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Performance improvements of algebraic statistical methods

Research Project

Project/Area Number 18H04092
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Review Section Medium-sized Section 60:Information science, computer engineering, and related fields
Research InstitutionShiga University

Principal Investigator

竹村 彰通  滋賀大学, 役員, 学長 (10171670)

Project Period (FY) 2018-04-01 – 2023-03-31
Project Status Granted (Fiscal Year 2022)
Budget Amount *help
¥43,810,000 (Direct Cost: ¥33,700,000、Indirect Cost: ¥10,110,000)
Fiscal Year 2022: ¥8,580,000 (Direct Cost: ¥6,600,000、Indirect Cost: ¥1,980,000)
Fiscal Year 2021: ¥8,580,000 (Direct Cost: ¥6,600,000、Indirect Cost: ¥1,980,000)
Fiscal Year 2020: ¥8,580,000 (Direct Cost: ¥6,600,000、Indirect Cost: ¥1,980,000)
Fiscal Year 2019: ¥8,580,000 (Direct Cost: ¥6,600,000、Indirect Cost: ¥1,980,000)
Fiscal Year 2018: ¥9,490,000 (Direct Cost: ¥7,300,000、Indirect Cost: ¥2,190,000)
Keywords数理統計学 / 統計的推測 / 仮定 / 仮説検定 / 計算代数統計 / 統計モデル / ホロノミック勾配法 / グレブナー基底 / 多変量解析 / 多数量解析
Outline of Annual Research Achievements

今年度は多変量解析におけるホロノミック法の概要と成果について、次の論文で発表することができた。Akimichi Takemura (2021) Holonomic gradient method for multivariate distribution theory. In: Filipiak K., Markiewicz A., von Rosen D. (eds) Multivariate, Multilinear and Mixed Linear Models. Contributions to Statistics. Springer, Cham. 1-15. doi:10.1007/978-3-030-75494-5_1. この論文では、具体的な例を用いてホロノミック関数の定義や性質をわかりやすく示すとともに、研究代表者によるこれまでのホロノミック勾配法に関する成果を示した。この論文は、Filipiak等の編集による論文集の巻頭論文として収録されたものである。
さらに以下の論文がオンライン刊行済みである。Satoshi Kuriki, Akimichi Takemura, Johathan Taylor (2022) The volume-of-tube method for Gaussian random fields with inhomogeneous variance, https://doi.org/10.1016/j.jmva.2021.104819. この論文では、チューブ法において分散が不均一であるというこれまで扱われていなかった場合について結果を得ており、例題としてはホロノミック勾配法でも扱ったウィシャート行列の最大根の分布の裾確率を評価している。

Current Status of Research Progress
Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

研究実績の概要に示したように,ホロノミック勾配法に関するサーベイ論文、及び、チューブ法で分散が不均一である場合の結果を得て論文として刊行することができた。このような研究は順調に進捗している。

Strategy for Future Research Activity

ホロノミック勾配法の実装においては、1) 初期点の選択と、2) 初期点から目的とする点までの積分経路の選択、の二つの選択が重要である。初期点の選択では原点などの自明な点は微分方程式系の特異点であることが多く、特異点から少し離れた点を初期点とする必要がある。初期点の選択については本研究において経験を積んできたが、積分経路の選択については自然な座標についての直線を用いるなど、これまでは単純な経路を選択しており、積分経路の最適化の検討は不十分であった。特に関数とその微分の絶対値が極端に大きくなったり小さくなったりする経路は避けなければならない。そこで、いくつかの実際的な例題を用いて、関数とその微分の絶対値が一定の範囲におさまるような方向に進んでいくような積分経路の選択のヒューリスティックスについて研究を進める。

Report

(4 results)
  • 2021 Annual Research Report
  • 2020 Annual Research Report
  • 2019 Annual Research Report
  • 2018 Annual Research Report

Research Products

(18 results)

All 2022 2021 2020 2019 2018

All Journal Article (8 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 8 results,  Open Access: 4 results) Presentation (8 results) (of which Int'l Joint Research: 5 results,  Invited: 6 results) Book (2 results)

  • [Journal Article] The volume-of-tube method for Gaussian random fields with inhomogeneous variance2022

    • Author(s)
      Satoshi.Kuriki, Akimichi.Takemura, Jonathan E.Taylor
    • Journal Title

      Journal of Multivariate Analysis

      Volume: vol.188

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Holonomic gradient method for multivariate distribution theory2021

    • Author(s)
      A. Takemura
    • Journal Title

      Multivariate, Multilinear and Mixed Linear Models(Contributions to Statistics)

      Volume: N/A Pages: 1-15

    • DOI

      10.1007/978-3-030-75494-5_1

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Holonomic gradient method for the cumulative distribution function of the largest eigenvalue of a complex Wishart matrix with noncentrality matrix of rank one2020

    • Author(s)
      Yuta Fukasawa and A. Takemura
    • Journal Title

      Recent Developments in Multivariate and Random Matrix Analysis

      Volume: 1 Pages: 83-101

    • DOI

      10.1007/978-3-030-56773-6_6

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Game-theoretic derivation of upper hedging prices of multivariate contingent claims and submodularity2020

    • Author(s)
      T. Matsuda and A. Takemura
    • Journal Title

      Japan J. Indust. Appl. Math.

      Volume: 37 Issue: 1 Pages: 213-248

    • DOI

      10.1007/s13160-019-00394-y

    • NAID

      210000175776

    • ISSN
      0916-7005, 1868-937X
    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithm for self-normalized martingales: a game-theoretic approach.2019

    • Author(s)
      akeyuki Sasai, Kenshi Miyabe and Akimichi Takemura
    • Journal Title

      The Annals of Probability

      Volume: 47 Pages: 1136-1151

    • DOI

      10.1214/18-aop1281

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] A-hypergeometric distributions and Newton polytopes2018

    • Author(s)
      Takayama, N., Kuriki, S. and Takemura, A.
    • Journal Title

      Adv. in Appl. Math.

      Volume: 99 Pages: 109-133

    • DOI

      10.1016/j.aam.2018.05.001

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Differential relations for the largest root distribution of complex non-central Wishart matrices2018

    • Author(s)
      Raimundas Vidunas and Akimichi Takemura
    • Journal Title

      The 50th Anniversary of Groebner basis, edited by Takayuki Hibi, Advanced Studies in Pure Mathematics

      Volume: 77 Pages: 411-436

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A new era of statistics and data science education in Japanese universities2018

    • Author(s)
      Takemura, A.
    • Journal Title

      Japanese Journal of Statistics and Data Science

      Volume: 1 Issue: 1 Pages: 109-116

    • DOI

      10.1007/s42081-018-0005-7

    • ISSN
      2520-8756, 2520-8764
    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Presentation] 健康医療のためのデータサイエンス- 滋賀県長寿の要因分析を例として2020

    • Author(s)
      竹村彰通
    • Organizer
      日本医療マネジメント学会
    • Related Report
      2020 Annual Research Report
  • [Presentation] Holonomic Gradient Method for the Cumulative Distribution Function of the Largest Eigenvalue of a Complex Wishart Matrix with Noncentrality Matrix of Rank One2020

    • Author(s)
      Akimichi Takemura
    • Organizer
      Symposium to celebrate Dietrich von Rosen 65th birthday
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Holonomic gradient method for evaluation of multivariate probabilities2019

    • Author(s)
      Akimichi Takemura
    • Organizer
      The 3rd International Conference on Statistical Distributions and Applications (ICOSDA 2019)
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Progress of statistics and data science education in Japanese universities2019

    • Author(s)
      Akimichi Takemura
    • Organizer
      The 16th Conference of International Federation of Classification Societies
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Holonomic gradient method for multivariate distribution theory2019

    • Author(s)
      Akimichi Takemura
    • Organizer
      Multivariate and Mixed Linear Models (MMLM 2019)
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] データサイエンス学部卒業生の人材像2018

    • Author(s)
      竹村彰通
    • Organizer
      2018年度統計関連学会連合大会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 滋賀大学のデータサインエンス研究科構想について2018

    • Author(s)
      竹村彰通
    • Organizer
      2018年度統計関連学会連合大会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] New Undergraduate Departments and Programs of Data Science in JAPAN2018

    • Author(s)
      Akimichi Takemura
    • Organizer
      The 10th International Conference on Teaching Statistics (ICOTS10)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Book] 新装改訂版 現代数理統計学2020

    • Author(s)
      竹村彰通
    • Total Pages
      368
    • Publisher
      学術図書出版社
    • ISBN
      9784780608601
    • Related Report
      2020 Annual Research Report
  • [Book] 代数的統計モデル2019

    • Author(s)
      青木敏、竹村彰通、原尚幸
    • Total Pages
      272
    • Publisher
      共立出版
    • ISBN
      9784320113534
    • Related Report
      2019 Annual Research Report

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Published: 2018-04-23   Modified: 2022-12-28  

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