An ultrasonic visual sensor for three-dimensional object recognition using neural networks. - Sumio Watanabe; Masahide Yoneyama (IEEE Trans. Robotics Autom., 1992)

An Optimization Method of Layered Neural Networks based on the Modified Information Criterion. - Sumio Watanabe (NIPS, 1993)

Solvable Models of Artificial Neural Networks. - Sumio Watanabe (NIPS, 1993)

A Modified Information Criterion for Automatic Model and Parameter Selection in Neural Network Learning. - Sumio Watanabe (IEICE Trans. Inf. Syst., 1995)

Genetic algorithms applied to bayesian image restoration. - Kazunori Takatsu; Hidefumi Sawai; Sumio Watanabe; Masahide Yoneyama (Syst. Comput. Jpn., 1995)

Probabilistic design of layered neural networks based on their unified framework. - Sumio Watanabe; Kenji Fukumizu (IEEE Trans. Neural Networks, 1995)

Solvable models of layered neural networks based on their differential structure. - Sumio Watanabe (Adv. Comput. Math., 1996)

A network of chaotic elements for information processing. - Shin Ishii; Kenji Fukumizu; Sumio Watanabe (Neural Networks, 1996)

Probabilistic design. - Sumio Watanabe; Kenji Fukumizu (Algorithms and Architectures, 1998)

Inequalities of Generalization Errors for Layered Neural Networks in Bayesian Learning. - Sumio Watanabe (ICONIP, 1998)

Algebraic Analysis for Singular Statistical Estimation. - Sumio Watanabe (ALT, 1999)

Algebraic Analysis for Non-regular Learning Machines. - Sumio Watanabe (NIPS, 1999)

Algebraic Information Geometry for Learning Machines with Singularities. - Sumio Watanabe (NIPS, 2000)

Algebraic Analysis for Nonidentifiable Learning Machines. - Sumio Watanabe (Neural Comput., 2001)

Algebraic geometrical methods for hierarchical learning machines. - Sumio Watanabe (Neural Networks, 2001)

Learning efficiency of redundant neural networks in Bayesian estimation. - Sumio Watanabe (IEEE Trans. Neural Networks, 2001)

The Effect of Singularities in a Learning Machine when the True Parameters Do Not Lie on such Singularities. - Sumio Watanabe; Shun-ichi Amari (NIPS, 2002)

Errata to "learning efficiency of redundant neural networks in bayesian estimation". - Sumio Watanabe (IEEE Trans. Neural Networks, 2002)

Stochastic complexities of hidden Markov models. - Keisuke Yamazaki; Sumio Watanabe (NNSP, 2003)

Stochastic Complexity of Bayesian Networks. - Keisuke Yamazaki; Sumio Watanabe (UAI, 2003)

Learning Coefficients of Layered Models When the True Distribution Mismatches the Singularities. - Sumio Watanabe; Shun-ichi Amari (Neural Comput., 2003)

Singularities in mixture models and upper bounds of stochastic complexity. - Keisuke Yamazaki; Sumio Watanabe (Neural Networks, 2003)

Estimation of the Data Region Using Extreme-Value Distributions. - Kazuho Watanabe; Sumio Watanabe (ALT, 2004)

Newton Diagram and Stochastic Complexity in Mixture of Binomial Distributions. - Keisuke Yamazaki; Sumio Watanabe (ALT, 2004)

Stochastic Complexity for Mixture of Exponential Families in Variational Bayes. - Kazuho Watanabe; Sumio Watanabe (ALT, 2005)

Generalization Error of Linear Neural Networks in an Empirical Bayes Approach. - Shinichi Nakajima; Sumio Watanabe (IJCAI, 2005)

Stochastic complexity of variational Bayesian hidden Markov models. - Tikara Hosino; Kazuho Watanabe; Sumio Watanabe (IJCNN, 2005)

Variational Bayesian Stochastic Complexity of Mixture Models. - Kazuho Watanabe; Sumio Watanabe (NIPS, 2005)

Algebraic geometry of singular learning machines and symmetry of generalization and training errors. - Sumio Watanabe (Neurocomputing, 2005)

Algebraic geometry and stochastic complexity of hidden Markov models. - Keisuke Yamazaki; Sumio Watanabe (Neurocomputing, 2005)

Stochastic complexities of reduced rank regression in Bayesian estimation. - Miki Aoyagi; Sumio Watanabe (Neural Networks, 2005)

Singularities in complete bipartite graph-type Boltzmann machines and upper bounds of stochastic complexities. - Keisuke Yamazaki; Sumio Watanabe (IEEE Trans. Neural Networks, 2005)

Generalization error of three layered learning model in bayesian estimation. - Miki Aoyagi; Sumio Watanabe (Computational Intelligence, 2006)

Analytic Equivalence of Bayes a Posteriori Distributions. - Takeshi Matsuda; Sumio Watanabe (ICANN (1), 2006)

Analytic Solution of Hierarchical Variational Bayes in Linear Inverse Problem. - Shinichi Nakajima; Sumio Watanabe (ICANN (2), 2006)

A Model Selection Method Based on Bound of Learning Coefficient. - Keisuke Yamazaki; Kenji Nagata; Sumio Watanabe; Klaus-Robert Müller (ICANN (2), 2006)

Free Energy of Stochastic Context Free Grammar on Variational Bayes. - Tikara Hosino; Kazuho Watanabe; Sumio Watanabe (ICONIP (1), 2006)

Asymptotic Behavior of Stochastic Complexity of Complete Bipartite Graph-Type Boltzmann Machines. - Yu Nishiyama; Sumio Watanabe (ICONIP (1), 2006)

Localized Bayes Estimation for Non-identifiable Models. - Shingo Takamatsu; Shinichi Nakajima; Sumio Watanabe (ICONIP (1), 2006)

Generalization Performance of Exchange Monte Carlo Method for Normal Mixture Models. - Kenji Nagata; Sumio Watanabe (IDEAL, 2006)

Upper Bounds for Variational Stochastic Complexities of Bayesian Networks. - Kazuho Watanabe; Motoki Shiga; Sumio Watanabe (IDEAL, 2006)

The Exchange Monte Carlo Method for Bayesian Learning in Singular Learning Machines. - Kenji Nagata; Sumio Watanabe (IJCNN, 2006)

Generalization Performance of Subspace Bayes Approach in Linear Neural Networks. - Shinichi Nakajima; Sumio Watanabe (IEICE Trans. Inf. Syst., 2006)

Stochastic Complexities of Gaussian Mixtures in Variational Bayesian Approximation. - Kazuho Watanabe; Sumio Watanabe (J. Mach. Learn. Res., 2006)

Analysis of Exchange Ratio for Exchange Monte Carlo Method. - Kenji Nagata; Sumio Watanabe (FOCI, 2007)

Almost All Learning Machines are Singular. - Sumio Watanabe (FOCI, 2007)

Estimation of Poles of Zeta Function in Learning Theory Using Padé Approximation. - Ryosuke Iriguchi; Sumio Watanabe (ICANN (1), 2007)

On a Singular Point to Contribute to a Learning Coefficient and Weighted Resolution of Singularities. - Takeshi Matsuda; Sumio Watanabe (ICANN (1), 2007)

Algebraic Geometric Study of Exchange Monte Carlo Method. - Kenji Nagata; Sumio Watanabe (ICANN (1), 2007)

Generalization Error of Automatic Relevance Determination. - Shinichi Nakajima; Sumio Watanabe (ICANN (1), 2007)

Theoretical Analysis of Accuracy of Gaussian Belief Propagation. - Yu Nishiyama; Sumio Watanabe (ICANN (1), 2007)

Asymptotic Bayesian generalization error when training and test distributions are different. - Keisuke Yamazaki; Motoaki Kawanabe; Sumio Watanabe; Masashi Sugiyama; Klaus-Robert Müller (ICML, 2007)

Experimental Analysis of Exchange Ratio in Exchange Monte Carlo Method. - Kenji Nagata; Sumio Watanabe (ICONIP (2), 2007)

Experimental Bayesian Generalization Error of Non-regular Models under Covariate Shift. - Keisuke Yamazaki; Sumio Watanabe (ICONIP (1), 2007)

Resolution of Singularities and Stochastic Complexity of Complete Bipartite Graph-Type Spin Model in Bayesian Estimation. - Miki Aoyagi; Sumio Watanabe (MDAI, 2007)

The Calculation Method of Learning Coefficients by Weighted Resolution of Singularities. - Takeshi Matsuda; Sumio Watanabe (MLMTA, 2007)

Variational Bayes Solution of Linear Neural Networks and Its Generalization Performance. - Shinichi Nakajima; Sumio Watanabe (Neural Comput., 2007)

Stochastic complexities of general mixture models in variational Bayesian learning. - Kazuho Watanabe; Sumio Watanabe (Neural Networks, 2007)

Stochastic complexity for mixture of exponential families in generalized variational Bayes. - Kazuho Watanabe; Sumio Watanabe (Theor. Comput. Sci., 2007)

On the Minima of Bethe Free Energy in Gaussian Distributions. - Yu Nishiyama; Sumio Watanabe (ICAISC, 2008)

Generalization of Concave and Convex Decomposition in Kikuchi Free Energy. - Yu Nishiyama; Sumio Watanabe (ICANN (1), 2008)

Model Selection Method for AdaBoost Using Formal Information Criteria. - Daisuke Kaji; Sumio Watanabe (ICONIP (2), 2008)

Experimental Study of Ergodic Learning Curve in Hidden Markov Models. - Masashi Matsumoto; Sumio Watanabe (ICONIP (1), 2008)

Design of Exchange Monte Carlo Method for Bayesian Learning in Normal Mixture Models. - Kenji Nagata; Sumio Watanabe (ICONIP (1), 2008)

A formula of equations of states in singular learning machines. - Sumio Watanabe (IJCNN, 2008)

Asymptotic behavior of exchange ratio in exchange Monte Carlo method. - Kenji Nagata; Sumio Watanabe (Neural Networks, 2008)

Exchange Monte Carlo Sampling From Bayesian Posterior for Singular Learning Machines. - Kenji Nagata; Sumio Watanabe (IEEE Trans. Neural Networks, 2008)

Optimal Hyperparameters for Generalized Learning and Knowledge Discovery in Variational Bayes. - Daisuke Kaji; Sumio Watanabe (ICONIP (1), 2009)

A Limit Theorem in Singular Regression Problem - Sumio Watanabe (CoRR, 2009)

Equations of States in Statistical Learning for a Nonparametrizable and Regular Case - Sumio Watanabe (CoRR, 2009)

Upper bound for variational free energy of Bayesian networks. - Kazuho Watanabe; Motoki Shiga; Sumio Watanabe (Mach. Learn., 2009)

Accuracy of Loopy belief propagation in Gaussian models. - Yu Nishiyama; Sumio Watanabe (Neural Networks, 2009)

On Generalization Error of Self-Organizing Map. - Fumiaki Saitoh; Sumio Watanabe (ICONIP (2), 2010)

Phase Transition of Variational Bayes Learning in Bernoulli Mixture. - Daisuke Kaji; Kazuho Watanabe; Sumio Watanabe (Aust. J. Intell. Inf. Process. Syst., 2010)

Asymptotic Learning Curve and Renormalizable Condition in Statistical Learning Theory - Sumio Watanabe (CoRR, 2010)

Equations of States in Statistical Learning for an Unrealizable and Regular Case. - Sumio Watanabe (IEICE Trans. Fundam. Electron. Commun. Comput. Sci., 2010)

Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory. - Sumio Watanabe (J. Mach. Learn. Res., 2010)

Equations of states in singular statistical estimation. - Sumio Watanabe (Neural Networks, 2010)

Asymptotic analysis of Bayesian generalization error with Newton diagram. - Keisuke Yamazaki; Miki Aoyagi; Sumio Watanabe (Neural Networks, 2010)

Two design methods of hyperparameters in variational Bayes learning for Bernoulli mixtures. - Daisuke Kaji; Sumio Watanabe (Neurocomputing, 2011)

Information criterion for variational Bayes learning in regular and singular cases. - Koshi Yamada; Sumio Watanabe (SCIS&ISIS, 2012)

Statistical Learning Theory of Quasi-Regular Cases. - Koshi Yamada; Sumio Watanabe (IEICE Trans. Fundam. Electron. Commun. Comput. Sci., 2012)

A Geometric Evaluation of Self-Organizing Map and Application to City Data Analysis. - Shigehiro Ohara; Keisuke Yamazaki; Sumio Watanabe (MIWAI, 2013)

A widely applicable Bayesian information criterion. - Sumio Watanabe (J. Mach. Learn. Res., 2013)

Bayesian Cross Validation and WAIC for Predictive Prior Design in Regular Asymptotic Theory. - Sumio Watanabe (CoRR, 2015)

Interpretation Method of Nonlinear Multilayer Principal Component Analysis by Using Sparsity and Hierarchical Clustering. - Natsuki Koda; Sumio Watanabe (ICMLA, 2016)

Phase Transition Structure of Variational Bayesian Nonnegative Matrix Factorization. - Masahiro Kohjima; Sumio Watanabe (ICANN (2), 2017)

Tighter upper bound of real log canonical threshold of non-negative matrix factorization and its application to Bayesian inference. - Naoki Hayashi; Sumio Watanabe (SSCI, 2017)

Upper Bound of Bayesian Generalization Error in Stochastic Matrix Factorization. - Naoki Hayashi; Sumio Watanabe (CoRR, 2017)

Upper bound of Bayesian generalization error in non-negative matrix factorization. - Naoki Hayashi; Sumio Watanabe (Neurocomputing, 2017)

Testing Homogeneity for Normal Mixture Models: Variational Bayes Approach. - Natsuki Kariya; Sumio Watanabe (IEICE Trans. Fundam. Electron. Commun. Comput. Sci., 2020)

Asymptotic Bayesian Generalization Error in Latent Dirichlet Allocation and Stochastic Matrix Factorization. - Naoki Hayashi; Sumio Watanabe (SN Comput. Sci., 2020)

Asymptotic Behavior of Bayesian Generalization Error in Multinomial Mixtures. - Takumi Watanabe; Sumio Watanabe (CoRR, 2022)

Mathematical Theory of Bayesian Statistics for Unknown Information Source. - Sumio Watanabe (CoRR, 2022)

Recent Advances in Algebraic Geometry and Bayesian Statistics. - Sumio Watanabe (CoRR, 2022)

Asymptotic behavior of free energy when optimal probability distribution is not unique. - Shuya Nagayasu; Sumio Watanabe (Neurocomputing, 2022)

Free Energy of Bayesian Convolutional Neural Network with Skip Connection. - Shuya Nagayasu; Sumio Watanabe (ACML, 2023)

Upper Bound of Real Log Canonical Threshold of Tensor Decomposition and its Application to Bayesian Inference. - Naoki Yoshida; Sumio Watanabe (CoRR, 2023)

Bayesian Free Energy of Deep ReLU Neural Network in Overparametrized Cases. - Shuya Nagayasu; Sumio Watanabe (CoRR, 2023)

Review and Prospect of Algebraic Research in Equivalent Framework between Statistical Mechanics and Machine Learning Theory. - Sumio Watanabe (CoRR, 2024)