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Paper & Talks

  1. Consideration on Singularities in Learning Theory and the Learning Coefficient, Entropy, vol. 15, No. 9, 3714-3733, 2013. paper.pdf.
  2. Learning coefficient in Bayesian estimation of restricted Boltzmann machine, Journal of Algebraic Statistics, vol. 4, No. 1, 30-57, 2013. paper.pdf.
  3. [Invited lecture] Learning coefficient and singular fluctuation in statistical learning theory, Algebraic Statistics in the Alleghenies(代数統計学), The Pennsylvania State University, USA, June, 2012. http://www.math.psu.edu/morton/aspsu2012/.
  4. [Invited lecture] Consideration on singularities in learning theory and real log canonical threshold, Singular learning theory: connecting algebraic geometry and model selection in statistics(特異学習理論：代数幾何学とモデル選択解析), AIM Research Conference Center (ARCC), Palo Alto, USA, December, 2011.
  5. (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.
  6. A 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.
  7. Stochastic Complexity and Generalization Error of a Restricted Boltzmann Machine in Bayesian Estimation, Journal of Machine Learning Research, vol. 11(Apr), 1243 – 1272, 2010paper.pdf.
  8. (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.
  9. (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.
  10. Log 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.
  11. (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.
  12. (With S. Watanabe) Stochastic Complexities of Reduced Rank Regression in Bayesian Estimation, Neural Networks, (2005) No. 18, pp.924-933.paper.pdf.
  13. (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
    論文(Japanese).pdf
    paper.pdf.
  14. (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.
  15. Dimca hypersurfaces and Nagata automorphisms, Mathematische Nachrichten, WILEY-VCH Verlag Berlin GmbH, vol. 218 (2000), pp. 175-184.
  16. Special 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・Basel), (2000), Chapter 57 pp. 549-581.
  17. Identification of density distribution with time parameter, Recent Developments in Complex Analysis and Computer Algebra, Kluwer Publisher (Netherlands, Utrecht), (1998), pp. 311-322.
  18. (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.
  19. (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.
  20. (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.
  21. On a problem of Ohsawa, Geometric Complex Analysis, World Scientific (Singapore・New Jersey・London・Hon Kong), (1996) pp. 617-621.
  22. (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.
  23. Counterexample 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.
  24. (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.

Books

  1. (渡辺澄夫, 萩原克幸, 赤穂昭太郎, 本村陽一, 福水健次, 岡田真人と共著） 学習システムの理論と実現, 森北出版, p.195
    青柳担当：第７章 特異点解消と学習システム への応用，

Invited Talks

  1. Learning coefficient and singular fluctuation in statistical learning theory, Algebraic Statistics in the Alleghenies(代数統計学), The Pennsylvania State University, USA. July, 2012.
  2. Consideration 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
  3. Resolution of singularities and its application to learning theory, IEICE, 2003

Proceedings

  1. The 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.
  2. (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.
  3. (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.
  4. (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.
  5. (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.
  6. (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.
  7. (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.
  8. (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.
    paper.pdf.
  9. (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.
  10. Artin component and Weyl group for dihedral singularity, RIMS Kokyuroku, (2003) No. 1314, pp.11-27.
  11. Deformation spaces of quotient surface singularities, Proceedings of the eighth international colloquium on complex analysis, (2000), pp. 229–223.
  12. Deformation of singularities via quivers, Proceedings of the Second ISAAC Congress, Kluwer Academic Publisher (Dortrect・Boston・London), (2000), Chapter {95}, pp. 839–848.
  13. Geometric Consideration of Extension Problem, RIMS Kokyuroku, (1998) No. 1058, pp.129-141.
  14. Extension Problem of Holomorphic Functions, RIMS Kokyuroku, CR geometry and isolated singularites conference, (1998) No. 1037, pp. 116-121.
  15. Numerical 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.
  16. Identification 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.
  17. (With J. Kajiwara, C. L. Parihar and V. M. Raffee) Numerical Analysis on ∂-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.
  18. Multi-Peak System Identification with Gauss-Weierstrass Transform, Proceedings of the Sixth International Colloquium on Differential Equations, VSP (Netherlands, Utrecht) (1996) pp. 305-312.
  19. Continuation 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.
  20. (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.
  21. (With J. Kajiwara and V. M. Raffee) Numerical Methods for ∂-Problem, Proceedings of the Beijing Workshop on Finite or Infinite Dimensional Complex Analysis, Beijing, China, 3-5, August (1996) pp. 23-33.
  22. (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.
  23. (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.
  24. A Multi-Peak System Identification, Proceedings of the Third International Colloquium on Numerical Analysis, VSP (Netherlands, Utrecht) (1995), pp.191-200.
  25. (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.
  26. (With J. Kajiwara) Inverse Formula for Laplace Transform, Proceedings of the Fifth International Colloquium on Differential Equations, VSP (Netherlands, Utrecht) (1995) pp. 163-172.
  27. (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.
  28. Domains 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.

Paper of Workshop

  1. (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.
  2. (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.
  3. (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.
    paper.pdf.
  4. (With S. Watanabe) The Generalization Error of Reduced Rank Regression Models and Resolution of Singularities, Technical report of IEICE, NC2004, (2004), pp. 13–18.
    paper.pdf.