Sumio Watanabe

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Mathematical Theory of Bayesian Statistics

Sumio Watanabe, 2018 .

Probabilistic design of layered neural networks based on their unified framework

Kenji Fukumizu, Sumio Watanabe, K. Fukumizu, 1995, IEEE Trans. Neural Networks.

Algebraic Geometry and Statistical Learning Theory

Sumio Watanabe, 2009 .

Algebraic Analysis for Non-identifiable Learning Machines

Sumio Watanabe, 2000 .

A network of chaotic elements for information processing

Shin Ishii, Kenji Fukumizu, Sumio Watanabe, 1996, Neural Networks.

Associative memory using spatiotemporal chaos

Kenji Fukumizu, Shin Ishii, Sumio Watanabe, 1993, Proceedings of 1993 International Conference on Neural Networks (IJCNN-93-Nagoya, Japan).

Kullback Information of Normal Mixture is not an Analytic Function

Keisuke Yamazaki, Miki Aoyagi, Sumio Watanabe, 2004 .

Resolution of Singularities and the Generalization Error with Bayesian Estimation for Layered Neural Network

Miki Aoyagi, Sumio Watanabe, Sumio Watanabe, 2005 .

Asymptotic Bayesian Generalization Error in Topic Model and Stochastic Matrix Factorization

Sumio Watanabe, Naoki Hayashi, 2017 .

WAIC AND WBIC ARE INFORMATION CRITERIA FOR SINGULAR STATISTICAL MODEL EVALUATION

Sumio Watanabe, Sumio Watanabe, 2013 .

1 Algebraic Geometrical Methods for Hierarchical Learning Machines

Sumio Watanabe, 2001 .

Asymptotic Behavior of Free Energy When Optimal Probability Distribution Is Not Unique.

Sumio Watanabe, Shuya Nagayasu, 2020, 2012.08338.

Probability density estimation by regularization method

Kenji Fukumizu, Sumio Watanabe, K. Fukumizu, 1993, Proceedings of 1993 International Conference on Neural Networks (IJCNN-93-Nagoya, Japan).

Information Matrix of a Mlp Network Information Matrix of a Mlp Network

Sumio Watanabe, 2007 .

S. Geer, Eva Riccomagno, P. Gibilisco, 2011 .

Estimating the Data Region Using Minimum and Maximum Values

Kazuho Watanabe, Sumio Watanabe, 2007 .

Upper Bound of Bayesian Generalization Error in Stochastic Matrix Factorization pdf

Naoki Hayashi, Sumio Watanabe, Sumio Watanabe, 2017, ArXiv.

Probabilistic design

Kenji Fukumizu, Sumio Watanabe, K. Fukumizu, 2020, Algorithms and Architectures.

Singularities in neural networks make Bayes generalization errors smaller even if they do not contain the true

S. Amari, Sumio Watanabe, S. Watanabe, 2002, Proceedings of the 9th International Conference on Neural Information Processing, 2002. ICONIP '02..

Bayes and Gibbs Estimations , Empirical Processes , and Resolution of Singularities

Sumio Watanabe, 2007 .

Higher Order Equivalence of Bayes Cross Validation and WAIC

Sumio Watanabe, 2016 .

Mathematical Theory of Bayesian Statistics for Unknown Information Source

Sumio Watanabe, 2022, ArXiv.

Mathematical Theory of Bayesian Statistics for Unknown Information Source

Sumio Watanabe, 2022, ArXiv.

Generalization Error of an Empirical Bayes Approach

Sumio Watanabe, 2004 .

O ct 2 01 7 Upper Bound of Bayesian Generalization Error in Non-Negative Matrix Factorization

Sumio Watanabe, Naoki Hayashi, 2018 .

Mathematical Theory of Bayesian Statistics for Unknown Information Source

Sumio Watanabe, 2022, ArXiv.

Asymptotic analysis of singular likelihood ratio of normal mixture by Bayesian learning theory for testing homogeneity

Sumio Watanabe, Natsuki Kariya, 2020, Communications in Statistics - Theory and Methods.

Mathematical Theory of Bayesian Statistics for Unknown Information Source

Sumio Watanabe, 2022, ArXiv.

Mathematical Theory of Bayesian Statistics for Unknown Information Source

Sumio Watanabe, 2022, ArXiv.

ALGEBRAIC GEOMETRICAL METHOD IN SINGULAR STATISTICAL ESTIMATION

Sumio Watanabe, 2008 .

Stochastic Complexities of Three Layered Learning Model in Bayesian Estimation

Sumio Watanabe, Miki Aoyagi, 2006 .

A CASE OF PRIMARY AMYLOIDOSIS WITH RAPIDLY PROGRESSIVE MULTIPLE ORGAN FAILURE

Sumio Watanabe, Y. Tomino, T. Yao, 2013 .

A Probabilistic Algorithm to Calculate the Learning Curves of Hierarchical Learning Machines with Singularities

Sumio Watanabe, Keisuke Yamazaki, Sumio Watanabe, 2002 .

Extraction of Image Entropy using Independent Component Analysis

Sumio Watanabe, Nobuhiko Ogura, Akira Shirai, 1999 .

Recent advances in algebraic geometry and Bayesian statistics

Sumio Watanabe, 2022, Information Geometry.

Stochastic Complexity and Singularities in Hierarchical Bayesian Networks

Sumio Watanabe, Keisuke Yamazaki, Sumio Watanabe, 2004 .

Algebraic Geometry and Statistical Learning Theory: Contents

Sumio Watanabe, Sumio Watanabe, Sumio Watanabe, 2009 .

A three-dimensional object recognition method using acoustical imasing and neural networks

Masahide Yoneyama, Sumio Watanabe, Sumio Watanabe, 1991 .

Equations of States in Statistical Learning for an Unrealizable and Regular Case

Sumio Watanabe, Sumio Watanabe, 2010, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

Topics in Bayesian Statistics

Sumio Watanabe, Sumio Watanabe, 2018 .

Inequalities of Generalization Errors for Layered Neural Networks in Bayesian Learning

Sumio Watanabe, Sumio Watanabe, 1998, ICONIP.

A Modified Information Criterion for Automatic Model and Parameter Selection in Neural Network Learning

Sumio Watanabe, Sumio Watanabe, 1995, IEICE Trans. Inf. Syst..

Definition of Bayesian Statistics

Sumio Watanabe, Sumio Watanabe, 2018 .

An ultrasonic 3-D robot vision system based on the statistical properties of artificial neural networks

Sumio Watanabe, Sumio Watanabe, 1996 .

An Ultrasonic Image Restoration Method Based on the Information Criteria

Masahide Yoneyama, Sumio Watanabe, Sadayuki Ueha, 1993 .

Mathematical Foundation for Redundant Statistical Estimation

Sumio Watanabe, Sumio Watanabe, 2000 .

Asymptotic Learning Curve and Renormalizable Condition in Statistical Learning Theory pdf

Sumio Watanabe, Sumio Watanabe, 2010, ArXiv.

Algebraic Geometry and Statistical Learning Theory: Bibliography

Sumio Watanabe, Sumio Watanabe, Sumio Watanabe, 2009 .

Singularities in Learning Theory(Recent Topics on Real and Complex Singularities)

Sumio Watanabe, Sumio Watanabe, 2006 .

Phase Diagram Study on Variational Bayes Learning of Bernoulli Mixture 梶大介

Sumio Watanabe, 2009 .

Generalization Properties of Variational Bayes Approach in Linear Neural Networks

Sumio Watanabe, 2007 .

Asymptotic Analysis of the Bayesian Likelihood Ratio for Testing Homogeneity in Normal Mixture Models.

Sumio Watanabe, Natsuki Kariya, 2018, 1812.03510.

Asymptotic Bayesian generalization error when training and test distributions are different

Motoaki Kawanabe, Klaus-Robert Müller, Masashi Sugiyama, 2007, ICML '07.

Information criteria and cross validation for Bayesian inference in regular and singular cases

Sumio Watanabe, Sumio Watanabe, 2021, Japanese Journal of Statistics and Data Science.

Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory pdf

Sumio Watanabe, Sumio Watanabe, 2010, J. Mach. Learn. Res..

A widely applicable Bayesian information criterion

Sumio Watanabe, Sumio Watanabe, 2012, J. Mach. Learn. Res..

Estimation of the Data Region Using Extreme-Value Distributions

Kazuho Watanabe, Sumio Watanabe, Kazuho Watanabe, 2004, ALT.

Equations of States in Singular Statistical Estimation

Sumio Watanabe, Sumio Watanabe, 2007, Neural Networks.

Solvable models of layered neural networks based on their differential structure

Sumio Watanabe, Sumio Watanabe, 1996, Adv. Comput. Math..

Asymptotic Bayesian Generalization Error in Latent Dirichlet Allocation and Stochastic Matrix Factorization

Naoki Hayashi, Sumio Watanabe, Sumio Watanabe, 2017, SN Computer Science.

A formula of equations of states in singular learning machines

Sumio Watanabe, Sumio Watanabe, 2008, 2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence).

Upper Bound of Real Log Canonical Threshold of Tensor Decomposition and its Application to Bayesian Inference

Sumio Watanabe, Naoki Yoshida, 2023, ArXiv.

Almost All Learning Machines are Singular

Sumio Watanabe, Sumio Watanabe, 2007, 2007 IEEE Symposium on Foundations of Computational Intelligence.

Algebraic Analysis for Nonidentifiable Learning Machines

Sumio Watanabe, Sumio Watanabe, 2001, Neural Computation.

Errata to "learning efficiency of redundant neural networks in bayesian estimation"

Sumio Watanabe, Sumio Watanabe, 2002, IEEE Trans. Neural Networks.

An ultrasonic visual sensor for three-dimensional object recognition using neural networks

Masahide Yoneyama, Sumio Watanabe, Sumio Watanabe, 1992, IEEE Trans. Robotics Autom..

An Ultrasonic Robot Eye Using Neural Networks

Masahide Yoneyama, Sumio Watanabe, Sumio Watanabe, 1991 .

Free Energy of Stochastic Context Free Grammar on Variational Bayes

Kazuho Watanabe, Sumio Watanabe, Tikara Hosino, 2006, ICONIP.

Bayesian Free Energy of Deep ReLU Neural Network in Overparametrized Cases

Sumio Watanabe, Shuya Nagayasu, 2023, ArXiv.

Mathematical theory of Bayesian statistics for unknown information source

Sumio Watanabe, 2022, Philosophical Transactions of the Royal Society A.

Asymptotic Behavior of Bayesian Generalization Error in Multinomial Mixtures

Sumio Watanabe, Takumi Watanabe, 2022, ArXiv.

WAIC and WBIC for mixture models

Sumio Watanabe, 2021, Behaviormetrika.

Bayesian Cross Validation and WAIC for Predictive Prior Design in Regular Asymptotic Theory pdf

Sumio Watanabe, Sumio Watanabe, 2015, ArXiv.

Information criterion for variational Bayes learning in regular and singular cases

Sumio Watanabe, Koshi Yamada, Sumio Watanabe, 2012, The 6th International Conference on Soft Computing and Intelligent Systems, and The 13th International Symposium on Advanced Intelligence Systems.

Statistical Learning Theory of Quasi-Regular Cases

Sumio Watanabe, Koshi Yamada, Sumio Watanabe, 2011, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

Phase Transition of Variational Bayes Learning in Bernoulli Mixture

Kazuho Watanabe, Sumio Watanabe, Daisuke Kaji, 2010, Aust. J. Intell. Inf. Process. Syst..

Equations of States in Statistical Learning for a Nonparametrizable and Regular Case pdf

Sumio Watanabe, Sumio Watanabe, 2009, ArXiv.

A Limit Theorem in Singular Regression Problem pdf

Sumio Watanabe, Sumio Watanabe, 2009, ArXiv.

Singular learning theory: connecting algebraic geometry and model selection in statistics

R. Steele, B. Sturmfels, Sumio Watanabe, 2015 .

An Introduction to Algebraic Geometry and Statistical Learning Theory

Sumio Watanabe, Sumio Watanabe, 2012 .

Asymptotic behavior of exchange ratio in exchange Monte Carlo method

Sumio Watanabe, Kenji Nagata, Sumio Watanabe, 2008, Neural Networks.

Tighter upper bound of real log canonical threshold of non-negative matrix factorization and its application to Bayesian inference

Naoki Hayashi, Sumio Watanabe, Sumio Watanabe, 2017, 2017 IEEE Symposium Series on Computational Intelligence (SSCI).

Upper bound of Bayesian generalization error in non-negative matrix factorization pdf

Naoki Hayashi, Sumio Watanabe, Sumio Watanabe, 2016, Neurocomputing.

Two design methods of hyperparameters in variational Bayes learning for Bernoulli mixtures

Sumio Watanabe, Daisuke Kaji, Sumio Watanabe, 2011, Neurocomputing.

On Generalization Error of Self-Organizing Map

Fumiaki Saitoh, Sumio Watanabe, Sumio Watanabe, 2010, ICONIP.

Stochastic complexities of general mixture models in variational Bayesian learning

Kazuho Watanabe, Sumio Watanabe, Kazuho Watanabe, 2007, Neural Networks.

Phase Transition Structure of Variational Bayesian Nonnegative Matrix Factorization

Sumio Watanabe, Masahiro Kohjima, Sumio Watanabe, 2017, ICANN.

Accuracy of Loopy belief propagation in Gaussian models

Sumio Watanabe, Yu Nishiyama, Sumio Watanabe, 2009, Neural Networks.

Learning efficiency of redundant neural networks in Bayesian estimation

Sumio Watanabe, Sumio Watanabe, 2001, IEEE Trans. Neural Networks.

Genetic algorithms applied to bayesian image restoration

Hidefumi Sawai, Kazunori Takatsu, Masahide Yoneyama, 1995, Systems and Computers in Japan.

WAIC and WBIC for mixture models

Sumio Watanabe, 2021, Behaviormetrika.