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Tackling individualized modeling with ultra-high dimensional data

Research Project

Project/Area Number 19K22837
Research Category

Grant-in-Aid for Challenging Research (Exploratory)

Allocation TypeMulti-year Fund
Review Section Medium-sized Section 60:Information science, computer engineering, and related fields
Research InstitutionUniversity of Tsukuba

Principal Investigator

AOSHIMA Makoto  筑波大学, 数理物質系, 教授 (90246679)

Co-Investigator(Kenkyū-buntansha) 矢田 和善  筑波大学, 数理物質系, 准教授 (90585803)
石井 晶  東京理科大学, 理工学部情報科学科, 講師 (20801161)
赤平 昌文  筑波大学, 数理物質系(名誉教授), 名誉教授 (70017424)
Project Period (FY) 2019-06-28 – 2022-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥6,240,000 (Direct Cost: ¥4,800,000、Indirect Cost: ¥1,440,000)
Fiscal Year 2021: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2020: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2019: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Keywords超高次元データ / 個別化モデリング / 天体スペクトル / 次世代シーケンサー / クラスタリング / 個別化医療
Outline of Research at the Start

超高次元データの解析技術が確立されないまま、国主導で遺伝情報を用いた個別化医療開発が進んでいる。今後、個別化医療を低コストで実現するためには、超高次元データについて、通常のPCでも処理できる高速計算と、高精度に処理できる統計解析、そして、それらの新技術を統合した個別化モデリング技法の確立が急務と考える。本研究は、既存の学術の体系を大きく見直し、個別化モデリングに着目して、超高次元データを高速で高精度に解析するための新たな技術の開発と、科学技術・産業への革新的展開を目指す。

Outline of Final Research Achievements

In this study, we reviewed previous academic systems and developed a new technology for analyzing ultra-high-dimensional data at high speed and with high accuracy. The novel idea is "individualized modeling". We aimed at innovative developments in science, technology and industry. We produced the following significant results: (1) Developments of high-speed clustering for ultra-high-dimensional data, and the creation of the I.I.D. transformation method. (2) Precise statistical analysis for the latent structure and noise structure of ultra-high-dimensional data. (3) Establishment of the "individualized modeling" method using ultra-high-dimensional data.
This novel approach now allows the high-speed, high-accurate analysis of ultra-high-dimensional data which had not been possible with existing methods. This will be of particular merit in the medical field.

Academic Significance and Societal Importance of the Research Achievements

国主導で遺伝情報を用いた個別化医療開発が進んでいるものの、超高次元データの解析技術が確立されているとは言い難い。本研究は、個別化医療を低コストで実現するために、超高次元データについて、モバイルPCでも処理できる高速計算と、高精度に処理できる統計解析、そして、それらの新技術を統合した個別化モデリング法を開発した。超高次元の天文データの解析にも使用され、モバイルPCであっても、個別化モデリング法はノイズを精密に処理して高速かつ高精度に潜在情報を抽出することが確認された。

Report

(4 results)
  • 2021 Annual Research Report   Final Research Report ( PDF )
  • 2020 Research-status Report
  • 2019 Research-status Report
  • Research Products

    (75 results)

All 2021 2020 2019 2018 Other

All Int'l Joint Research (10 results) Journal Article (18 results) (of which Peer Reviewed: 13 results,  Open Access: 18 results) Presentation (42 results) (of which Int'l Joint Research: 13 results,  Invited: 15 results) Book (1 results) Remarks (2 results) Funded Workshop (2 results)

  • [Int'l Joint Research] Princeton University/University of North Carolina(米国)

    • Related Report
      2021 Annual Research Report
  • [Int'l Joint Research] Academia Sinica(中国)

    • Related Report
      2021 Annual Research Report
  • [Int'l Joint Research] University of Stavanger(ノルウェー)

    • Related Report
      2021 Annual Research Report
  • [Int'l Joint Research] Seoul National University(韓国)

    • Related Report
      2021 Annual Research Report
  • [Int'l Joint Research] Princeton University/University of North Carolina(米国)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] Academia Sinica(中国)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] University of Stavanger(ノルウェー)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] Seoul National University(韓国)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] Princeton University/University of North Carolina(米国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Academia Sinica(中国)

    • Related Report
      2019 Research-status Report
  • [Journal Article] 論説:高次元小標本における統計的仮説検定2021

    • Author(s)
      青嶋 誠、石井 晶、矢田和善
    • Journal Title

      数学

      Volume: 73 Pages: 360-379

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Hypothesis tests for high-dimensional covariance structures2021

    • Author(s)
      Ishii Aki, Yata Kazuyoshi, Aoshima Makoto
    • Journal Title

      Annals of the Institute of Statistical Mathematics

      Volume: in press Issue: 3 Pages: 599-622

    • DOI

      10.1007/s10463-020-00760-5

    • NAID

      120007168344

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Clustering by principal component analysis with Gaussian kernel in high-dimension, low-sample-size settings2021

    • Author(s)
      Nakayama Yugo、Yata Kazuyoshi、Aoshima Makoto
    • Journal Title

      Journal of Multivariate Analysis

      Volume: 185 Pages: 104779-104779

    • DOI

      10.1016/j.jmva.2021.104779

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Asymptotic properties of distance-weighted discrimination and its bias correction for high-dimension, low-sample-size data2021

    • Author(s)
      Egashira Kento、Yata Kazuyoshi、Aoshima Makoto
    • Journal Title

      Japanese Journal of Statistics and Data Science

      Volume: 4 Issue: 2 Pages: 821-840

    • DOI

      10.1007/s42081-021-00135-x

    • NAID

      210000176902

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] High-dimensional Two-sample Test Procedures under the Strongly Spiked Eigenvalue Model2020

    • Author(s)
      石井 晶、矢田和善、青嶋 誠
    • Journal Title

      Ouyou toukeigaku

      Volume: 49 Issue: 3 Pages: 109-125

    • DOI

      10.5023/jappstat.49.109

    • NAID

      130008022515

    • ISSN
      0285-0370, 1883-8081
    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] 高次元におけるDistance Weighted Discriminationについて2020

    • Author(s)
      江頭健斗、矢田和善、青嶋 誠
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2157 Pages: 1-10

    • Related Report
      2020 Research-status Report
    • Open Access
  • [Journal Article] High-dimensional covariance matrix estimation under the SSE model2020

    • Author(s)
      Konishi Keisuke、Yata Kazuyoshi、Aoshima Makoto
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2157 Pages: 11-20

    • NAID

      120006956688

    • Related Report
      2020 Research-status Report
    • Open Access
  • [Journal Article] Tests for high-dimensional covariance structures under the non-strongly spiked eigenvalue model2020

    • Author(s)
      Ishii Aki、Yata Kazuyoshi、Aoshima Makoto
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2157 Pages: 21-30

    • NAID

      120006956689

    • Related Report
      2020 Research-status Report
    • Open Access
  • [Journal Article] A classifier under the strongly spiked eigenvalue model in high-dimension, low-sample-size context2020

    • Author(s)
      Ishii Aki
    • Journal Title

      Communications in Statistics - Theory and Methods

      Volume: 49 Issue: 7 Pages: 1561-1577

    • DOI

      10.1080/03610926.2018.1528365

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Geometric consistency of principal component scores for high‐dimensional mixture models and its application2019

    • Author(s)
      Yata Kazuyoshi、Aoshima Makoto
    • Journal Title

      Scandinavian Journal of Statistics

      Volume: - Issue: 3 Pages: 899-921

    • DOI

      10.1111/sjos.12432

    • NAID

      120007163354

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Bias-corrected support vector machine with Gaussian kernel in high-dimension, low-sample-size settings2019

    • Author(s)
      Nakayama Yugo、Yata Kazuyoshi、Aoshima Makoto
    • Journal Title

      Annals of the Institute of Statistical Mathematics

      Volume: - Issue: 5 Pages: 1-30

    • DOI

      10.1007/s10463-019-00727-1

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Equality tests of high-dimensional covariance matrices under the strongly spiked eigenvalue model2019

    • Author(s)
      Ishii Aki, Yata Kazuyoshi, Aoshima Makoto
    • Journal Title

      Journal of Statistical Planning and Inference

      Volume: 202 Pages: 99-111

    • DOI

      10.1016/j.jspi.2019.02.002

    • NAID

      120007133560

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Inference on high-dimensional mean vectors under the strongly spiked eigenvalue model2019

    • Author(s)
      A. ishii, K. Yata, M. Aoshima
    • Journal Title

      Japanese Journal of Statistics and Data Science

      Volume: 印刷中 Issue: 1 Pages: 105-128

    • DOI

      10.1007/s42081-018-0029-z

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] A quadratic classifier for high-dimension, low-sample-size data under the strongly spiked eigenvalue model2019

    • Author(s)
      Ishii Aki, Yata Kazuyoshi, Aoshima Makoto
    • Journal Title

      Springer Proceedings in Mathematics and Statistics

      Volume: 294 Pages: 131-142

    • DOI

      10.1007/978-3-030-28665-1_10

    • ISBN
      9783030286644, 9783030286651
    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Soft-margin SVMs in the HDLSS context2019

    • Author(s)
      Nakayama Yugo、Yata Kazuyoshi、Aoshima Makoto
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2124 Pages: 44-55

    • Related Report
      2019 Research-status Report
    • Open Access
  • [Journal Article] 強スパイク固有値モデルにおける高次元一標本検定とその応用について2019

    • Author(s)
      石井 晶、矢田和善、青嶋 誠
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2124 Pages: 56-64

    • Related Report
      2019 Research-status Report
    • Open Access
  • [Journal Article] Distance-based classifier by data transformation for high-dimension, strongly spiked eigenvalue models2018

    • Author(s)
      Aoshima, M., Yata, K.
    • Journal Title

      Annals of the Institute of Statistical Mathematics

      Volume: to appear Issue: 3 Pages: 473-503

    • DOI

      10.1007/s10463-018-0655-z

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] High-dimensional quadratic classifiers in non-sparse settings.2018

    • Author(s)
      Aoshima, M., Yata, K.
    • Journal Title

      Methodology and Computing in Applied Probability

      Volume: to appear Issue: 3 Pages: 663-682

    • DOI

      10.1007/s11009-018-9646-z

    • NAID

      120007132793

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] 高次元小標本の統計学:非スパース性と巨大ノイズ(特別講演)2021

    • Author(s)
      青嶋 誠
    • Organizer
      統計数理研究所リスク解析戦略研究センターシンポジウム
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] High-dimensional quadratic classifiers under the strongly spiked eigenvalue model2021

    • Author(s)
      Ishii A., Yata K., Aoshima M.
    • Organizer
      IISA 2021 Conference
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Tests for covariance structures in high-dimensional data2021

    • Author(s)
      Yata K., Ishii A., Aoshima M.
    • Organizer
      The 4th International Conference on Econometrics and Statistics
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] High-dimensional classifiers under the strongly spiked eigenvalue model2021

    • Author(s)
      Ishii A., Yata K., Aoshima M.
    • Organizer
      The 4th International Conference on Econometrics and Statistics
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Clustering by kernel PCA with Gaussian kernel and tuning for high-dimensional data2021

    • Author(s)
      Nakayama Y., Yata K., Aoshima M.
    • Organizer
      The 4th International Conference on Econometrics and Statistics
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Sparse PCA for high-dimensional data based on the noise-reduction methodology and its application2021

    • Author(s)
      Yata K., Aoshima M.
    • Organizer
      The 63rd ISI World Statistics Congress
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Asymptotic properties of high-dimensional kernel PCA and its applications2021

    • Author(s)
      Nakayama Y., Yata K., Aoshima M.
    • Organizer
      International Symposium on New Developments of Theories and Methodologies for Large Complex Data
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 単一強スパイク固有値モデルにおける高次元平均ベクトルの2標本検定(応用統計学会学会賞受賞者講演)2021

    • Author(s)
      石井 晶
    • Organizer
      統計関連学会連合大会
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] 高次元データにおけるノイズ構造の高精度な解析に基づく統計的推測2021

    • Author(s)
      矢田和善、石井 晶、青嶋 誠
    • Organizer
      統計関連学会連合大会
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] 高次元統計学の方法による銀河の分光マップの解析2021

    • Author(s)
      竹内 努、矢田和善、青嶋 誠、石井 晶、江頭健斗、河野 海、中西康一郎、Suchetha COORAY、河野孝太郎
    • Organizer
      科研費シンポジウム「多様な分野における統計科学に関する理論と方法論の革新的展開」
    • Related Report
      2021 Annual Research Report
  • [Presentation] 高次元相互共分散行列の特異値分解とその応用2021

    • Author(s)
      佐々木拓真、矢田和善、青嶋 誠
    • Organizer
      日本学術振興会科学研究費による研究集会「統計科学の革新にむけて」
    • Related Report
      2020 Research-status Report
  • [Presentation] 高次元におけるDWDとWDWDのバイアス補正とその比較2021

    • Author(s)
      江頭健斗、矢田和善、青嶋 誠
    • Organizer
      日本学術振興会科学研究費による研究集会「統計科学の革新にむけて」
    • Related Report
      2020 Research-status Report
  • [Presentation] 距離加重判別分析の高次元漸近的性質2021

    • Author(s)
      江頭健斗、矢田和善、青嶋 誠
    • Organizer
      日本数学会2021年度年会
    • Related Report
      2020 Research-status Report
  • [Presentation] High-Dimensional Statistical Analysis of ALMA Spectroscopic Mapping Data2021

    • Author(s)
      Takeuchi T、Kono K、Nakanishi K、Yata K、Aoshima M、Egashira K、Ishii A
    • Organizer
      自然科学研究機構:自然科学研究における機関間連携ネットワークによる拠点形成事業シンポジウム「自然科学における階層と全体」
    • Related Report
      2020 Research-status Report
  • [Presentation] High-Dimensional Statistical Analysis of the ALMA Spectroscopic Map of a Nearby Galaxy NGC 2532021

    • Author(s)
      Takeuchi T、Kono K、Yata K、Aoshima M、Ishii A、Nakanishi K、Egashira K、Cooray S、Kohno K
    • Organizer
      Galaxy Evolution Workshop 2020
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research
  • [Presentation] Analysis of Integral Field Spectroscopic Data as a High-Dimensional Low-Sample Size Data Problem2021

    • Author(s)
      竹内 努、河野 海、中西康一郎、矢田和善、青嶋 誠、石井 晶
    • Organizer
      日本天文学会2021年春季年会
    • Related Report
      2020 Research-status Report
  • [Presentation] Tests of high-dimensional correlation matrices under the strongly spiked eigenvalue model2020

    • Author(s)
      石井 晶、矢田和善、青嶋 誠
    • Organizer
      2020年度統計関連学会連合大会
    • Related Report
      2020 Research-status Report
  • [Presentation] 高次元固有ベクトルの検定について2020

    • Author(s)
      石井 晶、矢田和善、青嶋 誠
    • Organizer
      日本数学会2020年度秋季総合分科会
    • Related Report
      2020 Research-status Report
  • [Presentation] 高次元スパースPCAの一致性とその応用2020

    • Author(s)
      矢田和善、青嶋 誠
    • Organizer
      2020年度統計関連学会連合大会
    • Related Report
      2020 Research-status Report
  • [Presentation] ノイズ掃き出し法による高次元スパースPCAについて2020

    • Author(s)
      矢田和善、青嶋 誠
    • Organizer
      日本学術振興会科学研究費による研究集会「大規模複雑データの理論と方法論:最前線の動向と新たな展開」
    • Related Report
      2020 Research-status Report
  • [Presentation] Clustering by kernel principal component analysis for high-dimensional data2020

    • Author(s)
      中山優吾、矢田和善、青嶋 誠
    • Organizer
      日本数学会2020年度秋季総合分科会
    • Related Report
      2020 Research-status Report
  • [Presentation] 高次元データにおける距離加重判別分析の漸近的性質とバイアス補正2020

    • Author(s)
      江頭健斗、矢田和善、青嶋 誠
    • Organizer
      2020年度統計関連学会連合大会
    • Related Report
      2020 Research-status Report
  • [Presentation] High-Dimensional Statistics for Integral Field Spectroscopic Data2020

    • Author(s)
      Takeuchi T、Kono K、Nakanishi K、Yata K、Aoshima M、Egashira K、Ishii A
    • Organizer
      日本学術振興会科学研究費による研究集会「初代星・初代銀河研究会2020」
    • Related Report
      2020 Research-status Report
  • [Presentation] Analysis of Spatially Resolved Galaxy Spectra as a High-Dimensional Low-Sample Size Data Problem2020

    • Author(s)
      竹内 努、河野 海、中西康一郎、矢田和善,青嶋 誠、石井 晶、江頭健斗
    • Organizer
      日本学術振興会科学研究費による研究集会「大規模複雑データの理論と方法論:最前線の動向と新たな展開」
    • Related Report
      2020 Research-status Report
  • [Presentation] High-dimensional covariance matrix estimation under the strongly spiked eigenvalue model2020

    • Author(s)
      小西啓介、矢田和善、青嶋 誠
    • Organizer
      日本学術振興会科学研究費による研究集会「多様な高次元モデルにおける理論と方法論,及び,関連分野への応用」
    • Related Report
      2019 Research-status Report
  • [Presentation] Asymptotic properties of distance weighted discrimination and its bias correction in HDLSS settings2020

    • Author(s)
      江頭健斗、矢田和善、青嶋 誠
    • Organizer
      日本学術振興会科学研究費による研究集会「多様な高次元モデルにおける理論と方法論,及び,関連分野への応用」
    • Related Report
      2019 Research-status Report
  • [Presentation] データ変換を用いた高次元次判別分析について2020

    • Author(s)
      石井 晶、矢田和善、青嶋 誠
    • Organizer
      日本学術振興会科学研究費による研究集会「多様な高次元モデルにおける理論と方法論,及び,関連分野への応用」
    • Related Report
      2019 Research-status Report
  • [Presentation] High-Dimensional Statistical Analysis: Non-Sparsity, Strongly Spiked Noise and HDLSS2019

    • Author(s)
      Aoshima Makoto
    • Organizer
      The 7th International Workshop in Sequential Methodologies
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] A Test of Sphericity for High-Dimensional Data and Its Application for Detection of Divergently Spiked Noise2019

    • Author(s)
      Yata Kazuyoshi、Aoshima Makoto、Nakayama Yugo
    • Organizer
      The 7th International Workshop in Sequential Methodologies
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 強スパイク固有値モデルにおける高次元共分散行列の推定2019

    • Author(s)
      小西啓介、矢田和善、青嶋 誠
    • Organizer
      2019年度統計関連学会連合大会
    • Related Report
      2019 Research-status Report
  • [Presentation] カーネル主成分分析に基づく高次元データのクラスタリングとチューニング2019

    • Author(s)
      中山優吾、矢田和善、青嶋 誠
    • Organizer
      2019年度統計関連学会連合大会
    • Related Report
      2019 Research-status Report
  • [Presentation] Asymptotic properties of kernel PCA with Gaussian kernel for high-dimensional data2019

    • Author(s)
      中山優吾、矢田和善、青嶋 誠
    • Organizer
      日本学術振興会科学研究費による研究集会「統計学と機械学習の数理と展開」
    • Related Report
      2019 Research-status Report
  • [Presentation] A high-dimensional quadratic classifier by data transformation for strongly spiked eigenvalue models2019

    • Author(s)
      Yata Kazuyoshi、Aoshima Makoto
    • Organizer
      The 3rd International Conference on Econometrics and Statistics
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 高次元混合データにおける幾何学的一致性について2019

    • Author(s)
      矢田和善、青嶋 誠
    • Organizer
      日本数学会2019年度秋季総合分科会
    • Related Report
      2019 Research-status Report
  • [Presentation] データ変換を用いた高次元2次判別方式について2019

    • Author(s)
      矢田和善、石井 晶、青嶋 誠
    • Organizer
      2019年度統計関連学会連合大会
    • Related Report
      2019 Research-status Report
  • [Presentation] Geometrical quadratic discriminant analysis for high-dimension, strongly spiked eigenvalue models2019

    • Author(s)
      矢田和善、石井 晶、青嶋 誠
    • Organizer
      日本学術振興会科学研究費による研究集会「高次元複雑データの統計モデリング」
    • Related Report
      2019 Research-status Report
  • [Presentation] Tests of high-dimensional correlation matrices on the basis of eigenstructures2019

    • Author(s)
      Ishii Aki、Yata Kazuyoshi、Aoshima Makoto
    • Organizer
      The 7th International Workshop in Sequential Methodologies
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Inference on mean vectors for high-dimensional data with the strongly spiked eigenstructure2019

    • Author(s)
      Ishii Aki、Yata Kazuyoshi、Aoshima Makoto
    • Organizer
      The 3rd International Conference on Econometrics and Statistics
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Tests for high-dimensiomal covariance structures under the SSE model2019

    • Author(s)
      Ishii Aki、Yata Kazuyoshi、Aoshima Makoto
    • Organizer
      International Symposium on Theories and Methodologies for Large Complex Data
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 単一強スパイク固有値モデルにおける高次元二標本検定2019

    • Author(s)
      石井 晶、矢田和善、青嶋 誠
    • Organizer
      日本数学会2019年度秋季総合分科会
    • Related Report
      2019 Research-status Report
  • [Presentation] Tests for high-dimensional covariance structures based on eigenstructures2019

    • Author(s)
      Ishii Aki、Yata Kazuyoshi、Aoshima Makoto
    • Organizer
      2019年度統計関連学会連合大会
    • Related Report
      2019 Research-status Report
  • [Presentation] 単一強スパイク固有値モデルに対する高次元平均ベクトルの2標本検定2019

    • Author(s)
      石井 晶、矢田和善、青嶋 誠
    • Organizer
      日本学術振興会科学研究費による研究集会「統計的推測および確率解析に関する総合的研究」
    • Related Report
      2019 Research-status Report
  • [Book] 高次元の統計学2019

    • Author(s)
      青嶋 誠、矢田 和善
    • Total Pages
      120
    • Publisher
      共立出版
    • ISBN
      4320112636
    • Related Report
      2019 Research-status Report
  • [Remarks] 青嶋研究室ホームページ

    • URL

      https://www.math.tsukuba.ac.jp/~aoshima-lab/jp/

    • Related Report
      2021 Annual Research Report
  • [Remarks] 青嶋研究室ホームページ

    • URL

      http://www.math.tsukuba.ac.jp/~aoshima-lab/jp/

    • Related Report
      2020 Research-status Report 2019 Research-status Report
  • [Funded Workshop] International Symposium on New Developments of Theories and Methodologies for Large Complex Data2021

    • Related Report
      2021 Annual Research Report
  • [Funded Workshop] International Symposium on Theories and Methodologies for Large Complex Data2019

    • Related Report
      2019 Research-status Report

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Published: 2019-07-04   Modified: 2023-01-30  

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