Performance improvements of algebraic statistical methods

• Project/Area Number: 18H04092
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 一般
• Review Section: Medium-sized Section 60:Information science, computer engineering, and related fields
• Research Institution: Shiga University
• Principal Investigator: Takemura Akimichi 滋賀大学, 役員, 学長 (10171670)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Project Status: Completed (Fiscal Year 2022)
• Budget Amount: ¥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 / 漸近理論 / 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 Final Research Achievements

In this project, we have conducted research on performance improvements and practical implementation of methods of algebraic statistics. In particular, we focused on the method, called the holonomic gradient method, which uses partial differential equations with rational function coefficients to compute various integrals and probabilities appearing in statistics. Using the holonomic gradient method, we obtained practical results on the complex Wishart distribution, which appears in wireless communication. We also studied the tube method and obtained result on the tail probability of Wishart distribution under general covariance matrices.

Academic Significance and Societal Importance of the Research Achievements

ホロノミック勾配法は研究代表者が2010年頃に代数学者との共同研究の中から考案した新しい手法であり、統計学で必要とされる計算を高速かつ高精度でおこなうことのできる手法である。この方法は、統計学と代数学の双方で新たな研究テーマとなり、活発な研究が行われ、それ以前は困難と思われていたいくつかの数値計算が可能となった。このような数値計算は、統計学にとどまらず様々な分野の計算に用いることができものである。

Research Products

• [Journal Article] The volume-of-tube method for Gaussian random fields with inhomogeneous variance. (2022)
  • Author(s): Satoshi Kuriki, A. Takemura and Jonathan E. Taylor.
  • Journal Title: Journal of Multivariate Analysis Volume: 188 Pages: 104819-104819
  • DOI: 10.1016/j.jmva.2021.104819
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] DX時代のデータサイエンス (2022)
  • Author(s): 竹村 彰通、椎名 洋
  • Journal Title: 都市問題 Volume: 113 Pages: 4-9
• [Journal Article] The volume-of-tube method for Gaussian random fields with inhomogeneous variance (2022)
  • Author(s): Satoshi.Kuriki, Akimichi.Takemura, Jonathan E.Taylor
  • Journal Title: Journal of Multivariate Analysis Volume: vol.188
  • Peer Reviewed / Open Access
• [Journal Article] Holonomic gradient method for multivariate distribution theory (2021)
  • 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
  • ISBN: 9783030754938, 9783030754945
  • 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 one (2020)
  • 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
  • ISBN: 9783030567729, 9783030567736
  • Peer Reviewed
• [Journal Article] Game-theoretic derivation of upper hedging prices of multivariate contingent claims and submodularity (2020)
  • Author(s): T. Matsuda and A. Takemura
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 37 Issue: 1 Pages: 213-248
  • DOI: 10.1007/s13160-019-00394-y
  • NAID: 210000175776
  • 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 Issue: 2 Pages: 1136-1151
  • DOI: 10.1214/18-aop1281
  • Peer Reviewed / Open Access
• [Journal Article] A-hypergeometric distributions and Newton polytopes (2018)
  • Author(s): Takayama, N., Kuriki, S. and Takemura, A.
  • Journal Title: Advances in Applied Mathematics Volume: 99 Pages: 109-133
  • DOI: 10.1016/j.aam.2018.05.001
  • Peer Reviewed
• [Journal Article] Differential relations for the largest root distribution of complex non-central Wishart matrices (2018)
  • 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
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] A new era of statistics and data science education in Japanese universities (2018)
  • 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
  • Peer Reviewed / Open Access
• [Presentation] The volume-of-tube method for Gaussian random fields with inhomogeneous variance (2022)
  • Author(s): Satoshi Kuriki, Akimichi Takemura and Jonathan Taylor
  • Organizer: JMVA 50th Jubilee volume follow-up virtual meeting, April 20, 2022
  • Int'l Joint Research / Invited
• [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
• [Presentation] Holonomic Gradient Method for the Cumulative Distribution Function of the Largest Eigenvalue of a Complex Wishart Matrix with Noncentrality Matrix of Rank One (2020)
  • Author(s): Akimichi Takemura
  • Organizer: Symposium to celebrate Dietrich von Rosen 65th birthday
  • Int'l Joint Research
• [Presentation] Holonomic gradient method for evaluation of multivariate probabilities (2019)
  • Author(s): Akimichi Takemura
  • Organizer: The 3rd International Conference on Statistical Distributions and Applications (ICOSDA 2019)
  • Int'l Joint Research / Invited
• [Presentation] Progress of statistics and data science education in Japanese universities (2019)
  • Author(s): Akimichi Takemura
  • Organizer: The 16th Conference of International Federation of Classification Societies
  • Int'l Joint Research / Invited
• [Presentation] Holonomic gradient method for multivariate distribution theory (2019)
  • Author(s): Akimichi Takemura
  • Organizer: Multivariate and Mixed Linear Models (MMLM 2019)
  • 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
  • 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
  • Invited
• [Presentation] New Undergraduate Departments and Programs of Data Science in JAPAN (2018)
  • Author(s): Akimichi Takemura
  • Organizer: The 10th International Conference on Teaching Statistics (ICOTS10)
  • Int'l Joint Research / Invited
• [Book] 応用基礎としてのデータサイエンス AI×データ活用の実践 (2022)
  • Author(s): 北川源四郎、竹村彰通（共同編集）
  • Total Pages: 384
  • Publisher: 講談社
  • ISBN: 9784065307892
• [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
• [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