Updated on 2024/10/02

写真b

 
KOYAMA Tamio
 
*Items subject to periodic update by Rikkyo University (The rest are reprinted from information registered on researchmap.)
Affiliation*
College of Science Department of Mathematics
Title*
Assistant Professor
Degree
博士(理学) （ 神戸大学 ）
Research Interests

  • numerical calculation

  • D-modules

  • holonomic gradient method

  • 計算代数解析

    • Campus Career*
    • 4 2021 - Present 
      College of Science   Department of Mathematics   Assistant Professor
     

    Research Areas

    • Natural Science / Applied mathematics and statistics

    Research History

    • 4 2021 - Present 
      Rikkyo University   College of Science

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    • 4 2020 - 3 2021 
      Wakkanai Hokusei Gakuen College

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      Country：Japan

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    • 4 2019 - 9 2020 
      Rikkyo University

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      Country：Japan

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    • 4 2018 - 3 2020 
      Chiba Institute of Technology

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      Country：Japan

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    • 4 2018 - 3 2020 
      Rikkyo University   College of Science Department of Mathematics

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      Country：Japan

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    • 12 2016 - 3 2018 
      Kobe University   Graduate School of Science Division of Mathematics

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      Country：Japan

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    • 4 2016 - 11 2016 
      Shiga University   Center for Data Science Education and Research

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      Country：Japan

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    • 4 2014 - 3 2016 
      The University of Tokyo   The Graduate School of Information Science and Technology

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    Education

    • 4 2012 - 3 2014 
      Kobe University   Graduate School of Science   Division of Mathematics

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    • 4 2010 - 3 2012 
      Kobe University   Graduate School of Science   Division of Mathematics

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    • 4 2008 - 3 2010 
      Kobe University   Faculty of Science   Department of Mathematics

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    • 4 2003 - 3 2008 
      Gunma National College of Technology   Civil Engineering

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    Papers

    • Holonomic gradient method for two-way contingency tables

      Yoshihito Tachibana, Yoshiaki Goto, Tamio Koyama, Nobuki Takayama

      Algebraic Statistics11 ( 2 ) 125 - 153   28 12 2020

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      Publishing type：Research paper (scientific journal)   Publisher：Mathematical Sciences Publishers  

      DOI： 10.2140/astat.2020.11.125

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    • Numerical Calculation of the Fisher-Bingham Integral by the Holonomic Gradient Method Peer-reviewed

      T.Koyama

      2018 21st International Conference on Information Fusion (FUSION)   720 - 723   2018

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      Authorship：Lead author   Language：English   Publishing type：Research paper (international conference proceedings)  

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    • Holonomic gradient method for distribution function of a weighted sum of noncentral chi-square random variables Peer-reviewed

      Tamio Koyama, Akimichi Takemura

      COMPUTATIONAL STATISTICS31 ( 4 ) 1645 - 1659   12 2016

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER HEIDELBERG  

      We apply the holonomic gradient method to compute the distribution function of a weighted sum of independent noncentral chi-square random variables. It is the distribution function of the squared length of a multivariate normal random vector. We treat this distribution as an integral of the normalizing constant of the Fisher-Bingham distribution on the unit sphere and make use of the partial differential equations for the Fisher-Bingham distribution.

      DOI： 10.1007/s00180-015-0625-3

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    • Application of an integer-valued autoregressive model to hit phenomena Peer-reviewed

      Yasuko Kawahata, Tamio Koyama

      Proceedings - 2016 IEEE International Conference on Big Data, Big Data 2016   2513 - 2517   2016

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      Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Institute of Electrical and Electronics Engineers Inc.  

      We propose a new model for hit phenomena. Our model is based on the Integer-Valued autoregressive model in form of a stochastic difference equation, and it describes behaviors of count data sequences. Utilizing our model, we give a theoretical formulation of the concept 'hit', and a systematic method deciding whether given time series count data contains 'hit'.

      DOI： 10.1109/BigData.2016.7840890

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    • Holonomic modules associated with multivariate normal probabilities of Polyhedra Peer-reviewed

      Tamio Koyama

      Funkcialaj Ekvacioj59 ( 2 ) 217 - 242   2016

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：KOBE UNIV  

      The probability content of a convex polyhedron with a multivariate normal distribution can be regarded as a real analytic function. We give a system of linear partial differential equations with polynomial coefficients for the function and show that the system induces a holonomic module. The rank of the holonomic module is equal to the number of nonempty faces of the convex polyhedron, and we provide an explicit Pfaffian equation (an integrable connection) that is associated with the holonomic module. These are generalizations of results for the Schläfli function that were given by Aomoto.

      DOI： 10.1619/fesi.59.217

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    • Calculation of orthant probabilities by the holonomic gradient method Peer-reviewed

      Tamio Koyama, Akimichi Takemura

      JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS32 ( 1 ) 187 - 204   3 2015

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER JAPAN KK  

      We apply the holonomic gradient method (Nakayama et al. Adv Appl Math 47:639-658,2011) to the calculation of the probabilities of the multivariate normal distribution. The holonomic gradient method applied to finding the orthant probabilities is found to be a variant of Plackett's recurrence relation. However, an implementation of the method yields recurrence relations that are more suitable for numerical computation than is Plackett's recurrence relation. We derive some theoretical results on the holonomic system for the orthant probabilities. These results show that multivariate normal orthant probabilities possess some remarkable properties from the viewpoint of holonomic systems. Finally, we show that the numerical performance of our method is comparable or superior to that of existing methods.

      DOI： 10.1007/s13160-015-0166-8

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    • The holonomic rank of the Fisher-Bingham system of differential equations Peer-reviewed

      Tamio Koyama, Hiromasa Nakayama, Kenta Nishiyama, Nobuki Takayama

      JOURNAL OF PURE AND APPLIED ALGEBRA218 ( 11 ) 2060 - 2071   11 2014

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

      The Fisher-Bingham system is a system of linear partial differential equations satisfied by the Fisher-Bingham integral for the n-dimensional sphere S-n. The system is given in [4, Theorem 2] and it is shown that it is a holonomic system [1]. We show that the holonomic rank of the system is equal to 2n + 2. (C) 2014 Elsevier B.V. All rights reserved.

      DOI： 10.1016/j.jpaa.2014.03.004

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    • Holonomic gradient descent for the Fisher-Bingham distribution on the d-dimensional sphere Peer-reviewed

      Tamio Koyama, Hiromasa Nakayama, Kenta Nishiyama, Nobuki Takayama

      COMPUTATIONAL STATISTICS29 ( 3-4 ) 661 - 683   6 2014

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER HEIDELBERG  

      We propose an accelerated version of the holonomic gradient descent and apply it to calculating the maximum likelihood estimate (MLE) of the Fisher-Bingham distribution on a -dimensional sphere. We derive a Pfaffian system (an integrable connection) and a series expansion associated with the normalizing constant with an error estimation. These enable us to solve some MLE problems up to dimension with a specified accuracy.

      DOI： 10.1007/s00180-013-0456-z

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    • Software packages for holonomic gradient method Peer-reviewed

      Tamio Koyama, Hiromasa Nakayama, Katsuyoshi Ohara, Tomonari Sei, Nobuki Takayama

      Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)8592   706 - 712   2014

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      Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Springer Verlag  

      We present software packages for the holonomic gradient method (HGM). These packages compute normalizing constants and the probabilities of some regions. While many algorithms which compute integrals over high-dimensional regions utilize the Monte-Carlo method, our HGM utilizes algorithms for solving ordinary differential equations such as the Runge-Kutta-Fehlberg method. As a result, our HGM can evaluate many integrals with a high degree of accuracy and moderate computational time. The source code of our packages is distributed on our web page [12]. © 2014 Springer-Verlag.

      DOI： 10.1007/978-3-662-44199-2_105

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    • A Holonomic Ideal Which Annihilates the Fisher-Bingham Integral Peer-reviewed

      Tamio Koyama

      FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA56 ( 1 ) 51 - 61   4 2013

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：KOBE UNIV, DEPT MATHEMATICS  

      We calculate the integration ideal of a holonomic ideal which annihilates the non-normalized Fisher-Bingham distribution and show that the integration ideal agrees with the ideal which annihilates the Fisher-Bingham integral given in [9]. They conjectured that this ideal is a holonomic ideal and we prove their conjecture.

      DOI： 10.1619/fesi.56.51

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    Misc.

    Presentations

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    Professional Memberships

    •  
      THE MATHMATICAL SOCIETY OF JAPAN

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    Research Projects

    • ホロノミック勾配法の統計への応用

      日本学術振興会  科学研究費助成事業 

      小山 民雄

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      4 2014 - 3 2016

      Grant number：14J03125

      Grant amount：\2170000 （ Direct Cost: \1900000 、 Indirect Cost：\270000 ）

      【高次元におけるFisher--Bingham積分の計算】HGMの初期値計算の工夫と、Fisher-Bingham積分(とその微分)のラプラス近似を元にした常微分方程式系の改良により、従来では、次元が$7$以下の場合でしか計算が行えなかったFisher--Bingham積分の数値計算を、次元が$100$の場合でも可能にすることに成功した。この結果は、竹村彰通教授との共著論文``Holonomic gradient method for distribution function of a weighted sum of noncentral chi-square random variables''として、Computational Statistics に掲載された。
      【多面体領域の正規確率の数値計算に対するHGMの応用】未解決であった、HGMの適用における初期値計算ために必要な理論的な問題を解決した。この問題の解決の為に、Edelsbrunnerによって与えられた凸多面体の指示関数についての包除等式を、多面体の面の指示関数の場合に拡張することを行った。また、理論的な結果を元にして、多面体がsimplexの場合における正規確率を数値計算するプログラムを実装した。これらの結果は、単著論文``Holonomic gradient method for the probability content of a simplex region with a multivariate normal distribution''としてプレプリントを公開した。また、研究において開発したsimplexの正規確率を数値計算するプログラムを\\url{https://github.com/tkoyama-may10/simplex}において公開した。

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