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Constructing theoretical system for high-dimension, low-sample-size data

Research Project

Project/Area Number 23740066
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionUniversity of Tsukuba

Principal Investigator

YATA KAZUYOSHI  筑波大学, 数理物質系, 助教 (90585803)

Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords高次元小標本データ / 高次元漸近理論 / PCA / 判別分析 / クラスター分析 / マイクロアレイデータ / 高次元小標本 / パスウェイ解析 / 逐次解析
Research Abstract

We proposed statistical theories and methodologies for high-dimension, low-sample-size (HDLSS) data. We showed that HDLSS data have two distinct geometric representations. We proposed the noise-reduction methodology that was brought from the geometric representations. We proposed the extended Cross-data-matrix methodology, which offers an unbiased estimator having small asymptotic variance and low computational cost, for parameters appearing in high-dimensional data analysis. We provided two effective discriminant procedures: a distance-based classifier and a geometric classifier, which can ensure high accuracy in misclassification rates and hold misclassification rates less than a threshold.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (60 results)

All 2014 2013 2012 2011 Other

All Journal Article (17 results) (of which Peer Reviewed: 12 results,  Open Access: 2 results,  Acknowledgement Compliant: 1 results) Presentation (38 results) (of which Invited: 7 results) Book (2 results) Remarks (3 results)

  • [Journal Article] A distance-based, misclassification rate adjusted classifier for multiclass, high-dimensional data2014

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

      Annals of the Institute of Statistical Mathematics

      Volume: 66 Issue: 5 Pages: 983-1010

    • DOI

      10.1007/s10463-013-0435-8

    • NAID

      40020186813

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Asymptotic distribution of the largest eigenvalue via geometric representations of high-dimension, low-sample-size data2014

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

      Sri Lankan J. Appl. Statist.

      Volume: 印刷中

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] PCA consistency for the power spiked model in high-dimensional settings2013

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

      J. Multivariate Anal.

      Volume: 122 Pages: 334-354

    • DOI

      10.1016/j.jmva.2013.08.003

    • NAID

      120007136793

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Correlation tests for high-dimensional data using extended cross-data-matrix methodology2013

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

      J. Multivariate Anal.

      Volume: 117 Pages: 313-331

    • DOI

      10.1016/j.jmva.2013.03.007

    • NAID

      120007137031

    • Related Report
      2013 Final Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] 高次元データの統計的方法論2013

    • Author(s)
      青嶋誠,矢田和善
    • Journal Title

      日本統計学会誌

      Volume: 43 Pages: 123-150

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] 高次元小標本における統計的推測2013

    • Author(s)
      青嶋誠,矢田和善
    • Journal Title

      数学

      Volume: 65 Pages: 225-247

    • NAID

      10031195365

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic normality for inference on multisample, high-dimensional mean vectors under mild conditions2013

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

      Methodology and Computing in Applied Probability

      Volume: 印刷中 Issue: 2 Pages: 419-439

    • DOI

      10.1007/s11009-013-9370-7

    • NAID

      120007130238

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] On the distribution of the largest eigenvalue in high dimension, low sample size context2013

    • Author(s)
      矢田和善, 青嶋 誠
    • Journal Title

      数理解析研究所講究録

      Volume: 1860 Pages: 120-128

    • Related Report
      2013 Annual Research Report
  • [Journal Article] 高次元小標本における統計的推測 (論説)2013

    • Author(s)
      青嶋 誠,矢田和善
    • Journal Title

      数学

      Volume: 65

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Effective PCA for high-dimension, low-sample-size data with noise reduction via geometric reprensentations2012

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

      J.Multivariate Anal.

      Volume: 105 Issue: 1 Pages: 193-215

    • DOI

      10.1016/j.jmva.2011.09.002

    • Related Report
      2013 Final Research Report 2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Asymptotic properties of a distance-based classifier for high-dimensional data2012

    • Author(s)
      矢田和善,青嶋 誠
    • Journal Title

      数理解析研究所講究録

      Volume: 1804 Pages: 53-64

    • Related Report
      2012 Research-status Report
  • [Journal Article] Note on classification for high-dimensional data2012

    • Author(s)
      永橋幸大,矢田和善,青嶋 誠
    • Journal Title

      数理解析研究所講究録

      Volume: 1804 Pages: 40-52

    • Related Report
      2012 Research-status Report
  • [Journal Article] Inference on high-dimensional mean vectors with fewer observations than the dimension2012

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

      Methodol. Comput. Appl. Probab.

      Volume: 14 Issue: 3 Pages: 459-476

    • DOI

      10.1007/s11009-011-9233-z

    • NAID

      120007137200

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Two-stage procedures for high-dimensional data (Editor's special invited paper)2011

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

      Sequential Analysis

      Volume: 30 Issue: 4 Pages: 356-399

    • DOI

      10.1080/07474946.2011.619088

    • Related Report
      2013 Final Research Report 2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Authors' response : Two-stage procedures for high-dimensional data2011

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

      Sequential Analysis

      Volume: 30 Issue: 4 Pages: 432-440

    • DOI

      10.1080/07474946.2011.619102

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] 高次元小標本における平均ベクトルの推測とその周辺2011

    • Author(s)
      矢田和善
    • Journal Title

      数理解析研究所講究録

      Volume: 1758 Pages: 136-149

    • Related Report
      2011 Research-status Report
  • [Journal Article] Note on robust model selection by density power divergence in a contaminated regression model2011

    • Author(s)
      矢田和善, 青嶋 誠, 小林裕子
    • Journal Title

      数理解析研究所講究録

      Volume: 1758 Pages: 150-159

    • Related Report
      2011 Research-status Report
  • [Presentation] Cluster analysis for multiclass, high-dimension, low-sample-size data2014

    • Author(s)
      矢田和善, 青嶋 誠
    • Organizer
      京都大学数理解析研究所研究集会「Asymptotic Statistics and Its Related Topics」
    • Place of Presentation
      京都大学数理解析研究所(京都府)
    • Related Report
      2013 Annual Research Report
  • [Presentation] 高次元小標本における最大固有値の分布とその応用2014

    • Author(s)
      石井 晶, 矢田和善, 青嶋 誠
    • Organizer
      京都大学数理解析研究所研究集会「Asymptotic Statistics and Its Related Topics」
    • Place of Presentation
      京都大学数理解析研究所(京都府)
    • Related Report
      2013 Annual Research Report
  • [Presentation] 高次元データの2次判別分析について2014

    • Author(s)
      矢田和善, 青嶋 誠
    • Organizer
      日本数学会年会
    • Place of Presentation
      学習院大学(東京都)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Effective classifiers for high-dimensional data2014

    • Author(s)
      Kazuyoshi Yata
    • Organizer
      Workshop on Statistics for High-Dimensional and Dependent Data
    • Place of Presentation
      Taipei (Taiwan)
    • Related Report
      2013 Annual Research Report
  • [Presentation] PCA consistency for high-dimensional data under the power spiked model2013

    • Author(s)
      K. Yata, M. Aoshima
    • Organizer
      KSS/JSS/CSA International Session in KSS Semi-Annual Meeting
    • Place of Presentation
      Seoul (Korea)
    • Year and Date
      2013-11-02
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Invited
  • [Presentation] Asymptotic normality for inference on multi-sample, high-dimensional mean vectors under mild conditions2013

    • Author(s)
      K. Yata
    • Organizer
      Fourth International Workshop in Sequential Methodologies
    • Place of Presentation
      Georgia (U.S.A.)
    • Year and Date
      2013-07-18
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Invited
  • [Presentation] 高次元データにおける統計的推測について2013

    • Author(s)
      矢田和善
    • Organizer
      早稲田大学理工学研究所プロジェクト研究「金融数理および年金数理研究」セミナー
    • Place of Presentation
      早稲田大学(東京都)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Effective PCA for high-dimensional data and its applications2013

    • Author(s)
      Makoto Aoshima, Kazuyoshi Yata
    • Organizer
      The 59th ISI World Statistics Congress
    • Place of Presentation
      Hong kong (China)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 主成分スコアに基づく高次元データのクラスタリングについて2013

    • Author(s)
      矢田和善, 青嶋 誠
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      大阪大学(大阪府)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Asymptotic normality for inference on high-dimensional mean vectors under mild conditions2013

    • Author(s)
      矢田和善, 青嶋 誠
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      愛媛大学(愛媛県)
    • Related Report
      2013 Annual Research Report
  • [Presentation] 高次元小標本の幾何学的表現と最大固有値の漸近分布2013

    • Author(s)
      石井 晶, 矢田和善, 青嶋 誠
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      愛媛大学(愛媛県)
    • Related Report
      2013 Annual Research Report
  • [Presentation] On the distribution of the largest eigenvalue via geometric representation in high-dimension, low sample size context2013

    • Author(s)
      石井 晶, 矢田和善, 青嶋 誠
    • Organizer
      科研費シンポジウム「高次元データ解析の理論と方法論,及び,関連分野への応用」
    • Place of Presentation
      筑波大学(茨城県)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Misclassification rate adjusted classifiers for high-dimensional data2013

    • Author(s)
      矢田和善, 青嶋 誠
    • Organizer
      科研費シンポジウム「高次元データ解析の理論と方法論,及び,関連分野への応用」
    • Place of Presentation
      筑波大学(茨城県)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Eigenvalue estimation of large dimensional covariance matrices and its applications2013

    • Author(s)
      矢田和善, 青嶋 誠
    • Organizer
      科研費シンポジウム「ランダム作用素のスペクトルと関連する話題」
    • Place of Presentation
      京都大学(京都府)
    • Related Report
      2013 Annual Research Report
  • [Presentation] 高次元小標本データの統計学 (日本統計学会各賞受賞者講演)2012

    • Author(s)
      青嶋誠,矢田和善
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      北海道大学
    • Year and Date
      2012-09-10
    • Related Report
      2013 Final Research Report
  • [Presentation] Effective PCA for large p, small n scenario under generalized models2012

    • Author(s)
      K. Yata
    • Organizer
      Sixth International Workshop on Applied Probability
    • Place of Presentation
      Jerusalem (Israel)
    • Year and Date
      2012-06-14
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Cluster Analysis for High-Dimensional Data2012

    • Author(s)
      栗下和義,矢田和善,青嶋 誠
    • Organizer
      科研費シンポジウム「高次元データの推測理論の開発と応用」
    • Place of Presentation
      中央大学(東京都)
    • Related Report
      2011 Research-status Report
  • [Presentation] Distance-based classifiers for High-dimensional data2012

    • Author(s)
      矢田和善,青嶋 誠
    • Organizer
      京都大学数理解析研究所研究集会「A New Perspective to Statistical Models and Related Topics」
    • Place of Presentation
      京都大学数理解析研究所(京都府)
    • Related Report
      2011 Research-status Report
  • [Presentation] 高次元小標本における回帰と分類2012

    • Author(s)
      永橋幸大,矢田和善,青嶋 誠
    • Organizer
      京都大学数理解析研究所研究集会「A New Perspective to Statistical Models and Related Topics」
    • Place of Presentation
      京都大学数理解析研究所(京都府)
    • Related Report
      2011 Research-status Report
  • [Presentation] 高次元小標本における拡張クロスデータ行列法について2012

    • Author(s)
      矢田和善,青嶋 誠
    • Organizer
      日本数学会年度会
    • Place of Presentation
      東京理科大学(東京都)
    • Related Report
      2011 Research-status Report
  • [Presentation] 高次元小標本における統計的推測 (特別講演)2011

    • Author(s)
      矢田和善
    • Organizer
      日本数学会秋季総合分科会特別講演
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-30
    • Related Report
      2013 Final Research Report
  • [Presentation] Effective PCA for large p, small n context with sample size determination2011

    • Author(s)
      K. Yata
    • Organizer
      Third International Workshop in Sequential Methodologies
    • Place of Presentation
      Stanford (U.S.A.)
    • Year and Date
      2011-06-15
    • Related Report
      2013 Final Research Report
  • [Presentation] Effective PCA for large p, small n context with sample size determination2011

    • Author(s)
      Kazuyoshi Yata
    • Organizer
      Third International Workshop in Sequential Methodologies 2011(招待講演)
    • Place of Presentation
      Stanford University(アメリカ合衆国)
    • Related Report
      2011 Research-status Report
  • [Presentation] 高次元小標本における統計的推測2011

    • Author(s)
      矢田和善
    • Organizer
      日本数学会秋季総合分科会特別講演(招待講演)
    • Place of Presentation
      信州大学(長野県)
    • Related Report
      2011 Research-status Report
  • [Presentation] Statistical Inference for High-Dimension, Low-Sample-Size Data2011

    • Author(s)
      矢田和善
    • Organizer
      統計数学セミナー
    • Place of Presentation
      東京大学(東京都)
    • Related Report
      2011 Research-status Report
  • [Presentation] Multiple Correlation Test for High-Dimension, Low-Sample-Size Data2011

    • Author(s)
      矢田和善,青嶋 誠
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      九州大学(福岡県)
    • Related Report
      2011 Research-status Report
  • [Presentation] Robust model selection by density power divergence in a contaminated regression model2011

    • Author(s)
      小林裕子,矢田和善,青嶋 誠
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      信州大学(長野県)
    • Related Report
      2011 Research-status Report
  • [Presentation] Extended Cross-Data-Matrix Methodology for High-Dimension, Low-Sample-Size Data2011

    • Author(s)
      矢田和善
    • Organizer
      データ科学特別セミナー
    • Place of Presentation
      大阪大学(大阪府)
    • Related Report
      2011 Research-status Report
  • [Presentation] Effective PCA for large p, small n scenario under generalized models

    • Author(s)
      Kazuyoshi Yata
    • Organizer
      Sixth International Workshop on Applied Probability
    • Place of Presentation
      Jerusalem (イスラエル国)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Effective PCA for high-dimension, low-sample-size data with geometric representations

    • Author(s)
      Kazuyoshi Yata
    • Organizer
      Second Institute of Mathematical Statistics Asia Pacific Rim Meeting
    • Place of Presentation
      つくば国際会議場 (茨城県)
    • Related Report
      2012 Research-status Report
  • [Presentation] 高次元小標本データの統計学

    • Author(s)
      青嶋 誠,矢田和善
    • Organizer
      統計関連学会連合大会 (日本統計学会各賞受賞者講演)
    • Place of Presentation
      北海道大学 (北海道)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] PCA consistency for high-dimensional data under genelized models

    • Author(s)
      矢田和善,青嶋 誠
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      九州大学 (福岡県)
    • Related Report
      2012 Research-status Report
  • [Presentation] たった30個の標本で,10000次元のデータを,どこまで精密に解析できるか?

    • Author(s)
      青嶋 誠,矢田和善
    • Organizer
      筑波大学数学談話会
    • Place of Presentation
      筑波大学 (茨城県)
    • Related Report
      2012 Research-status Report
  • [Presentation] 高次元小標本における幾何学的表現とその応用

    • Author(s)
      矢田和善,青嶋 誠
    • Organizer
      科研費シンポジウム「統計科学における深化と横断的展開」
    • Place of Presentation
      松江テルサ (島根県)
    • Related Report
      2012 Research-status Report
  • [Presentation] Effective PCA for high-dimensional, non-Gaussian data under power spiked model

    • Author(s)
      矢田和善
    • Organizer
      統計数学セミナー
    • Place of Presentation
      東京大学 (東京都)
    • Related Report
      2012 Research-status Report
  • [Presentation] PCA consistency for power spiked model in high-dimensional settings

    • Author(s)
      矢田和善,青嶋 誠
    • Organizer
      日本統計学会春季集会
    • Place of Presentation
      学習院大学 (東京都)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Cluster analysis for high-dimensional non-Gaussian data

    • Author(s)
      矢田和善,青嶋 誠
    • Organizer
      京都大学数理解析研究所研究集会「Asymptotic Expansions for Various Models and Their Related Topics」
    • Place of Presentation
      京都大学数理解析研究所 (京都府)
    • Related Report
      2012 Research-status Report
  • [Presentation] Power spiked モデルをもつ高次元データの固有値推定について

    • Author(s)
      矢田和善,青嶋 誠
    • Organizer
      日本数学会年度会
    • Place of Presentation
      京都大学 (京都府)
    • Related Report
      2012 Research-status Report
  • [Book] Effective methodologies for statistical inference on microarray studies. In P.E. Spiess (Ed.), Prostate Cancer -From Bench to Bedside2011

    • Author(s)
      M. Aoshima, K. Yata
    • Publisher
      InTech
    • Related Report
      2013 Final Research Report
  • [Book] Effective methodologies for statistical inference on microarray studies, in: P.E. Spiess (Ed.), Prostate Cancer - From Bench to Bedside, InTech, 2011, pp. 13-32.2011

    • Author(s)
      Makoto Aoshima, Kazuyoshi Yata
    • Publisher
      InTech
    • Related Report
      2011 Research-status Report
  • [Remarks] 研究者総覧(筑波大学)

    • URL

      http://www.trios.tsukuba.ac.jp/researcher/0000000526

    • Related Report
      2013 Final Research Report
  • [Remarks] trios

    • URL

      http://www.trios.tsukuba.ac.jp/researcher/0000000526

    • Related Report
      2013 Annual Research Report
  • [Remarks] TRIOS (矢田和善)

    • URL

      http://www.trios.tsukuba.ac.jp/Profiles/0003/0006954/profile.html

    • Related Report
      2012 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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