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Establishment of Information Physics based on algebraic geometry

Research Project

Project/Area Number 18079007
Research Category

Grant-in-Aid for Scientific Research on Priority Areas

Allocation TypeSingle-year Grants
Review Section Science and Engineering
Research InstitutionTokyo Institute of Technology

Principal Investigator

WATANABE Sumio  Tokyo Institute of Technology, 精密工学研究所, 教授 (80273118)

Co-Investigator(Kenkyū-buntansha) 山崎 啓介  東京工業大学, 精密工学研究所 (60376936)
Co-Investigator(Renkei-kenkyūsha) YAMAZAKI Keisuke  東京工業大学, 精密工学研究所, 助教 (60376936)
Project Period (FY) 2006 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥45,800,000 (Direct Cost: ¥45,800,000)
Fiscal Year 2009: ¥13,200,000 (Direct Cost: ¥13,200,000)
Fiscal Year 2008: ¥14,000,000 (Direct Cost: ¥14,000,000)
Fiscal Year 2007: ¥14,000,000 (Direct Cost: ¥14,000,000)
Fiscal Year 2006: ¥4,600,000 (Direct Cost: ¥4,600,000)
Keywords代数幾何 / 情報物理学 / 学習理論 / 特異点論 / 超関数論 / 確率過程論 / 特異モデル / 実対数閾植 / 特異ゆらぎ / 学習の状態方程式 / 特異点 / 双有理不変量 / 実対数閾値 / ゼータ関数 / 広中の定理 / 佐藤幹夫のb関数 / 対数正規値 / 状態方程式 / 特異点解消定理 / 代数解析 / 厳密な数理物理
Research Abstract

Almost all learning machines used in information science are singular because they have degenerate Fisher Information matrices. Regular statistical theory can not be applied to singular learning machines. In this research, we established new information physics theory for singular learning machines based on higher dimensional algebraic geometry, and clarified that the asymptotic behaviors of generalization and training errors are determined by two birational invariants. Based on new theory, we derived a widely applicable information criterion, by which the generalization error can be estimated from training error in both singular and regular learning machines.

Report

(6 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report   Self-evaluation Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (89 results)

All 2010 2009 2008 2007 2006 Other

All Journal Article (35 results) (of which Peer Reviewed: 29 results) Presentation (42 results) Book (7 results) Remarks (5 results)

  • [Journal Article] Equations of states in statistical learning for an unrealizable and regular case2010

    • Author(s)
      S. Watanabe
    • Journal Title

      IEICE Transactions Vol.E93-A,No.3

      Pages: 617-626

    • NAID

      10026863556

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Equations of states in singular statistical estimation2010

    • Author(s)
      S. Watanabe
    • Journal Title

      Neural Networks Vol.23,No.1

      Pages: 20-34

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic Analysis of Bayesian Generalization Error with Newton Diagram2010

    • Author(s)
      K. Yamazaki, M. Aoyagi, S. Watanabe
    • Journal Title

      Neural Networks Vol.23,No.1

      Pages: 35-43

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A limit theorem in singular regression problem2010

    • Author(s)
      Sumio Watanabe
    • Journal Title

      Advanced Studies in Pure Mathematics Vol.57

      Pages: 473-492

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Equations of states in statistical learning for an unrealizable and regular case2010

    • Author(s)
      Sumio Watanabe
    • Journal Title

      IEICE Transactions Vol.E93-A, No.3

      Pages: 617-626

    • NAID

      10026863556

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic Analysis of Bayesian Generalization Error with Newton Diagram2010

    • Author(s)
      K Yamazaki, M Aoyagi, S Watanabe
    • Journal Title

      Neural Networks Vol.23, No.1

      Pages: 35-43

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Equations of states in singular statistical estimation2010

    • Author(s)
      Sumio Watanabe
    • Journal Title

      Neural Networks Vol.23, No.1

      Pages: 20-34

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Upper bound for variational free energy of Bayesian networks2009

    • Author(s)
      K. Watanabe, M. Shiga, S. Watanabe
    • Journal Title

      Machine Learning vol.75,no.2

      Pages: 199-215

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] 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2009

    • Author(s)
      梶大介, 渡辺澄夫
    • Journal Title

      電子情報通信学会誌D Vol.J92-D,Vol.J92-D,No.11

      Pages: 2051-2058

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic Behavior of Exchange Ratio in Exchange Monte Carlo Method2008

    • Author(s)
      K. Nagata, S. Watanabe
    • Journal Title

      Neural Networks Vol.21,No.7

      Pages: 980-988

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Exchange Monte Carlo Sampling From Bayesian Posterior for Singular Learning Machines2008

    • Author(s)
      K. Nagata, S. Watanabe
    • Journal Title

      IEEE Transactions on Neural Networks Vol.19,No.7

      Pages: 1253-1266

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Theory and Experiments of Exchange Ratio for Exchange Monte Carlo Method2008

    • Author(s)
      K. Nagata, S. Watanabe
    • Journal Title

      Neural Information Processing - Letters and Reviews Vol.12,No.1-3

      Pages: 21-30

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] 特異モデルにおけるベイズ検定と時系列解析への応用2008

    • Author(s)
      藤原香織, 渡辺澄夫
    • Journal Title

      電子情報通信学会論文誌D VolumeJ91-D,No.4

      Pages: 889-896

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic Behavior of Exchange Ratio in Exchange Monte Carlo Method2008

    • Author(s)
      Kenji Nagata, Sumio Watanabe
    • Journal Title

      Neural Networks Vol. 21, No. 7

      Pages: 980-988

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Asymptotic Behavior of Exchange Ratio in Exchange Monte Carlo Method2008

    • Author(s)
      Kenji Nagata, Sumio Watanabe
    • Journal Title

      Neural Networks 21

      Pages: 980-988

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Exchange Monte Carlo Sampling From Bayesian Posterior for Singular Learning Machines2008

    • Author(s)
      Kenji Nagata, Sumio Watanabe
    • Journal Title

      IEEE Transactions on Neural Networks 19

      Pages: 1253-1266

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 特異モデルにおけるベイズ検定と時系列解析への応用2008

    • Author(s)
      藤原香織, 渡辺澄夫
    • Journal Title

      電子情報通信学会論文誌D J91-D

      Pages: 889-896

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Variational Bayes Solution of Linear Neural Networks and its Generalization Performance2007

    • Author(s)
      S. Nakajima, S. Watanabe
    • Journal Title

      Neural Computation vol.19,no.4

      Pages: 1112-1153

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Estimating the Data Region Using Minimum and Maximum Values2007

    • Author(s)
      K. Watanabe, S. Watanabe
    • Journal Title

      Interdisciplinary Information Sciences Vol.13,No.2

      Pages: 151-161

    • NAID

      110006463579

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stochastic complexity for mixture of exponential families in generalized variational Bayes2007

    • Author(s)
      K. Watanabe, S. Watanabe
    • Journal Title

      Theoretical Computer Science Vol.387

      Pages: 4-17

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Variational Bayes Solution of Linear Neural Networks and its Generalization Performance2007

    • Author(s)
      S. Nakajima, S.Watanabe
    • Journal Title

      Neural Computation vol.19, no.4

      Pages: 1112-1153

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Stochastic complexities of general mixture models in variation al Bayesian learning2007

    • Author(s)
      K. Watanabe, S. Watanabe
    • Journal Title

      Neural Networks 20

      Pages: 210-217

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Variational Bayes Solution of Linear Neural Networks and its Generalization Performance2007

    • Author(s)
      S. Nakajima, S. Watanabe
    • Journal Title

      Neural Computation 19

      Pages: 1112-1153

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Estimating the Data Region Using Minimum and Maximum Values2007

    • Author(s)
      K. Watanabe, S. Watanabe
    • Journal Title

      Interdisciplinary Information Sciences 13

      Pages: 151-161

    • NAID

      110006463579

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stochastic complexities of gaussian mixtures in variational bayesian approximation2006

    • Author(s)
      K. Watanabe, S. Watanabe
    • Journal Title

      Journal of Machine Learning Research Vol.7

      Pages: 625-644

    • Related Report
      2009 Final Research Report 2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Generalization Performance of Subspace Bayes Approach in Linear Neural Networks2006

    • Author(s)
      S. Nakajima, S. Watanabe
    • Journal Title

      IEICE Transactions Vol.E89-D,no.3

      Pages: 1128-1138

    • NAID

      110004719390

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] 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2006

    • Author(s)
      西山悠, 渡辺澄夫
    • Journal Title

      電子情報通信学会論文誌 Vol.J89-A,no.8

      Pages: 671-678

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] 局所化ベイズ学習法2006

    • Author(s)
      高松慎吾, 中島伸一, 渡辺澄夫
    • Journal Title

      電子情報通信学会論文誌 Vol.J89-D-II,no.10

      Pages: 2260-2268

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] 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2006

    • Author(s)
      星野力, 渡辺一帆, 渡辺澄夫
    • Journal Title

      電子情報通信学会論文誌 Vol.J89-D-II,No.6

      Pages: 1279-1287

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stochastic complexities of gaussian mixtures in variational bayesian approximation2006

    • Author(s)
      K Watanabe, S Watanabe
    • Journal Title

      Journal of Machine Learning Research Vol. 7

      Pages: 625-644

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Generalization Performance of Subspace Bayes Approach in Linear Neural Networks2006

    • Author(s)
      S Nakajima, S Watanabe
    • Journal Title

      IEICE Transactions Vol. E89-D, no. 3

      Pages: 1128-1138

    • NAID

      110004719390

    • Related Report
      2006 Annual Research Report
  • [Journal Article] 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2006

    • Author(s)
      西山 悠, 渡辺澄夫
    • Journal Title

      電子情報通信学会論文誌 Vol. J89-A, no. 8

      Pages: 671-678

    • Related Report
      2006 Annual Research Report
  • [Journal Article] 局所化ベイズ学習法2006

    • Author(s)
      高松慎吾, 中島伸一, 渡辺澄夫
    • Journal Title

      電子情報通信学会論文誌 vol. J89-D-II, no. 10

      Pages: 2260-2268

    • Related Report
      2006 Annual Research Report
  • [Journal Article] 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2006

    • Author(s)
      星野力, 渡辺一帆, 渡辺澄夫
    • Journal Title

      電子情報通信学会論文誌 Vol. J89-D-II, No. 6

      Pages: 1279-1287

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Variational bayesian stochastic complexity of mixture models2006

    • Author(s)
      K Watanabe, S Watanabe
    • Journal Title

      Proc. of Advances in Neural Information Processing Systems Vol. 18

      Pages: 1465-1472

    • Related Report
      2006 Annual Research Report
  • [Presentation] Two birational invariants in statistical learning theory2009

    • Author(s)
      Sumio Watanabe
    • Organizer
      JSPS Forum on Singularities
    • Place of Presentation
      IRMA, France
    • Year and Date
      2009-08-24
    • Related Report
      2009 Annual Research Report
  • [Presentation] Optimal Hyperparameters for Generalized Learning and Knowledge Discovery in Variational Bayes2009

    • Author(s)
      D. Kaji, S. Watanabe
    • Organizer
      International Conference on Neural Information Processing
    • Place of Presentation
      Bangkok, Thailand
    • Related Report
      2009 Final Research Report
  • [Presentation] A Singular limit theorem in statistical learning theory2009

    • Author(s)
      S. Watanabe
    • Organizer
      Mathematical Quantum Field Theory and Renormalization Theory
    • Place of Presentation
      Kyushu Univ
    • Related Report
      2009 Final Research Report
  • [Presentation] Determining the Number of the Components of Gaussian Mixture Models by Bayesian Hypothesis Testing2009

    • Author(s)
      K. Fujiwara, S. Watanabe
    • Organizer
      The 12th IASTED International Conference on Intelligent systems and control
    • Place of Presentation
      Cambridge, Massachusetts, USA
    • Related Report
      2009 Final Research Report
  • [Presentation] Generalization Error by Langevin Equation in Singular Learning Machines2009

    • Author(s)
      T. Iwagaki, S. Watanabe
    • Organizer
      International Symposium on Nonlinear Theory and its Applications
    • Place of Presentation
      Sapporo, Japan
    • Related Report
      2009 Final Research Report
  • [Presentation] Phase Transition of Generalization Errors in Variational Bayes Learning2009

    • Author(s)
      S. Oyama, S. Watanabe
    • Organizer
      International Symposium on Nonlinear Theory and its Applications
    • Place of Presentation
      Sapporo, Japan
    • Related Report
      2009 Final Research Report
  • [Presentation] A formula of equations of states in singular learning machines2008

    • Author(s)
      Sumio Watanabe
    • Organizer
      IEEE World Congress in Computational Intelligence
    • Place of Presentation
      香港コンベンションセンター
    • Year and Date
      2008-06-06
    • Related Report
      2008 Annual Research Report
  • [Presentation] Algebraic geometrical method in singular statistical estimation2008

    • Author(s)
      S. Watanabe
    • Organizer
      Algebraic Statistics, Mathematical Sciences Research Institute, Univesity of California
    • Place of Presentation
      Berkeley, USA
    • Related Report
      2009 Final Research Report
  • [Presentation] An Analysis of Generalization Error in Relevant Subtask Learning2008

    • Author(s)
      K. Yamazaki, S. Kaski
    • Organizer
      International Conference on Neural Information Processing of the Asia- Pacific Neural Network Assembly
    • Place of Presentation
      Auckland, New Zealand
    • Related Report
      2009 Final Research Report
  • [Presentation] Design of Exchange Monte Carlo Method for Bayesian Learning in Normal Mixture Models2008

    • Author(s)
      K. Nagata, S. Watanabe
    • Organizer
      International Conference on Neural Information Processing of the Asia-Pacific Neural Network Assembly
    • Place of Presentation
      Auckland, New Zealand
    • Related Report
      2009 Final Research Report
  • [Presentation] Model Selection Method for AdaBoost Using Formal Information Criteria2008

    • Author(s)
      D. Kaji, S. Watanabe
    • Organizer
      International Conference on Neural Information Processing of the Asia- Pacific Neural Network Assembly
    • Place of Presentation
      Auckland, New Zealand
    • Related Report
      2009 Final Research Report
  • [Presentation] Experimental Study of Ergodic Learning Curve in Hidden Markov Models2008

    • Author(s)
      M. Matsumoto, S. Watanabe
    • Organizer
      International Conference on Neural Information Processing of the Asia-Pacific Neural Network Assembly
    • Place of Presentation
      Auckland, New Zealand
    • Related Report
      2009 Final Research Report
  • [Presentation] Algebraic Geometry, Empirical Process, and Singular Model Evaluation2008

    • Author(s)
      S. Watanabe
    • Organizer
      Algebraic Methods in Systems Biology and Statistics
    • Place of Presentation
      Research Triangle Park, NC, USA
    • Related Report
      2009 Final Research Report 2008 Self-evaluation Report
  • [Presentation] Weighted Blowups of Kullback Information and Application to Multinomial Distributions2008

    • Author(s)
      T. Matsuda, S. Watanabe
    • Organizer
      Proceedings of International Symposium on Nonlinear Theory and Its Applications
    • Place of Presentation
      Budapest, Republic of Hungary
    • Related Report
      2009 Final Research Report
  • [Presentation] Generalization of Concave and Convex Decomposition in Kikuchi Free Energy2008

    • Author(s)
      Y. Nishiyama, S. Watanabe
    • Organizer
      International Conference on Artificial Neural Networks
    • Place of Presentation
      Czech Republic
    • Related Report
      2009 Final Research Report
  • [Presentation] On the Minima of Bethe Free Energy in Gaussian Distributions2008

    • Author(s)
      Y. Nishiyama, S. Watanabe
    • Organizer
      Proceedings of International Conference on Artificial Intelligence and Softcomputing
    • Place of Presentation
      Palma de Mallorca, Spain
    • Related Report
      2009 Final Research Report
  • [Presentation] What we can estimate about singularity from random samples2008

    • Author(s)
      S. Watanabe
    • Organizer
      Seasonal Institute of the mathematical society of Japan, Kyoto, Japan
    • Place of Presentation
      Kyoto, Japan
    • Related Report
      2009 Final Research Report
  • [Presentation] A foumula of equations of states in singular learning machines2008

    • Author(s)
      S. Watanabe
    • Organizer
      IEEE World Congress in Computational Intelligence
    • Place of Presentation
      Hong kong, China
    • Related Report
      2009 Final Research Report
  • [Presentation] What we can estimate about singularity from random samples2008

    • Author(s)
      Sumio Watanabe
    • Organizer
      Seasonal Institute of the mathematical society of Japan
    • Place of Presentation
      Kyoto, Japan
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] Algebraic geometrical method in singular statistical estimation2008

    • Author(s)
      Sumio Watanabe
    • Organizer
      Albebraic Statistics
    • Place of Presentation
      Berkeley, USA
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] Almost All Learning Machines are Singular2007

    • Author(s)
      S. Watanabe
    • Organizer
      Proc. of FOCI
    • Place of Presentation
      Hawaii, USA
    • Year and Date
      2007-04-04
    • Related Report
      2007 Annual Research Report
  • [Presentation] Experimental Bayesian generalization error of nonregular models in covariate shift2007

    • Author(s)
      K. Yamazaki, S. Watanabe
    • Organizer
      Proc. of ICONIP2007
    • Place of Presentation
      Kitakyushu, Japan
    • Related Report
      2009 Final Research Report
  • [Presentation] Experimental Analysis of Exchange Ratio in Exchange Monte Carlo Method2007

    • Author(s)
      Kenji Nagata, S. Watanabe
    • Organizer
      Proc. of ICONIP2007
    • Place of Presentation
      Kitakyushu, Japan
    • Related Report
      2009 Final Research Report
  • [Presentation] Generalization Error of Automatic Relevance Determination2007

    • Author(s)
      S. Nakajima, S. Watanabe
    • Organizer
      Proc. of ICANN, 2007
    • Place of Presentation
      Porto, Portugal
    • Related Report
      2009 Final Research Report
  • [Presentation] On a Singular Point to Contribute to a Learning Coefficient and Weighted Resolution of Singularities2007

    • Author(s)
      T. Matsuda, S. Watanabe
    • Organizer
      Proc. of ICANN
    • Place of Presentation
      Porto, Portugal
    • Related Report
      2009 Final Research Report
  • [Presentation] Theoretical Analysis of Accuracy of Gaussian Belief Propagation2007

    • Author(s)
      Y. Nishiyama, S. Watanabe
    • Organizer
      Proc. of ICANN
    • Place of Presentation
      Porto, Portugal
    • Related Report
      2009 Final Research Report
  • [Presentation] Algebraic Geometric Study of Exchange Monte Carlo Method2007

    • Author(s)
      K. Nagata, S. Watanabe
    • Organizer
      Proc. of ICANN
    • Place of Presentation
      Porto, Portugal
    • Related Report
      2009 Final Research Report
  • [Presentation] Estimation of Poles of Zeta Function in Learning Theory Using Pade Approximation2007

    • Author(s)
      R. Iriguchi, S. Watanabe
    • Organizer
      Proc. of ICANN
    • Place of Presentation
      Porto, Portugal
    • Related Report
      2009 Final Research Report
  • [Presentation] Resolution of Singularities and Stochastic Complexity of Complete Bipartite Graph-Type Spin Model in Bayesian Estimation2007

    • Author(s)
      M. Aoyagi, S. Watanabe
    • Organizer
      Proc. of MDAI
    • Place of Presentation
      Kitakyushu, Japan
    • Related Report
      2009 Final Research Report
  • [Presentation] Asymptotic Bayesian Generalization Error When Training and Test Distributions Are Different2007

    • Author(s)
      K. Yamazaki, M. Kawanabe, S. Watanabe, M. Sugiyama, K. -R. Muller
    • Organizer
      Proc. of ICML
    • Place of Presentation
      Corvallis, Oregon, USA
    • Related Report
      2009 Final Research Report
  • [Presentation] Analysis of Exchange Ratio for Exchange Monte Carlo Method2007

    • Author(s)
      K. Nagata, S. Watanabe
    • Organizer
      Proc. of FOCI2007
    • Place of Presentation
      Honolulu, Hawaii
    • Related Report
      2009 Final Research Report
  • [Presentation] Almost All Learning Machines are Singular2007

    • Author(s)
      S. Watanabe
    • Organizer
      Proc. of FOCI
    • Place of Presentation
      Honolulu, Hawaii
    • Related Report
      2009 Final Research Report
  • [Presentation] Generalization Error of Three Layered Learning Model in Bayesian Estimation2006

    • Author(s)
      M. Aoyagi, S. Watanabe
    • Organizer
      Proc. of the 2nd IASTED International Conference on Computational Intelligence
    • Place of Presentation
      San Francisco, California, USA
    • Related Report
      2009 Final Research Report
  • [Presentation] Free Energy of Stochastic Context Free Grammar on Variational Bayes2006

    • Author(s)
      T. Hosino, K. Watanabe, S. Watanabe
    • Organizer
      Proc. of ICONIP
    • Place of Presentation
      Honkong, China
    • Related Report
      2009 Final Research Report
  • [Presentation] Localized Bayes Estimation for Non-identifiable Models2006

    • Author(s)
      S. Takamatsu, S. Nakajima, S. Watanabe
    • Organizer
      Proc. of International Conference on Neural Information Processing
    • Place of Presentation
      Honkong, China
    • Related Report
      2009 Final Research Report
  • [Presentation] Asymptotic Behavior of Stochastic Complexity of Complete Bipartite Graph-Type Boltzmann Machines2006

    • Author(s)
      Yu Nishiyama, S. Watanabe
    • Organizer
      Proc. of ICONIP
    • Place of Presentation
      Honkong, China
    • Related Report
      2009 Final Research Report
  • [Presentation] Upper bounds for variational stochastic complexities of Bayesian networks2006

    • Author(s)
      K. Watanabe, M. Shiga, S. Watanabe
    • Organizer
      Proc. of International Conference on Intelligent Data Engineering and Automated Learning
    • Place of Presentation
      Burgos, Spain
    • Related Report
      2009 Final Research Report
  • [Presentation] Generalization Performance of Exchange Monte Carlo Method for Normal Mixture Models2006

    • Author(s)
      K. Nagata, S. Watanabe
    • Organizer
      Proc. of 7th International Conference on Intelligent Data Engineering and Automated Learning
    • Place of Presentation
      Burgos, Spain
    • Related Report
      2009 Final Research Report
  • [Presentation] Analytic Equivalence of Bayes a Posteriori Distributions2006

    • Author(s)
      T. Matsuda, S. Watanabe
    • Organizer
      Proc. of ICANN
    • Place of Presentation
      Athens, Greece
    • Related Report
      2009 Final Research Report
  • [Presentation] A Model Selection Method Based on Bound of Learning Coefficient2006

    • Author(s)
      K. Yamazaki, K. Nagata, S. Watanabe, Klaus-Robert Muller
    • Organizer
      Proc. of ICANN
    • Place of Presentation
      Athens, Greece
    • Related Report
      2009 Final Research Report
  • [Presentation] Analytic Solution of Hierarchical Variational Bayes in Linear Inverse Problem2006

    • Author(s)
      S. Nakajima, S. Watanabe
    • Organizer
      Proc. of International Conference on Artificial Neural Networks
    • Place of Presentation
      Athens, Greece
    • Related Report
      2009 Final Research Report
  • [Presentation] The Exchange Monte Carlo Method for Bayesian Learning in Singular Learning Machines2006

    • Author(s)
      K. Nagata, S. Watanabe
    • Organizer
      Proc. of IEEE World Congress on Computational Intelligence
    • Place of Presentation
      Vancouver, Canada
    • Related Report
      2009 Final Research Report
  • [Book] 特異モデルの学習理論(数理科学事典)2010

    • Author(s)
      渡邊澄夫
    • Publisher
      丸善
    • Related Report
      2009 Annual Research Report
  • [Book] Algebraic Geometry and Statistical Learning Theory2009

    • Author(s)
      Watanabe
    • Publisher
      Cambridge University Press
    • Related Report
      2009 Final Research Report
  • [Book] Algebraic geometry and statistical learning theory2009

    • Author(s)
      渡邊澄夫
    • Publisher
      Cambridge University Press
    • Related Report
      2009 Annual Research Report
  • [Book] lgebraic Geometrical Method in Singular Statistical Estimation, in Quantum Bio-Informatics2008

    • Author(s)
      S. Watanabe
    • Publisher
      World Scientific(Singapole)
    • Related Report
      2008 Self-evaluation Report
  • [Book] Quantum Bio-Informatics2008

    • Author(s)
      Sumio Watanabe
    • Total Pages
      452
    • Publisher
      Algebraic geometrical method in singular statistical estimation
    • Related Report
      2008 Annual Research Report
  • [Book] Quantum Bio-Informatics2008

    • Author(s)
      Sumio Watanabe
    • Total Pages
      455
    • Publisher
      World Scientific
    • Related Report
      2007 Annual Research Report
  • [Book] 代数幾何と学習理論2006

    • Author(s)
      渡辺澄夫
    • Total Pages
      218
    • Publisher
      森北出版
    • Related Report
      2008 Self-evaluation Report 2006 Annual Research Report
  • [Remarks]

    • URL

      http://watanabe-www.pi.titech.ac.jp/~swatanab/index-j.html

    • Related Report
      2009 Final Research Report
  • [Remarks]

    • URL

      http://watanabe-www.pi.titech.ac.jp/~swatanab/

    • Related Report
      2009 Annual Research Report
  • [Remarks] ホームページ

    • URL

      http://watanabe-www.pi.titech.ac.jp/~swatanab/index-j.html

    • Related Report
      2008 Self-evaluation Report
  • [Remarks]

    • URL

      http://watanabe-www.pi.titech.ac.jp/~swatanab/index-j.html

    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://watanabe-www.pi.titech.ac.jp/~swatanab/index-j.html

    • Related Report
      2007 Annual Research Report

URL: 

Published: 2006-04-01   Modified: 2018-03-28  

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