青柳 美輝 (Miki Aoyagi)
EMail: aoyagi.miki AT math.cst.nihon-u dot ac dot jp
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履歴
New Information!
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論文
"Consideration on Singularities in Learning Theory and the
Learning Coefficient,"
雑誌 Entropy に掲載が決定しました。
paper.pdf.
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論文
"Learning coefficient in Bayesian estimation of restricted Boltzmann machine,"
雑誌 Journal of Algebraic Statisticsに掲載が決定しました。
paper.pdf.
Research
Papers and Talks
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Consideration on Singularities in Learning Theory and the
Learning Coefficient,
Entropy, vol. 15, No. 9, 3714-3733, 2013.
paper.pdf.
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Learning coefficient in Bayesian estimation of restricted Boltzmann machine,
Journal of Algebraic Statistics, vol. 4, No. 1, 30-57, 2013.
paper.pdf.
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[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/.
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[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.
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(With Kenji Nagata)
Learning coefficient of generalization error
in Bayesian estimation and Vandermonde matrix type singularity,
Neural Computation,
vol. 24, No. 6, 1569 -1610, 2012
paper.pdf.
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A Bayesian Learning Coefficient of Generalization Error and
Vandermonde Matrix-Type Singularities,
Communications in Statistics -
Theory and Methods, vol. 39, No.15, 2667 - 2687, 2010
paper.pdf.
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Stochastic Complexity and Generalization Error of a Restricted Boltzmann
Machine in Bayesian Estimation,
Journal of Machine Learning Research,
vol. 11(Apr), 1243 - 1272, 2010
paper.pdf.
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(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.
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(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.
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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.
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(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.
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(With S. Watanabe)
Stochastic Complexities
of Reduced Rank Regression in Bayesian Estimation,
Neural Networks,
(2005) No. 18, pp.924-933.
paper.pdf
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(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
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(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.
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Dimca hypersurfaces and Nagata automorphisms,
Mathematische Nachrichten,
WILEY-VCH Verlag Berlin GmbH, vol. 218 (2000), pp. 175-184.
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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.
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Identification of density distribution
with time parameter,
Recent Developments in Complex Analysis and Computer Algebra,
Kluwer Publisher (Netherlands, Utrecht), (1998), pp. 311-322.
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(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.
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(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.
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(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.
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On a problem of Ohsawa,
Geometric Complex Analysis, World Scientific (Singapore・New Jersey・London・Hon Kong), (1996) pp. 617-621.
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(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.
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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.
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(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
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(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
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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.
-
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
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Resolution of
singularities and its application to learning theory,
IEICE, 2003
Proceedings
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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.
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(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
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(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
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(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
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(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
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(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
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(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
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(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
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(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
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Artin component and Weyl group for dihedral singularity,
RIMS Kokyuroku,
(2003) No. 1314, pp.11-27.
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Deformation spaces of quotient surface singularities,
Proceedings of the eighth international colloquium
on complex analysis, (2000), pp. 229--223.
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Deformation of singularities via quivers,
Proceedings of the Second ISAAC Congress,
Kluwer Academic Publisher (Dortrect・Boston・London),
(2000), Chapter { 95}, pp. 839--848.
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Geometric Consideration of Extension Problem,
RIMS Kokyuroku, (1998) No. 1058, pp.129-141.
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Extension Problem of Holomorphic Functions,
RIMS Kokyuroku, CR geometry and isolated singularites conference,
(1998) No. 1037, pp. 116-121.
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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.
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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.
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(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.
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Multi-Peak System Identification with Gauss-Weierstrass
Transform,
Proceedings of the Sixth International Colloquium on Differential
Equations, VSP (Netherlands, Utrecht) (1996) pp. 305-312.
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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.
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(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.
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(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.
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(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.
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(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.
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A Multi-Peak System Identification,
Proceedings of the Third International Colloquium on Numerical Analysis, VSP (Netherlands, Utrecht) (1995), pp.191-200.
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(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.
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(With J. Kajiwara)
Inverse Formula for Laplace Transform,
Proceedings of the Fifth International Colloquium on Differential
Equations, VSP (Netherlands, Utrecht) (1995) pp. 163-172.
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(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.
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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
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(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
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(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
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(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
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(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