Sumio Watanabe

Q: What Schools Are Affiliated With Sumio Watanabe

Sumio Watanabe is affiliated with the following schools: University of Tokyo, Institute of Science Tokyo, Kyoto University

Sumio Watanabe's AcademicInfluence.com Rankings

Sumio Watanabe

Mathematics

#3525

World Rank

#5182

Historical Rank

Measure Theory

#2536

World Rank

#3044

Historical Rank

mathematics Degrees

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Mathematics

Sumio Watanabe's Degrees

PhD Mathematics University of Tokyo

Why Is Sumio Watanabe Influential?

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According to Wikipedia, Sumio Watanabe is a Japanese mathematician and engineer working in probability theory, applied algebraic geometry and Bayesian statistics. He is currently a professor at Tokyo Institute of Technology in the Department of Computational Intelligence and Systems Science. He is the author of the text, Algebraic Geometry and Statistical Learning Theory, which proposes a generalization of Fisher's regular statistical theory to singular statistical models.

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Sumio Watanabe's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory (2010) (1901)
A widely applicable Bayesian information criterion (2012) (592)
Algebraic Analysis for Nonidentifiable Learning Machines (2001) (228)
Singularities in mixture models and upper bounds of stochastic complexity (2003) (122)
Stochastic complexities of reduced rank regression in Bayesian estimation (2005) (117)
Algebraic Geometry and Statistical Learning Theory (2009) (113)
Algebraic geometrical methods for hierarchical learning machines (2001) (95)
Equations of States in Singular Statistical Estimation (2007) (79)
Stochastic Complexities of Gaussian Mixtures in Variational Bayesian Approximation (2006) (78)
An ultrasonic visual sensor for three-dimensional object recognition using neural networks (1992) (77)
Algebraic geometry and stochastic complexity of hidden Markov models (2005) (68)
A network of chaotic elements for information processing (1996) (67)
Learning Coefficients of Layered Models When the True Distribution Mismatches the Singularities (2003) (56)
Variational Bayes Solution of Linear Neural Networks and Its Generalization Performance (2007) (54)
Mathematical Theory of Bayesian Statistics (2018) (50)
Algebraic Analysis for Non-identifiable Learning Machines (2000) (49)
Algebraic Analysis for Singular Statistical Estimation (1999) (48)
Stochastic complexities of general mixture models in variational Bayesian learning (2007) (47)
Asymptotic analysis of Bayesian generalization error with Newton diagram (2010) (46)
Asymptotic behavior of exchange ratio in exchange Monte Carlo method (2008) (44)
Upper bound for variational free energy of Bayesian networks (2009) (40)
Almost All Learning Machines are Singular (2007) (39)
Stochastic Complexity of Bayesian Networks (2002) (38)
Algebraic Geometry and Statistical Learning Theory: Contents (2009) (34)
Asymptotic Bayesian generalization error when training and test distributions are different (2007) (32)
Singularities in complete bipartite graph-type Boltzmann machines and upper bounds of stochastic complexities (2005) (31)
Algebraic Information Geometry for Learning Machines with Singularities (2000) (30)
Phase Transition of Variational Bayes Learning in Bernoulli Mixture (2010) (30)
Kullback Information of Normal Mixture is not an Analytic Function (2004) (29)
Probabilistic design of layered neural networks based on their unified framework (1995) (26)
Algebraic Analysis for Non-regular Learning Machines (1999) (24)
Learning efficiency of redundant neural networks in Bayesian estimation (2001) (24)
Exchange Monte Carlo Sampling From Bayesian Posterior for Singular Learning Machines (2008) (23)
Desingularization and the Generalization Error of Reduced Rank Regression in Bayesian Estimation (2004) (19)
Resolution of Singularities and the Generalization Error with Bayesian Estimation for Layered Neural Network (2005) (19)
Newton Diagram and Stochastic Complexity in Mixture of Binomial Distributions (2004) (18)
Upper bound of Bayesian generalization error in non-negative matrix factorization (2016) (18)
Stochastic complexities of hidden Markov models (2003) (16)
An Ultrasonic Robot Eye Using Neural Networks (1991) (15)
Algebraic geometry of singular learning machines and symmetry of generalization and training errors (2005) (14)
Asymptotic Learning Curve and Renormalizable Condition in Statistical Learning Theory (2010) (13)
On the generalization error by a layered statistical model with Bayesian estimation (2000) (12)
Stochastic Complexity for Mixture of Exponential Families in Variational Bayes (2005) (12)
A New Method of Model Selection Based on Learning Coecien t (2005) (11)
A Probabilistic Algorithm to Calculate the Learning Curves of Hierarchical Learning Machines with Singularities (2002) (11)
Variational Bayesian Stochastic Complexity of Mixture Models (2005) (10)
Genetic algorithms applied to bayesian image restoration (1995) (10)
Generalization Error of Linear Neural Networks in an Empirical Bayes Approach (2005) (10)
WAIC AND WBIC ARE INFORMATION CRITERIA FOR SINGULAR STATISTICAL MODEL EVALUATION (2013) (10)
A New Method of Model Selection Based on Learning Coefficient (9)
The Exchange Monte Carlo Method for Bayesian Learning in Singular Learning Machines (2006) (9)
Tighter upper bound of real log canonical threshold of non-negative matrix factorization and its application to Bayesian inference (2017) (9)
WAIC and WBIC for mixture models (2021) (8)
Bayesian Generalization Error of Poisson Mixture and Simplex Vandermonde Matrix Type Singularity (2019) (8)
Free Energy of Stochastic Context Free Grammar on Variational Bayes (2006) (7)
Generalization Performance of Subspace Bayes Approach in Linear Neural Networks (2006) (7)
A Limit Theorem in Singular Regression Problem (2009) (7)
Equations of States in Statistical Learning for an Unrealizable and Regular Case (2010) (6)
Bayesian Cross Validation and WAIC for Predictive Prior Design in Regular Asymptotic Theory (2015) (6)
Equations of States in Statistical Learning for a Nonparametrizable and Regular Case (2009) (5)
Analytic Solution of Hierarchical Variational Bayes in Linear Inverse Problem (2006) (5)
A Model Selection Method Based on Bound of Learning Coefficient (2006) (5)
ALGEBRAIC GEOMETRICAL METHOD IN SINGULAR STATISTICAL ESTIMATION (2008) (5)
Weighted Blowup and Its Application to a Mixture of Multinomial Distributions (2010) (5)
Stochastic Complexity and Newton Diagram (2004) (5)
Analysis of Exchange Ratio for Exchange Monte Carlo Method (2007) (5)
Accuracy of Loopy belief propagation in Gaussian models (2009) (5)
A formula of equations of states in singular learning machines (2008) (5)
Two design methods of hyperparameters in variational Bayes learning for Bernoulli mixtures (2011) (4)
Asymptotic Bayesian Generalization Error in Latent Dirichlet Allocation and Stochastic Matrix Factorization (2017) (4)
Stochastic complexity for mixture of exponential families in generalized variational Bayes (2007) (4)
Inequalities of Generalization Errors for Layered Neural Networks in Bayesian Learning (1998) (4)
Information criteria and cross validation for Bayesian inference in regular and singular cases (2021) (4)
Upper Bounds for Variational Stochastic Complexities of Bayesian Networks (2006) (4)
Asymptotic behavior of free energy when optimal probability distribution is not unique (2020) (4)
A Nonlinear Ultrasonic Imaging Method Based on the Modified Information Criterion (1996) (3)
Optimal Hyperparameters for Generalized Learning and Knowledge Discovery in Variational Bayes (2009) (3)
Algebraic Geometry and Statistical Learning Theory: Bibliography (2009) (3)
Generalization of Concave and Convex Decomposition in Kikuchi Free Energy (2008) (3)
Higher Order Equivalence of Bayes Cross Validation and WAIC (2016) (3)
Statistical Learning Theory of Quasi-Regular Cases (2011) (3)
An Optimization Method of Layered Neural Networks based on the Modified Information Criterion (1993) (3)
Mathematical theory of Bayesian statistics for unknown information source (2022) (3)
Algebraic Geometry and Statistical Learning Theory: Algebraic geometry (2009) (3)
On Generalization Error of Self-Organizing Map (2010) (3)
Phase Transition Structure of Variational Bayesian Nonnegative Matrix Factorization (2017) (3)
A Modified Information Criterion for Automatic Model and Parameter Selection in Neural Network Learning (1995) (3)
Generalization Error of Automatic Relevance Determination (2007) (2)
Simulation Data Generation from Extended EGA Model and Optimization of Alignment Strategy for Lithography (2004) (2)
Design of Exchange Monte Carlo Method for Bayesian Learning in Normal Mixture Models (2008) (2)
Asymptotic analysis of singular likelihood ratio of normal mixture by Bayesian learning theory for testing homogeneity (2020) (2)
Asymptotic Behavior of Stochastic Complexity of Complete Bipartite Graph-Type Boltzmann Machines (2006) (2)
Estimation of the Data Region Using Extreme-Value Distributions (2004) (2)
Mathematical Foundation for Redundant Statistical Estimation (2000) (2)
Solvable models of layered neural networks based on their differential structure (1996) (1)
Learning machine and neural network, and device and method for data analysis (1992) (1)
Singular Model and Bayesian Learning. (2003) (1)
Generalization error of three layered learning model in bayesian estimation (2006) (1)
Definition of Bayesian Statistics (2018) (1)
Testing Homogeneity for Normal Mixture Models: Variational Bayes Approach (2019) (1)
Algebraic Geometric Study of Exchange Monte Carlo Method (2007) (1)
Singular learning theory: connecting algebraic geometry and model selection in statistics (2015) (1)
Model Selection Method for AdaBoost Using Formal Information Criteria (2009) (1)
An Automatic 3-D Object Identification System Combining Ultrasonic Imaging with a Probability Competition Neural Network (1993) (1)
Information criterion for variational Bayes learning in regular and singular cases (2012) (1)
Solvable Models of Artificial Neural Networks (1993) (1)
Theoretical Analysis of Accuracy of Gaussian Belief Propagation (2007) (1)
1 Algebraic Geometrical Methods for Hierarchical Learning Machines (2001) (1)
Resolution of Singularities and Stochastic Complexity of Complete Bipartite Graph-Type Spin Model in Bayesian Estimation (2007) (1)
Analytic Equivalence of Bayes a Posteriori Distributions (2006) (1)
Experimental Study of Ergodic Learning Curve in Hidden Markov Models (2008) (1)
Asymptotic Bayesian Generalization Error in a General Stochastic Matrix Factorization for Markov Chain and Bayesian Network (2017) (1)
The Effect of Singularities in a Learning Machine when the True Parameters Do Not Lie on such Singularities (2002) (1)
On Variational Bayes Algorithms for Exponential Family Mixtures (2005) (1)
An Ultrasonic Image Restoration Method Based on the Information Criteria (1993) (0)
Theory and Experiments of Exchange Ratio for Exchange Monte Carlo Method (2008) (0)
Experimental Bayesian Generalization Error of Non-regular Models under Covariate Shift (2007) (0)
Experimental Analysis of Exchange Ratio in Exchange Monte Carlo Method (2007) (0)
Stochastic Complexity and Singularities in Hierarchical Bayesian Networks (2004) (0)
Algebraic Geometry and Statistical Learning Theory: Singular learning theory (2009) (0)
Topics in Bayesian Statistics (2018) (0)
Probabilistic design (2020) (0)
O ct 2 01 7 Upper Bound of Bayesian Generalization Error in Non-Negative Matrix Factorization (2018) (0)
A three-dimensional object recognition method using acoustical imasing and neural networks (1991) (0)
WAIC and WBIC for mixture models (2021) (0)
Bayesian Free Energy of Deep ReLU Neural Network in Overparametrized Cases (2023) (0)
On Relation between Exchange Ratio and Kullback Divergence in Exchange Monte Carlo Method (2006) (0)
Upper Bound of Bayesian Generalization Error in Stochastic Matrix Factorization (2017) (0)
Algebraic Geometry and Statistical Learning Theory: Singular learning machines (2009) (0)
Bayes and Gibbs Estimations , Empirical Processes , and Resolution of Singularities (2007) (0)
An Introduction to Algebraic Geometry and Statistical Learning Theory (2012) (0)
Algebraic Geometry and Statistical Learning Theory: Singularity theory (2009) (0)
Algebraic Geometry and Statistical Learning Theory: Singular statistics (2009) (0)
A Geometric Evaluation of Self-Organizing Map and Application to City Data Analysis (2013) (0)
Effects of priors in model selection problem of learning machines with singularities (2005) (0)
Asymptotic Behavior of Bayesian Generalization Error in Multinomial Mixtures (2022) (0)
Algebraic Geometry and Statistical Learning Theory: Empirical processes (2009) (0)
Phase Diagram Study on Variational Bayes Learning of Bernoulli Mixture 梶大介 (2009) (0)
A 3-D Object Classification Method Combining Acoustical Imaging with Probability Competition Neural Networks (1993) (0)
Basic Formula of Bayesian Observables (2018) (0)
Numerical behavior of training and generalization errors in HMM (2004) (0)
Localized Bayesian Learning for Singular Learning Machines (2005) (0)
Estimation of Poles of Zeta Function in Learning Theory Using Padé Approximation (2007) (0)
Two birational invariants in statistical learning theory (2012) (0)
Analytical and Numerical Solutions of Bethe Approximation in Normal Distributions (2008) (0)
Generalization Performance of Exchange Monte Carlo Method for Normal Mixture Models (2006) (0)
Generalization Error of an Empirical Bayes Approach (2004) (0)
Regular Posterior Distribution (2018) (0)
The Calculation Method of Learning Coefficients by Weighted Resolution of Singularities (2007) (0)
医学会会長挨拶(第20回都民公開講座《気になる肝臓病,肝がん-肝がんにならない方法,なった場合の対処法-》) (2007) (0)
Markov Chain Monte Carlo (2018) (0)
Errata to "learning efficiency of redundant neural networks in bayesian estimation" (2002) (0)
Algebraic Geometry and Statistical Learning Theory: Introduction (2009) (0)
Stochastic Complexities of Three Layered Learning Model in Bayesian Estimation (2006) (0)
Book Reviews (2011) (0)
An ultrasonic 3-D robot vision system based on the statistical properties of artificial neural networks (1996) (0)
General Posterior Distribution (2018) (0)
A CASE OF PRIMARY AMYLOIDOSIS WITH RAPIDLY PROGRESSIVE MULTIPLE ORGAN FAILURE (2013) (0)
A Topic Recognition System of Spoken Dialogue Based on Thesaurus Information (1999) (0)
Asymptotic Analysis of the Bayesian Likelihood Ratio for Testing Homogeneity in Normal Mixture Models. (2018) (0)
On a Singular Point to Contribute to a Learning Coefficient and Weighted Resolution of Singularities (2007) (0)
恥 1 athelnaticalFoundation for Redundant Statistical Estimation (2017) (0)
Generalization Properties of Variational Bayes Approach in Linear Neural Networks (2007) (0)
On the Minima of Bethe Free Energy in Gaussian Distributions (2006) (0)
Recent Advances in Algebraic Geometry and Bayesian Statistics (2022) (0)
Asymptotic Bayesian Generalization Error in Topic Model and Stochastic Matrix Factorization (2017) (0)
Singularities in Learning Theory (2006) (0)
Estimating the Data Region Using Minimum and Maximum Values (2007) (0)
Algebraic Geometry and Statistical Learning Theory: Zeta function and singular integral (2009) (0)
Standard Posterior Distribution (2018) (0)
Interpretation Method of Nonlinear Multilayer Principal Component Analysis by Using Sparsity and Hierarchical Clustering (2016) (0)
Singularities in Learning Theory(Recent Topics on Real and Complex Singularities) (2006) (0)
A finite wavelet decomposition method (1997) (0)
Localized Bayes Estimation for Non-identifiable Models (2006) (0)
Upper Bound of Real Log Canonical Threshold of Tensor Decomposition and its Application to Bayesian Inference (2023) (0)
THE ZETA FUNCTION FOR LEARNING THEORY AND RESOLUTION OF SINGULARITIES (2009) (0)
Extraction of Image Entropy using Independent Component Analysis (1999) (0)
Real Log Canonical Threshold of General Stochastic Matrix Factorization for Markov Chain and Bayesian Network (2017) (0)
Stochastic complexity of complete bipartite graph-type Boltzmann machines in mean field approximation (2007) (0)
Basic Probability Theory (2018) (0)

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What Schools Are Affiliated With Sumio Watanabe?

Sumio Watanabe is affiliated with the following schools:

Sumio Watanabe's Academic­Influence.com Rankings