independent Samples","The Tenth Workshop on Information Theoretic Methods in Science and Engineering",,,,,,2017,Sept.
"Masahiro Koujima,SUMIO WATANABE","Phase Transition Structure of Variational Bayesian Nonnegative Matrix Factorization.","26th International Conference on Artificial Neural Networks 2017",,,,,,2017,Sept.
"SUMIO WATANABE","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","2017年統計サマーセミナー",,,,,,2017,Aug.
"SUMIO WATANABE","学習の代数的理論（人工知能学大辞典）",,,"共立出版",,,,2017,July
"Koda, N.,SUMIO WATANABE","Interpretation method of nonlinear multilayer principal component analysis by using sparsity and hierarchical clustering",,"Proceedings - 2016 15th IEEE International Conference on Machine Learning and Applications, ICMLA 2016",,,,"pp. 1063-1066",2017,
"Sumio Watanabe","Higher Order Analysis of Bayesian Cross Validation  in Regular Asymptotic Theory","Information Geometry and its Applications IV","Information Geometry and its Applications IV",,,,,2016,July
"Fumito Nakamura,SUMIO WATANABE","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",,"信学技報",,"Vol. IBISML2015",,"pp. 25-29",2016,Mar.
"Shoji Sugai,SUMIO WATANABE","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",,"信学技報",,"Vol. 115","No. 514","pp. 77-82",2016,Mar.
"SUMIO WATANABE","潜在変数を持つモデルの評価について","データ科学シンポジウム","欠測データ解析とモデル選択",,"Vol. 1",,"pp. 105-112",2016,Jan.
"SUMIO WATANABE","Cross validation and WAIC in statistical model evaluation","Symposium - What is a good model ?",,,,,,2016,Jan.
"Natsuki Koda,SUMIO WATANABE","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","情報論的学習理論と機械学習研究会","信学技報","電子情報通信学会","Vol. 115","No. 323","pp. 19-24",2015,Nov.
"DAI MIYAZAKI,SUMIO WATANABE","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",,,,"Vol. IEICE-114","No. 515","pp. 331-336",2015,Mar.
"SUMIO WATANABE","Discovery Phenomenon and Information Criteria","The Seventh Workshop on Information Theoretic Methods in Science and Engineering",,,,,,2014,July
"SUMIO WATANABE","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","電子情報通信学会音声研究会",,,,,,2014,July
"SUMIO WATANABE","Birational Invariants in Marginal Likelihood Computation","NIMS Thematic Program on Algebraic Statistics",,,,,,2014,July
"Fumito Nakamura,Sumio Watanabe","Asymptotic Behavior of Variational Free Energy for Normal Mixtures Using General Dirichlet Distribution",,"IEICE Transactions on Information and Systems",,"Vol. 97.5","No. 5","pp. 1001-1013",2014,May
"SUMIO WATANABE,Taro Nagao,YOSHIYUKI KABASHIMA,TOSHIYUKI TANAKA,SHINICHI NAKAJIMA","ランダム行列の数理と科学",,,"森北出版",,,,2014,Apr.
"SUMIO WATANABE","ラプラスとフィッシャーから荒野へ",,"電子情報通信学会 情報システムソサイエティ誌",,"Vol. 18","No. 4","pp. 17-18",2014,Feb.
"SUMIO WATANABE","Resolution of Singularities and Statistical Model Evaluation","SIAM Conference on Applied Algebraic Geometry",,,,,,2013,Aug.
"SUMIO WATANABE","Model Selection for Non-Regular Statistical Models","2013 Joint Statistical Meetings","JSM 2013 Program book,",,,,"pp. 265",2013,Aug.
"SUMIO WATANABE","WAIC and WBIC are Information Criteria for Singular Statistical Model Evaluation","The Sixth Workshop on Information Theoretic Methods in Science and Engineering",,,,,,2013,Aug.
"SUMIO WATANABE","A Widely Applicable Bayesian Information Criterion",,"Journal of Machine Learning Research",,"Vol. 14",,"pp. 867-897",2013,Mar.
"Ohara, S.,Yamazaki, K.,SUMIO WATANABE","A geometric evaluation of self-organizing map and application to city data analysis",,"Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",,"Vol. 8271 LNAI",,"pp. 165-174",2013,
"SUMIO WATANABE","ベイズ統計の理論と方法",,,"コロナ社",,,,2012,Apr.
"Yamada, K.,SUMIO WATANABE","Information criterion for variational Bayes learning in regular and singular cases",,"6th International Conference on Soft Computing and Intelligent Systems, and 13th International Symposium on Advanced Intelligence Systems, SCIS/ISIS 2012",,,,"pp. 1551-1556",2012,
"Yamada, K.,SUMIO WATANABE","Statistical learning theory of quasi-regular cases",,"IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences",,"Vol. E95-A","No. 12","pp. 2479-2487",2012,
"Sumio Watanabe","Algebraic geometry and model selection","Singular Learning Theory : connecting algebraic geometry and statistical model selection",,,,,,2011,Dec.
"Daisuke Kaji,SUMIO WATANABE","Two Design Methods of Hyperparameters in Variational Bayes Learning for Bernoulli Mixtures",,"Neurocomputing","Elsevior","Vol. 74","No. 11","pp. 2002-2007",2011,May
"SUMIO WATANABE","Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory",,"Journal of Machine Learning Research",,"Vol. 11",,"pp. 3571-3591",2010,Dec.
"SUMIO WATANABE","学習理論に現れる数学",,"現代思想",,"Vol. 2010年","No. 9","pp. 164-173",2010,Sept.
"SUMIO WATANABE","Asymptotic learning curve and renormalizable condition in statistical learning theory",,"Journal of Physics Conference Series",,"Vol. 233","No. 1","  012014",2010,July
"SUMIO WATANABE","A limit theorem in singular regression problem",,"Advanced Studies in Pure Mathematics",,"Vol. 57",,"pp. 473-492",2010,Apr.
"TAKESHI MATSUDA,SUMIO WATANABE","重みつきブローアップの混合正規分布への応用",,"電子情報通信学会誌",,"Vol. J93-A","No. 4","pp. 300-308",2010,Apr.
"SUMIO WATANABE","確率論における極限定理と双有理不変量",,"日本数学会２０１０年春季大会",,"Vol. 2010年",,,2010,Mar.
"SUMIO WATANABE","Equations of states in statistical learning for an unrealizable and regular case",,"IEICE Transactions",,"Vol. E93-A","No. 3","pp. 617-626",2010,Mar.
"Kaori Fujiwara,SUMIO WATANABE","Determining the Number of the Components of Gaussian Mixture Models","Massachusetts, USA","Proc. of IASTED",,,"  CD-ROM",,2010,Feb.
"SUMIO WATANABE","特異モデルの学習理論",,"現代数理科学事典",,,,,2010,Jan.
"Keisuke Yamazaki,Miki Aoyagi,Sumio Watanabe","Asymptotic Analysis of Bayesian Generalization Error with Newton Diagram",,"Neural Networks","Elsevior","Vol. 23","No. 1","pp. 35-43",2010,Jan.
"SUMIO WATANABE","Equations of states in singular statistical estimation",,"Neural Networks","Elsevier","Vol. 23","No. 1","pp. 20-34",2010,Jan.
"Saitoh F.,SUMIO WATANABE","On generalization error of self-organizing map",,"Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",,"Vol. 6444 LNCS","No. PART 2","pp. 399-406",2010,
"Daisuke Kaji,SUMIO WATANABE","Optimal Hyperparameters for Generalized Learning and Knowledge Discovery in Variational Bayes",,"Proc. of ICONIP",,,"  CD-ROM",,2009,Dec.
"SUMIO WATANABE","A Singular limit theorem in statistical learning theory",,"Proc. of Mathematical Quantum Field Theory and Renormalization Theory",,"Vol. 1",,,2009,Nov.
"Daisuke Kaji,SUMIO WATANABE","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",,"電子情報通信学会誌",,"Vol. J92-D","No. 11","pp. 2051-2058",2009,Nov.
"Taruhi Iwagaki,SUMIO WATANABE","Generalization Error by Langevin Equation in Singular Learning Machines",,"Proc. of ISITA",,"Vol. 1","  CD-ROM",,2009,Oct.
"Shinji Oyama,SUMIO WATANABE","Phase Transition of Generalization Errors in Variational Bayes Learning",,"Proc. of ISITA",,,"  CD-ROM",,2009,Oct.
"SUMIO WATANABE","Two birational invariants in statistical learning theory","JSPS Forum on Singularities",,,,,,2009,Aug.
"SUMIO WATANABE","Algebraic geometry and statistical learning theory",,,"Cambridge University Press",,,"pp. 1-286",2009,Aug.
"SUMIO WATANABE","有理型関数と学習理論",,"数理科学","サイエンス社","Vol. 554",,"pp. 50-51",2009,Aug.
"Yu Nishiyama,Sumio Watanabe","Accuracy of Loopy Belief Propagation in Gaussian Models",,"Neural Networks","Elsevior","Vol. 22","No. 4","pp. 385-394",2009,May
"Miki Aoyagi,SUMIO WATANABE","The zeta function for learning theory and resolution of singularities",,"More Progresses in Analysis","World Scientific","Vol. 1",,"pp. 279-288",2009,Mar.
"Kazuho Watanabe,Shiga Motoki,SUMIO WATANABE","Upper bound for variational free energy of Bayesian networks",,"Machine Learning",,"Vol. 75","No. 2","pp. 199-215",2009,Feb.
"SUMIO WATANABE","Algebraic geometrical method in singular statistical estimation","Algebraic Statistics",,,,,,2008,Dec.
"Masashi Matsumoto,SUMIO WATANABE","Experimental Study of Ergodic Learning Curve in Hidden Markov Models","International Conference on Neural Information Processing of the Asia-Pacific Neural Network Assembly",,,,,,2008,Nov.
"Daisuke Kaji,SUMIO WATANABE","Model Selection Method for AdaBoost Using Formal Information Criteria","International Conference on Neural Information Processing of the Asia-Pacific Neural Network Assembly",,,,,,2008,Nov.
"Kenji Nagata,SUMIO WATANABE","Design of Exchange Monte Carlo Method for Bayesian Learning in Normal Mixture Models","International Conference on Neural Information Processing of the Asia-Pacific Neural Network Assembly",,,,,,2008,Nov.
"SUMIO WATANABE","Algebraic Geometry, Empirical Process, and Singular Model Evaluation","Algebraic Methods in Systems Biology and Statistics",,,,,,2008,Sept.
"TOSHIO KUWAKO,SUMIO WATANABE,他","大学授業がやってきた！ 知の冒険",,,"水曜社",,,"pp. 86-96",2008,May
"KAZUHO WATANABE,SUMIO WATANABE","Variational Bayesian Algorithm and Stochastic Complexity for Mixture Models",,"Proc. of ICONIP2005",,,,,2008,Mar.
"Kenji Nagata,SUMIO WATANABE","A Method to Approximate the Baysian Posterior Distribution in Singular Learning Machines",,"Proc. of ICONIP2005",,,,,2008,Mar.
"Kenji Nagata,SUMIO WATANABE","Exchange Monte Carlo Sampling From Bayesian Posterior for Singular Learning Machines",,"IEEE Transactions on Neural Networks",,"vol. 19","no. 7","pp. 1253-1266",2008,
"Kenji Nagata,SUMIO WATANABE","Asymptotic Behavior of Exchange Ratio in Exchange Monte Carlo Method",,,,"vol. 21","no. 7","pp. 980-988",2008,
"Kenji Nagata,SUMIO WATANABE","Theory and Experiments of Exchange Ratio for Exchange Monte Carlo Method",,"Neural Information Processing - Letters and Reviews",,"vol. 12","no. 1-3","pp. 21-30",2008,
"Kaori Fujiwara,SUMIO WATANABE","特異モデルにおけるベイズ検定と時系列解析への応用",,"電子情報通信学会論文誌D",,"vol. J91-D","no. 4","pp. 889-896",2008,
"TAKESHI MATSUDA,SUMIO WATANABE","Weighted Blowups of Kullback Information and Application to Multinomial Distributions","Proceedings of International Symposium on Nonlinear Theory and Its Applications",,,,,,2008,
"Yu Nishiyama,SUMIO WATANABE","Generalization of Concave and Convex Decomposition in Kikuchi Free Energy","International Conference on Aritificial Neural Networks",,,,,,2008,
"SUMIO WATANABE","A foumula of equations of states in singular learning machines","IEEE World Congress in Computational Intelligence",,,,,,2008,
"SUMIO WATANABE","What we can estimate about singularity from random samples","Seasonal Institute of the mathematical society of Japan",,,,,,2008,
"SUMIO WATANABE","Algebraic geometrical method in singular statistical estimation",,"Quantum Bio-Informatics","World Scientific (Singapole)",,,"pp. 325-336",2008,
"Keisuke Yamazaki,Sumio Watanabe","Experimental Bayesian Generalization Error of Non-Regular Models under  Covariate Shift","International Conference on Neural Information Processing","Proc. of ICONIP 2007",,,,,2007,Nov.
"KAZUHO WATANABE,SUMIO WATANABE","Stochastic complexities of general mixture models in variational Bayesian learning",,"Neural Networks",,"Vol. 20","No. 2","pp. 210-217",2007,Mar.
"Keisuke Yamazaki,SUMIO WATANABE,Masashi Sugiyama","Asymptotic Bayesian Generalization Error When Training and Test Distributions Are Different",,"Proc. of ICML",,,,,2007,
"Kenji Nagata,SUMIO WATANABE","Analysis of Exchange Ratio for Exchange Monte Carlo Method",,"Proc. of FOCI2007",,,,,2007,
"SUMIO WATANABE","物理学者でない人にとって平衡統計力学とは",,"日本神経回路学会誌",,"Vol. 14","No. 3","pp. 218-225",2007,
"miki aoyagi,SUMIO WATANABE","Resolution of Singularities and Stochastic Complexity of Complete Bipartite Graph-Type Spin Model in Bayesian Estimation",,"Proc. of MDAI",,,,"pp. 443-454",2007,
"Ryosuke Iriguchi,SUMIO WATANABE","Estimation of Poles of Zeta Function in Learning Theory Using Pade Approximation",,"Proc.of  ICANN",,,,"pp. 88-97",2007,
"Kenji Nagata,SUMIO WATANABE","Algebraic Geometric Study of Exchange Monte Carlo Method",,"Proc. of ICANN",,,,"pp. 687-696",2007,
"YU NISHIYAMA,SUMIO WATANABE","Theoretical Analysis of Accuracy of Gaussian Belief Propagation",,"Proc. of ICANN",,,,"pp. 29-38",2007,
"TAKESHI MATSUDA,SUMIO WATANABE","On a Singular Point to Contribute to a Learning Coefficient and Weighted Resolution of Singularities",,"Proc. of ICANN",,,,"pp. 11-18",2007,
"SHINICHI NAKAJIMA,SUMIO WATANABE","Generalization Error of Automatic Relevance Determination",,"Proc. of ICANN",,,,"pp. 1-10",2007,
"SUMIO WATANABE","Almost All Learning Machines are Singular","IEEE International Conference on Foundation of Computational Intelligence","Proc. of FOCI",,,,"pp. 383-388",2007,
"SHINICHI NAKAJIMA,SUMIO WATANABE","Variational Bayes Solution of Linear Neural Networks and its Generalization Performance",,"Neural Computation",,"Vol. 19","No. 4","pp. 1112-1153",2007,
"KAZUHO WATANABE,SUMIO WATANABE","Estimating the Data Region Using Minimum and Maximum Values",,"Interdisciplinary Information Sciences",,"Vol. 13","No. 2","pp. 151-161",2007,
"SUMIO WATANABE,KAZUHO WATANABE","Stochastic complexity for mixture of exponential families in generalized variational Bayes",,"Theoretical Computer Science",,"Vol. 387",,"pp. 4-17",2007,
"Keisuke Yamazaki,Motoaki Kawanabe,Sumio Watanabe,Masashi Sugiyama,Klaus-Robert Mueller","Asymptotic Bayesian generalization error when training and test distributions are different","24th International Conference on Machine Learning (ICML2007)","Proceedings of 24th International Conference on Machine Learning (ICML2007)",,,,"pp. 1079-1086",2007,
"Yu  Nishiyama,SUMIO WATANABE","Asymptotic Behavior of Stochastic Complexity of Complete Bipartite Graph-Type Boltzmann Machines",,"Proc. of ICONIP",,"Vol. 1",,"pp. 417-426",2006,Dec.
"Miki  Aoyagi,SUMIO WATANABE","Generalization Error of Three Layered Learning Model in Bayesian Estimation",,"Proc. of the 2nd IASTED International Conference on Computational Intelligence",,,,"pp. 405-410",2006,Dec.
"KAZUHO WATANABE,SUMIO WATANABE","Variational bayesian stochastic complexity of mixture models","Advances in Neural Information Processing Systems","Proc. of Advances in Neural Information Processing Systems","The MIT Press","Vol. 18",,"pp. 1465-1472",2006,Dec.
"KAZUHO WATANABE,Motoki  Shiga,SUMIO WATANABE","Upper bounds for variational stochastic complexities of Bayesian networks","International Conference on Intelligent Data Engineering and Automated Learning","Proc. of International Conference on Intelligent Data Engineering and Automated Learning",,,,"pp. 139-146",2006,Dec.
"Tikara  Hosino,KAZUHO WATANABE,SUMIO WATANABE","Free Energy of Stochastic Context Free Grammar on Variational Bayes",,"Proc. of  ICONIP",,"Vol. 1",,"pp. 407-416",2006,Dec.
"高松 慎吾,SHINICHI NAKAJIMA,SUMIO WATANABE","局所化ベイズ学習法",,"電子情報通信学会論文誌",,"Vol. J89-D-II","No. 10","pp. 2260-2268",2006,Dec.
"Shingo Takamatsu,SHINICHI NAKAJIMA,SUMIO WATANABE","Localized Bayes Estimation for Non-identifiable Models",,"Proc. of International Conference on Neural Information Processing",,,,"pp. 650-659",2006,Oct.
"YU NISHIYAMA,SUMIO WATANABE","Asymptotic Behavior of Stochastic Complexity of Complete Bipartite Graph-type Boltzmann Machines","ICONIP","LNCS 4232","Springer",,,"pp. 671-678",2006,Oct.
"Keisuke Yamazaki,Kenji  Nagata,SUMIO WATANABE,Klaus-Robert  Mueller","A Model Selection Method Based on Bound of Learning Coefficient",,"Proc. of International Conference on Artificial Neural Networks",,,,"pp. 371-380",2006,Sept.
"Kenji  Nagata,SUMIO WATANABE","Generalization Performance of Exchange Monte Carlo Method for Normal Mixture Models",,"Proc. of 7th International Conference on Intelligent Data Engineering and Automated Learning",,,,"pp. 125-132",2006,Sept.
"SHINICHI NAKAJIMA,SUMIO WATANABE","Analytic Solution of Hierarchical Variational Bayes in Linear Inverse Problem",,"Proc. of International Conference on Artificial Neural Networks",,,,"pp. 240-249",2006,Sept.
"西山 悠,渡辺澄夫","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",,"電子情報通信学会論文誌",,"Vol. J89-A","No. 8","pp. 671-678",2006,Aug.
"Kenji  Nagata,SUMIO WATANABE","The Exchange Monte Carlo Method for Bayesian Learning in Singular Learning Machines",,"Proc. of IEEE World Congress on Computational Intelligence",,,,"pp. 6383-6389",2006,July
"YU NISHIYAMA,SUMIO WATANABE","Asymptotic Behavior of Free Energy of General Boltzmann Machines in Mean Field Approximation","Neurocomputing Technical Group","IEICE Technical Report","IEICE","Vol. 106","No. 163","pp. 1-6",2006,July
"星野力,渡辺一帆,渡辺澄夫","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",,"電子情報通信学会論文誌",,"Vol. J89-D","No. 6","pp. 1279-1287",2006,June
"SUMIO WATANABE","代数幾何と学習理論の関係について","情報幾何への入門と応用ミニスクール",,,,,,2006,June
"YU NISHIYAMA,SUMIO WATANABE","Stochastic Complexity of Complete Bipartite Graph-type Boltzmann Machines","Neurocomputing Technical Group","IEICE Technical Report","IEICE","Vol. 105","No. 659","pp. 125-130",2006,Mar.
"KAZUHO WATANABE,SUMIO WATANABE","Stochastic complexities of gaussian mixtures in variational bayesian approximation",,"Journal of Machine Learning Research",,"Vol. 7",,"pp. 625-644",2006,Feb.
"SUMIO WATANABE","代数幾何と学習理論",,,"森北出版",,,,2006,Feb.
"SHINICHI NAKAJIMA,SUMIO WATANABE","Generalization Performance of Subspace Bayes Approach in Linear Neural Networks",,"IEICE Transactions",,"Vol. E89-D","No. 3","pp. 1128-1138",2006,Feb.
"KAZUHO WATANABE,SUMIO WATANABE","Variational Bayesian Stochastic Complexity of Mixture Models",,"Proc. of Advances in Neural Information Processing Systems",,,,,2006,
"中野修弘　高橋克之　渡辺澄夫","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",,"電子情報通信学会誌",,"Vol. 88-D-II","No. 10","pp. 2011-2020",2005,Oct.
"青柳美輝　渡辺澄夫","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",,"電子情報通信学会誌",,"Vol. 88-D-II","No. 10","pp. 2112-2124",2005,Oct.
"Sumio Watanabe Katuyuki Hagiwara Shotaro Akaho Yoichi Motomura Kenji Fukumizu Masato Okada Miki Aoyagi","Theory and Practice of Learning System",,,"森北出版",,,,2005,May
"渡辺澄夫　村田昇","Probability and Statistics - a bridge to information science -",,,"コロナ社",,,,2005,Mar.
"SHINICHI NAKAJIMA,SUMIO WATANABE","Generalization Error of Linear Neural Networks in an Empirical Bayes Approach",,"Proc. of IJCAI2005",,,,,2005,
"Keisuke Yamazaki,Kenji Nagata,SUMIO WATANABE","A New Method of Model Selection Based on Learning Coefficient",,"Proc. of International Symposium on Nonlinear Theory and its Applications",,,,,2005,
"Miki Aoyagi Sumio Watanabe","Stochastic complexities of reduced rank regression in Bayesian estimation",,"International Journal of Neural Networks",,"Vol. 18","No. 7","pp. 924-933",2005,
"SHINICHI NAKAJIMA,SUMIO WATANABE","Generalization Error and Free Energy of Linear Neural Networks in Variational Bayes Approach",,"Proc. of ICONIP2005",,,,,2005,
"KAZUHO WATANABE,SUMIO WATANABE","Stochastic complexity for mixture of exponential families in variational bayes",,"Proc. of ALT2005",,,,,2005,
"Keisuke Yamazaki Sumio Watanabe","Algebraic geometry and stochastic complexity of hidden Markov models",,"Neurocomputing",,"Vol. 69",,"pp. 62-84",2005,
"miki aoyagi,SUMIO WATANABE","The zeta function for learning theory and resolution of singularities",,"Proc. of ISAAC",,,,,2005,
"TIKARA HOSHINO,KAZUHO WATANABE,SUMIO WATANABE","Stochastic Complexity of Variational Bayesian Hidden Markov Models",,"Proc. of IJCNN",,,,,2005,
"渡邊澄夫 福水健次 萩原克幸 甘利俊一","Mathematica Theory of Sigular Learning Machines",,"電子情報通信学会誌",,"Vol. 88","No. 2","pp. 159-169",2005,
"Sumio Watanabe","Algebraic geometry of singular learning machines and  symmetry of generalization and training errors",,"Neurocomputing",,"Vol. 67",,"pp. 198-213",2005,
"Keisuke Yamazaki Sumio Watanabe","Singularities in complete bipartite graph-type Boltzmann machines and upper bounds of stochastic complexities",,"IEEE Transactions on Neural Networks",,"Vol. 16","No. 2","pp. 312-324",2005,
"Keisuke Yamazaki,SUMIO WATANABE","Generalization Errors in Estimation of Stochastic Context-Free Grammar",,"The IASTED International Conference on Artificial Intelligence and Soft Computing",,,,"pp. 183-188",2005,
"KAZUHO WATANABE,SUMIO WATANABE","On Variational Bayes Algorithms for Exponential Family Mixtures",,"Proc. of International Symposium on Nonlinear Theory and its Applications",,,,,2005,
"Kazuho Watanabe Sumio Watanabe","Learning method of the data region based on extreme-value theory",,"Proceedings of International Symposium on Information Theory and its Applications",,,,"pp. CD-ROM",2004,
"Kazuho Watanabe Sumio Watanabe","Lower bounds of stochastic complexities in variational bayes learning of gaussian mixture models",,"Proceedings of IEEE International Conference on Cybernetics and Intelligent Systems",,,,"pp. 99-104",2004,
"Kazuho Watanabe Sumio Watanabe","Estimation of the Data region using Extreme-value distributions",,"Lecture Notes in Computer Science","Lecture Notes in Computer Science",,,"pp. 206-220",2004,
"SUMIO WATANABE","数学と統計科学",,"統計科学のフロンティア　岩波書店","統計科学のフロンティア　岩波書店","Vol. ３",,,2004,
"SUMIO WATANABE","学習理論と数学的自然",,"数学のたのしみ　日本評論社","数学のたのしみ　日本評論社",,,"pp. 100-112",2004,
"Miki Aoyagi Sumio Watanabe","The generalization error of reduced rank regression in Bayesian estimation",,"International Symposium on Information Theory and its Applications",,,,"pp. CD-ROM",2004,
"SUMIO WATANABE","人工知能と特異な学習モデル",,"人工知能学会誌",,"Vol. １９","No. 6","pp. 637-641",2004,
"Shin-ichi Nakajima Sumio Watanabe","Simulation Data Generation from Extended EGA Model and Optimization of Alignment Strategy for Lithography",,"Proceedings of International Symposium on Information Theory and its Applications,",,,,"pp. CD-ROM",2004,
"Keisuke Yamazaki Sumio Watanabe","Stochastic Complexity and Newton Diagram",,"International Symposium on Information Theory and its Applications",,,,"pp. CD-ROM",2004,
"Keisuke Yamazaki Sumio Watanabe","Stochastic complexities of hidden Markov models",,"Proceedings of IEEE Neural Networks and Signal Processing",,"Vol. CD-ROM",,,2003,
"SUMIO WATANABE","特異モデルとベイズ学習",,"日本神経回路学会誌",,"Vol. 10","No. 4","pp. 211-219",2003,
"Keisuke Yamazaki Sumio Watanabe","Stochastic complexity of Bayesian networks",,"Proceedings of Uncertainty in Artificial Intelligence",,"Vol. CD-ROM",,,2003,
"渡辺一帆　渡辺澄夫","縮小ランク回帰モデルのベイズ汎化誤差について",,"電子情報通信学会誌",,"Vol. J86-A","No. 3","pp. 278",2003,
"西上功一郎　渡辺澄夫","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",,"電子情報通信学会誌",,"Vol. J86-D-2","No. 1","pp. 119",2003,
"Sumio Watanabe Shun-ichi Amari","Learning coefficients of layered models when the true distribution mismatches the singularities",,"Neural Computation",,"Vol. 15","No. 5","pp. 1013",2003,
"Sumio Watanabe,Shunichi Amari","Singularities in neural networks make Bayes generalization erros smaller even if they do not contain the true",,"Proceedings of International Conference on Neural Information Processing",,"Vol. 9",,,2002,
"Keisuke Yamazaki,Sumio Watanabe","Resolution of Singularities in Mixture Models and its Stochastic Complexity",,"Proceedings of International Conference on Neural Information Processing",,"Vol. 9",,,2002,
"Sumio Watanabe,Shunichi Amari","The effect of singularities when the true parameters do not lie on such singularities",,"Advances in Neural Information Processing Systems",,"Vol. 15","No. 1",,2002,
"渡辺澄夫","脳情報数理科学の発展",,"サイエンス社","サイエンス社","Vol. Chap.3",,,2002,
"SUMIO WATANABE","Algebraic Analysis for nonidentifiable learning machines",,"Neural Computation",,"Vol. 13","No. 4","pp. 899-933",2001,Apr.
"SUMIO WATANABE","特異点を持つ学習モデルと事前分布の代数幾何",,"人工知能学会誌",,"Vol. 16","No. 2","pp. 308-315",2001,
"SUMIO WATANABE","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",,"電子情報通信学会誌(A)",,"Vol. 84","No. 1","pp. 99-108",2001,
"SUMIO WATANABE","Algebraic geometrical methods for hierarchical learning machines",,"Neural Networks",,"Vol. 14","No. 8","pp. 1049-1060",2001,
"SUMIO WATANABE","Algebraic information geometry for learning machines with singularities",,"Advances in neural information processing systems",,"Vol. 13","No. 1","pp. 329-336",2001,
"SUMIO WATANABE","Learning efficiency of redundant neural networks in Bayesian estimation",,"IEEE Transactions on Neural Networks",,"Vol. 12","No. 6","pp. 1475-1486",2001,
"SUMIO WATANABE","データ学習アルゴリズム",,"共立出版","共立出版",,,,2001,
"SUMIO WATANABE","Algebraic Analysis for Non-regular Learning Machines",,"Advances in Neural Information Processing Systems",,"Vol. 12",,"pp. 356-362",2000,
"SUMIO WATANABE","Mathematical foundation for Redundant Statistical Estimation",,"Proceedings of Stochastic Systems Symposium",,"Vol. 32",,,1999,
"SUMIO WATANABE","Algebraic Analysis for Singular Statistical Estimation",,"Algorithmic Learning Theory, Lecture Notes in Computer Science.",,"Vol. 10",,,1999,
"Sumio Watanabe Kenji Fukumizu","Algorithms and Architectures.",,"Academic Press","Academic Press","Vol. 1",,,1998,
"SUMIO WATANABE","ベイズ法による階層型統計モデルの推定誤差について",,"電子情報通信学会誌",,"Vol. J81-A",,"pp. 1442-1452",1998,
"SUMIO WATANABE","有限ウェーブレット展開の一手法",,"電子情報通信学会誌",,"Vol. J79-A",,"pp. 1948-1956",1996,
"S.Ishii,K.Fukumizu,S.Watanabe","A Network of Chaotic Elements for Information Processing.",,"Neural Networks",,"Vol. 9",,"pp. 25-40",1996,
"SUMIO WATANABE","Solvable models of layered neural networks based on their differential structure.",,"Advances in Computational Mathematics",,"Vol. 5","No. 1","pp. 205-231",1996,
"SUMIO WATANABE","Neural Networks for Robotic Control-Theory and Applications.",,"Ellis Horwood","Ellis Horwood",,,,1996,
"福水健次　渡辺澄夫","多項式近似における学習データの最適設計と予測誤差",,"電子情報通信学会誌",,"Vol. J79-A",,"pp. 1100-1108",1996,
"Sumio Watanabe Kenji Fukumizu","Probabilistic design of layered neural networks based on their unified framework.",,"IEEE Transactions on Neural Networks",,"Vol. 6","No. 3","pp. 691-702",1995,
"SUMIO WATANABE","A modified information criterion for automatic model and parameter selection in neural network learning.",,"IEICE Transactions",,"Vol. E78-D",,"pp. 490-499",1995,
"K Takatsu,H. Sawai,S. Watanabe,M.Yoneyama","遺伝的アルゴリズムによる画像のベイズ復元",,"電子情報通信学会誌",,"Vol. 77-D-2",,"pp. 1768-1777",1994,
"SUMIO WATANABE","神経回路網援用超音波影像法による３次元物体認識",,,,,,,1993,
"SUMIO WATANABE","An Ultrasonic 3-D visual Sensor Using Neural Networks.",,"IEEE Transactions on Robotics and Automation",,"Vol. 6","No. 2","pp. 240-249",1992,Feb.
"SUMIO WATANABE","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",,"日本音響学会誌",,"Vol. 48",,"pp. 720-726",1992,
"SUMIO WATANABE","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",,"日本音響学会誌",,"Vol. 48",,"pp. 711-719",1992,
"SUMIO WATANABE","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",,"日本音響学会誌",,"Vol. 47",,"pp. 825-833",1991,
"SUMIO WATANABE","Ultrasonic Robot Eyes Using Neural Networks.",,"IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control",,"Vol. 37",,"pp. 141-127",1990,
"SUMIO WATANABE","Spectral analysis for multipole ghost",,,,,,,1984,