{"id":69,"date":"2014-12-19T01:51:15","date_gmt":"2014-12-18T16:51:15","guid":{"rendered":"http:\/\/www2.math.cst.nihon-u.ac.jp\/aoyagi\/?page_id=69"},"modified":"2025-02-04T20:57:19","modified_gmt":"2025-02-04T11:57:19","slug":"publication","status":"publish","type":"page","link":"http:\/\/www2.math.cst.nihon-u.ac.jp\/aoyagi\/publication","title":{"rendered":"Publication"},"content":{"rendered":"
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Paper & Talks<\/h3>\n
    \n
  1. \n\t\t\t\tConsideration on the learning efficiency of multiple-layered neural networks with linear units, Neural Networks 172 (2024) 106132, p. 1-11.
    \nDOI https:\/\/doi.org\/10.1016\/j.neunet.2024.106132 paper.pdf.<\/a><\/li>\n
  2. \n\t\t\t\tLeaning coefficients for hierarchical learning models in Bayesian estimation, Algebraic and geometric methods in inference in 2023 Joint Statistical Meetings, Toronto Canada. paper.pdf.<\/a><\/li>\n
  3. \n\t\t\t\tLearning coefficients and information criteria, Frontiers in Artificial Intelligence and Applications, DOI 10.3233\/FAIA190199, 2019, pp. 351 – 362. paper.pdf.<\/a><\/li>\n
  4. \n\t\t\t\tLearning Coefficient of Vandermonde Matrix-Type Singularities in Model Selection, Entropy (Information Theory, Probability and Statistics), 2019, 21(6), 561;
    \nhttps:\/\/doi.org\/10.3390\/e21060561, pp. 1 – 12.
    \n    paper.pdf.<\/a><\/li>\n
  5. \n\t\t\t\tLearning coefficients and reproducing true probability functions in learning systems, New Trends in Analysis and Interdisciplinary Applications, Trends in Mathematics, DOI 10.1007\/978-3-319-48812-7, 44, Springer, 2017, pp. 347 – 353.<\/li>\n
  6. \n\t\t\t\tConsideration on Singularities in Learning Theory and the Learning Coefficient, Entropy, vol. 15, No. 9, 3714-3733, 2013. paper.pdf.<\/a><\/li>\n
  7. \n\t\t\t\tLearning coefficient in Bayesian estimation of restricted Boltzmann machine, Journal of Algebraic Statistics, vol. 4, No. 1, 30-57, 2013. paper.pdf.<\/a><\/li>\n
  8. \n\t\t\t\t[Invited lecture] Learning coefficient and singular fluctuation in statistical learning theory, Algebraic Statistics in the Alleghenies(\u4ee3\u6570\u7d71\u8a08\u5b66), The Pennsylvania State University, USA, June, 2012. http:\/\/www.math.psu.edu\/morton\/aspsu2012\/. <\/a><\/li>\n
  9. \n\t\t\t\t[Invited lecture] Consideration on singularities in learning theory and real log canonical threshold, Singular learning theory: connecting algebraic geometry and model selection in statistics(\u7279\u7570\u5b66\u7fd2\u7406\u8ad6\uff1a\u4ee3\u6570\u5e7e\u4f55\u5b66\u3068\u30e2\u30c7\u30eb\u9078\u629e\u89e3\u6790), AIM Research Conference Center (ARCC), Palo Alto, USA, December, 2011.<\/li>\n
  10. \n\t\t\t\t(With Kenji Nagata) Learning coefficient of generalization error in Bayesian estimation and Vandermonde matrix type singularity, Neural Computation, vol. 24, No. 6, 1569 -1610, 2012paper.pdf.<\/a><\/li>\n
  11. \n\t\t\t\tA Bayesian Learning Coefficient of Generalization Error and Vandermonde Matrix-Type Singularities, Communications in Statistics – Theory and Methods, vol. 39, No.15, 2667 – 2687, 2010paper.pdf.<\/a><\/li>\n
  12. \n\t\t\t\tStochastic Complexity and Generalization Error of a Restricted Boltzmann Machine in Bayesian Estimation, Journal of Machine Learning Research, vol. 11(Apr), 1243 – 1272, 2010paper.pdf.<\/a><\/li>\n
  13. \n\t\t\t\t(With K. Yamazaki and S. Watanabe) Asymptotic Analysis of Bayesian Generalization Error with Newton Diagram, Neural Networks, vol. 23, No.1, 35 – 43, 2010. paper.pdf.<\/a><\/li>\n
  14. \n\t\t\t\t(With S. Watanabe) The zeta function for learning theory and resolution of singularities, More Progresses in Analysis, World Scientific, pp. 279 – 288, 2009. paper.pdf.<\/a><\/li>\n
  15. \n\t\t\t\tLog canonical threshold of Vandermonde matrix type singularities and generalization error of a three layered neural network in Bayesian estimation, International Journal of Pure and Applied Mathematics, vol. 52, No. 2, 177-204, 2009.paper.pdf.<\/a><\/li>\n
  16. \n\t\t\t\t(With S. Watanabe) Resolution of Singularities and and Stochastic Complexity of Complete Bipartite Graph-Type Spin Model in Bayesian Estimation, Modeling Decisions for Artificial Intelligence, Lecture Notes in Artificial Intelligence, Springer-Verlag, (2007) No. 4617, pp. 443-454. paper.pdf.<\/a><\/li>\n
  17. \n\t\t\t\t(With S. Watanabe) Stochastic Complexities of Reduced Rank Regression in Bayesian Estimation, Neural Networks, (2005) No. 18, pp.924-933.paper.pdf.<\/a><\/li>\n
  18. \n\t\t\t\t(With S. Watanabe) Resolution of Singularities and the Generalization Error with Bayesian Estimation for Layered Neural Network, IEICE Vol.J88-D-II, No. 10, pp.2112-2124, 2005
    \n    \u8ad6\u6587(Japanese).pdf<\/a>
    \n    paper.pdf.<\/a><\/li>\n
  19. \n\t\t\t\t(With K. Tsuji) Recognition of planar shapes by a semi-differential invariant for moving triangles, Journal of Computational and Applied Mathematics, Elsevier Science, vol. 152\/1-2, (2003) pp. 533-544.<\/li>\n
  20. \n\t\t\t\tDimca hypersurfaces and Nagata automorphisms, Mathematische Nachrichten, WILEY-VCH Verlag Berlin GmbH, vol. 218 (2000), pp. 175-184.<\/li>\n
  21. \n\t\t\t\tSpecial reflexive modules and the first Chern class, Finite or Infinite Dimensional Complex Analysis, Lecture Notes in Pure and Applied Mathematics 214, Marcel Dekker Inc, (New York\u30fbBasel), (2000), Chapter 57 pp. 549-581.<\/li>\n
  22. \n\t\t\t\tIdentification of density distribution with time parameter, Recent Developments in Complex Analysis and Computer Algebra, Kluwer Publisher (Netherlands, Utrecht), (1998), pp. 311-322.<\/li>\n
  23. \n\t\t\t\t(With J. Kajiwara and K. H. Shon) Parameter Analysis, Recent Developments in Complex Analysis and Computer Algebra, Kluwer Publisher (Netherlands, Utrecht), (1998), pp. 155-168.<\/li>\n
  24. \n\t\t\t\t(With M. Abe and M. Furushima) Equicontinuity Domain and the Disk Property, Complex Variables Theory and Application, Gordon and Breach Science Publishers (Basel, Switzerland), vol. 39 (1998), pp. 19-25.<\/li>\n
  25. \n\t\t\t\t(With J. Kajiwara and K. H. Shon) Localization of global existence of holomorphic solutions of holomorphic differential equations with infinite dimensional parameter, Czechoslovak Mathematical Journal (Praha), vol. 48(123) (1998), pp. 687-700.<\/li>\n
  26. \n\t\t\t\tOn a problem of Ohsawa, Geometric Complex Analysis, World Scientific (Singapore\u30fbNew Jersey\u30fbLondon\u30fbHon Kong), (1996) pp. 617-621.<\/li>\n
  27. \n\t\t\t\t(With H. Hamada) Counterexample of a bounded domain for Ohsawa’s problem, Complex Variables Theory and Application, Gordon and Breach Science Publishers (Basel, Switzerland), vol. 28 (1996), pp. 285-287.<\/li>\n
  28. \n\t\t\t\tCounterexample of an unbounded domain for Ohsawa’s problem, Complex Variables Theory and Application, Gordon and Breach Science Publishers (Basel, Switzerland), vol. 27 (1995), pp. 335-338.<\/li>\n
  29. \n\t\t\t\t(With J. Kajiwara and L. Li) Real Zeros of Holomorphic Functions with Parameters II: Complex Numerical Integration Using Fortran 77, Math. J. Toyama Univ. vol. 16(1993), pp. 195 – 216.<\/li>\n<\/ol>\n<\/section>\n
    \n

    Books<\/h3>\n
      \n
    1. \n\t\t\t\t(\u6e21\u8fba\u6f84\u592b, \u8429\u539f\u514b\u5e78, \u8d64\u7a42\u662d\u592a\u90ce, \u672c\u6751\u967d\u4e00, \u798f\u6c34\u5065\u6b21, \u5ca1\u7530\u771f\u4eba\u3068\u5171\u8457\uff09 \u5b66\u7fd2\u30b7\u30b9\u30c6\u30e0\u306e\u7406\u8ad6\u3068\u5b9f\u73fe, \u68ee\u5317\u51fa\u7248, p.195
      \n\u9752\u67f3\u62c5\u5f53\uff1a\u7b2c\uff17\u7ae0 \u7279\u7570\u70b9\u89e3\u6d88\u3068\u5b66\u7fd2\u30b7\u30b9\u30c6\u30e0 \u3078\u306e\u5fdc\u7528\uff0c<\/li>\n<\/ol>\n<\/section>\n
      \n

      Invited Talks<\/h3>\n
        \n
      1. \n\t\t\t\tLearning coefficient and singular fluctuation in statistical learning theory, Algebraic Statistics in the Alleghenies(\u4ee3\u6570\u7d71\u8a08\u5b66), The Pennsylvania State University, USA. July, 2012.<\/li>\n
      2. \n\t\t\t\tConsideration on singularities in learning theory and real log canonical threshold, Singular learning theory: connecting algebraic geometry and model selection in statistics, AIM Research Conference Center (ARCC), Palo Alto, USA. 2011<\/li>\n
      3. \n\t\t\t\tResolution of singularities and its application to learning theory, IEICE, 2003<\/li>\n<\/ol>\n<\/section>\n
        \n

        Proceedings<\/h3>\n
          \n
        1. \n\t\t\t\tThe zeta function of learning theory and generalization error of three layered neural perceptron, RIMS Kokyuroku, Recent Topics on Real and Complex Singularities, (2006) (in press) paper.pdf.<\/a><\/li>\n
        2. \n\t\t\t\t(With Sumio Watanabe) Generalization Error of Three Layered Learning Model in Bayesian Estimation, Proceedings of the Second IASTED International Conference on Computational Intelligence, (San Francisco, California, USA), (2006), pp.405–410. paper.pdf.<\/a><\/li>\n
        3. \n\t\t\t\t(With K. Tsuji) Eye Direction by Stereo Image Processing using Corneal Reflection on an Iris, Proceedings of the Second IASTED International Conference on Computational Intelligence, (San Francisco, California, USA), (2006), pp.355–360.paper.pdf.<\/a><\/li>\n
        4. \n\t\t\t\t(With K. Tsuji) A modified genetic algorithm for feature clustering, Proceedings of The 12th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, Kyushu University Press, (2005), pp.9–16.paper.pdf.<\/a><\/li>\n
        5. \n\t\t\t\t(With S. Watanabe) The maximum pole of the zeta function for learning theory, Proceedings of The 12th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, Kyushu University Press, (2005), pp.17–24.paper.pdf.<\/a><\/li>\n
        6. \n\t\t\t\t(With K. Yamazaki and S. Watanabe) Stochastic Complexity and Newton Diagram, International Symposium on Information Theory and its Applications, (Parma, Italy), (2004), pp. 105–110.paper.pdf.<\/a><\/li>\n
        7. \n\t\t\t\t(With K. Tsuji) A modified genetic algorithm for image segmentation based on feature clustering, International Symposium on Information Theory and its Applications, (Parma, Italy), (2004), pp. 1074–1079. paper.pdf.<\/a><\/li>\n
        8. \n\t\t\t\t(With S. Watanabe) The Generalization Error of Reduced Rank Regression in Bayesian Estimation, International Symposium on Information Theory and its Applications, (Parma, Italy), (2004), pp. 1068–1073.
          \n          paper.pdf.<\/a><\/li>\n
        9. \n\t\t\t\t(With S. Watanabe) Resolution of singularities and its application to learning theory, Technical report of IEICE, NC2003-26, (2003) No. 26, pp.25-30. paper.pdf.<\/a><\/li>\n
        10. \n\t\t\t\tArtin component and Weyl group for dihedral singularity, RIMS Kokyuroku, (2003) No. 1314, pp.11-27.<\/li>\n
        11. \n\t\t\t\tDeformation spaces of quotient surface singularities, Proceedings of the eighth international colloquium on complex analysis, (2000), pp. 229–223.<\/li>\n
        12. \n\t\t\t\tDeformation of singularities via quivers, Proceedings of the Second ISAAC Congress, Kluwer Academic Publisher (Dortrect\u30fbBoston\u30fbLondon), (2000), Chapter {95}, pp. 839–848.<\/li>\n
        13. \n\t\t\t\tGeometric Consideration of Extension Problem, RIMS Kokyuroku, (1998) No. 1058, pp.129-141.<\/li>\n
        14. \n\t\t\t\tExtension Problem of Holomorphic Functions, RIMS Kokyuroku, CR geometry and isolated singularites conference, (1998) No. 1037, pp. 116-121.<\/li>\n
        15. \n\t\t\t\tNumerical Analysis of Real Inverse Formula, Proceedings of the Sixth International Conference on Finite or Infinite Dimensional Complex Analysis, Andong National Univ., Korea, 26-31, July (1998) pp. 151-155.<\/li>\n
        16. \n\t\t\t\tIdentification of Density Distribution due to One-codimensional Projected Figures, Proceedings of the Seventh International Colloquium on Differential Equations, VSP (Netherlands, Utrecht) (1997) pp. 429-436.<\/li>\n
        17. \n\t\t\t\t(With J. Kajiwara, C. L. Parihar and V. M. Raffee) Numerical Analysis on \u2202-Problem and Extension of Holomorphic Functions from Lower Dimensional Subvarieties, Proceedings of the Seventh International Colloquium on Differential Equations, VSP (Netherlands, Utrecht) (1997) pp. 181-188.<\/li>\n
        18. \n\t\t\t\tMulti-Peak System Identification with Gauss-Weierstrass Transform, Proceedings of the Sixth International Colloquium on Differential Equations, VSP (Netherlands, Utrecht) (1996) pp. 305-312.<\/li>\n
        19. \n\t\t\t\tContinuation of bounded holomorphic functions from one-codimensional subspace to pseudoconvex domains, Proceedings of the Sixth International Colloquium on Differential Equations, VSP (Netherlands, Utrecht) (1996) pp. 313-320.<\/li>\n
        20. \n\t\t\t\t(With S. Kado and V. M. Raffee) Comparison of Pseudozeros and Pseudospectra for Polynomials with Multiple Zeros, Proceedings of the Fourth International Colloquium on Finite or Infinite Dimensional Complex Analysis, Kumamoto, 29-31, July (1996) pp. 199-214.<\/li>\n
        21. \n\t\t\t\t(With J. Kajiwara and V. M. Raffee) Numerical Methods for \u2202-Problem, Proceedings of the Beijing Workshop on Finite or Infinite Dimensional Complex Analysis, Beijing, China, 3-5, August (1996) pp. 23-33.<\/li>\n
        22. \n\t\t\t\t(With J. Kajiwara and L. Li) Real Zeros of Holomorphic Functions with Parameters IV: Repeated Complex and Real Numerical Integration, Proceedings of the Fourth International Colloquium on Numerical Analysis, Impulse-M (Sofia) (1995), pp. 75-82.<\/li>\n
        23. \n\t\t\t\t(With J. Kajiwara and D. K. Kim) Spectrum for Infinite Dimensional Domains, Proceedings of the Sixth International Colloquium on Differential Equations, Impulse-M (Sofia) (1995), pp. 213-220.<\/li>\n
        24. \n\t\t\t\tA Multi-Peak System Identification, Proceedings of the Third International Colloquium on Numerical Analysis, VSP (Netherlands, Utrecht) (1995), pp.191-200.<\/li>\n
        25. \n\t\t\t\t(With J. Kajiwara and K. H. Shon) Localization of Global Existence of Holomorphic Solutions of Analytic Linear Differential Equations with Infinite Dimensional Parameter, Proceedings of the Third International Colloquium on Finite or Infinite Dimensional Complex Analysis, Seoul, July 31-August 2 (1995) pp. 289-298.<\/li>\n
        26. \n\t\t\t\t(With J. Kajiwara) Inverse Formula for Laplace Transform, Proceedings of the Fifth International Colloquium on Differential Equations, VSP (Netherlands, Utrecht) (1995) pp. 163-172.<\/li>\n
        27. \n\t\t\t\t(With J. Kajiwara) Surfaces Associated to Real Zeros of Holomorphic Functions with Parameters, Proceedings of the Third International Colloquium on Numerical Analysis, VSP (Netherlands, Utrecht) (1995), pp. 107-116.<\/li>\n
        28. \n\t\t\t\tDomains of Definition of Adjoint Operators, Proceedings of the Second Korean-Japanese Colloquium on Finite or Infinite Dimensional Complex Analysis, Fukuoka, 27-29, July (1994) pp. 203-207.<\/li>\n<\/ol>\n<\/section>\n
          \n

          Paper of Workshop<\/h3>\n
            \n
          1. \n\t\t\t\t(With S. Watanabe) Generalization Error of Three-Layer Neural Perceptron in Bayesian Estimation, 2005 Workshop on Information-Based Induction Sciences (2005), pp. 75–80. paper.pdf.<\/a><\/li>\n
          2. \n\t\t\t\t(With S. Watanabe) Desingularization and the Generalization Error of Reduced Rank Regression in Bayesian Estimation, 2004 Workshop on Information-Based Induction Sciences (2004), pp. ?–?.paper.pdf.<\/a><\/li>\n
          3. \n\t\t\t\t(With S. Watanabe and K. Yamazaki) Kullback Information of Normal Mixture is not an Analytic Function, Technical report of IEICE, NC2004, (2004), pp. 41–46.
            \n            paper.pdf.<\/a><\/li>\n
          4. \n\t\t\t\t(With S. Watanabe) The Generalization Error of Reduced Rank Regression Models and Resolution of Singularities, Technical report of IEICE, NC2004, (2004), pp. 13–18.
            \n            paper.pdf.<\/a><\/li>\n<\/ol>\n<\/section>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

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