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Statistics for Big Data: Development of Theories and Tackling the 3Vs

Research Project

Project/Area Number 26540010
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Statistical science
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)
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) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywordsビッグデータ / 潜在構造分析 / 異常値 / 欠損値 / 非正則推定論
Outline of Final Research Achievements

In this research project, we aim to pioneer new statistical theories for big data, ahead of the world. We have developed new theories and methodologies in latent structural analysis for big data: irregular and non-Gaussian data contaminated with outliers and missing values. New theories and methodologies guarantee stable and high accuracy at low computational cost. The findings of this research project are as follows: (1) Developments of the irregular inference theory for big data with diversity. (2) Developments of high-speed and highly accurate latent structural analysis for big data. (3) Pioneering latent structural analysis robust against outliers and missing values.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (34 results)

All 2017 2016 2015 2014 Other

All Int'l Joint Research (1 results) Journal Article (10 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 4 results,  Open Access: 7 results,  Acknowledgement Compliant: 6 results) Presentation (20 results) (of which Int'l Joint Research: 5 results,  Invited: 10 results) Remarks (2 results) Funded Workshop (1 results)

  • [Int'l Joint Research] モスクワ大学(ロシア連邦)

    • Related Report
      2016 Annual Research Report
  • [Journal Article] Non-asymptotic results for Cornish-Fisher expansions2016

    • Author(s)
      Ulyanov, V.V., Aoshima, M., Fujikoshi, Y.
    • Journal Title

      Journal of Mathematical Sciences

      Volume: 218 Issue: 3 Pages: 363-368

    • DOI

      10.1007/s10958-016-3036-2

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] High-dimensional inference on covariance structures via the extended cross-data-matrix methodology2016

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

      Journal of Multivariate Analysis

      Volume: 151 Pages: 151-166

    • DOI

      10.1016/j.jmva.2016.07.011

    • NAID

      120007129372

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Estimation of a signal matrix for high-dimensional non-Gaussian data2016

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

      京都大学数理解析研究所講究録

      Volume: 1999 Pages: 36-46

    • Related Report
      2016 Annual Research Report
    • Acknowledgement Compliant
  • [Journal Article] Reconstruction of a high-dimensional low-rank matrix2016

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

      Electronic Journal of Statistics

      Volume: 10 Issue: 1 Pages: 895-917

    • DOI

      10.1214/16-ejs1128

    • NAID

      120007135234

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Second order asymptotic comparison of the MLE and MCLE of a natural parameter for a truncated exponential family of distributions2015

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

      Ann. Inst. Statist. Math.

      Volume: 印刷中 Issue: 3 Pages: 469-490

    • DOI

      10.1007/s10463-014-0502-9

    • NAID

      120007135429

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Reconstruction of a signal matrix for high-dimension, low-sample-size data2015

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

      京都大学数理解析研究所講究録

      Volume: 1954 Pages: 23-31

    • Related Report
      2015 Research-status Report
    • Acknowledgement Compliant
  • [Journal Article] Asymptotic comparison in maximum likelihood estimation of a natural parameter up to the second order for a truncated exponential family of distributions2015

    • Author(s)
      赤平昌文
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1954 Pages: 134-150

    • Related Report
      2015 Research-status Report
  • [Journal Article] 高次元小標本における混合データの幾何学的表現とクラスター分析への応用2014

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

      京都大学数理解析研究所講究録

      Volume: 1910 Pages: 125-133

    • Related Report
      2014 Research-status Report
    • Open Access / Acknowledgement Compliant
  • [Journal Article] Largest Eigenvalue Estimation for High-Dimension, Low-Sample-Size Data and its Application2014

    • 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: 1910 Pages: 115-124

    • Related Report
      2014 Research-status Report
    • Open Access / Acknowledgement Compliant
  • [Journal Article] The generalized amount of information between the prior distribution and the asymptotic posterior one2014

    • Author(s)
      赤平昌文, 小池健一
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1910 Pages: 144-153

    • Related Report
      2014 Research-status Report
    • Open Access
  • [Presentation] 高次元固有空間の推測と高次元統計解析2017

    • Author(s)
      青嶋 誠
    • Organizer
      第11回日本統計学会春季集会
    • Place of Presentation
      政策研究大学院大学(東京都港区)
    • Year and Date
      2017-03-05
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] スパイクノイズと高次元統計解析2016

    • Author(s)
      青嶋 誠, 矢田和善
    • Organizer
      日本学術振興会科学研究費による研究集会「数理統計ひこね2016」
    • Place of Presentation
      滋賀大学(滋賀県彦根市)
    • Year and Date
      2016-12-02
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Statistical inference in strongly spiked eigenvalue models2016

    • Author(s)
      Yata, K., Aoshima, M.
    • Organizer
      International Symposium “Statistical Analysis for Large Complex Data”
    • Place of Presentation
      筑波大学(茨城県つくば市)
    • Year and Date
      2016-11-23
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Reconstruction of a high-dimensional low-rank matrix and its applications2016

    • Author(s)
      Yata, K., Aoshima, M.
    • Organizer
      Waseda International Symposium “High Dimensional Statistical Analysis for Time Spatial Processes, Quantile and Empirical Likelihood Analysis for Time Series
    • Place of Presentation
      早稲田大学(東京都新宿区)
    • Year and Date
      2016-10-25
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] High-dimensional two-sample tests under strongly spiked eigenvalue models2016

    • Author(s)
      青嶋 誠
    • Organizer
      研究集会「大規模統計モデリングと計算統計III」
    • Place of Presentation
      東京大学(東京都目黒区)
    • Year and Date
      2016-09-27
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Strongly spiked eigenvalue モデルにおける高次元判別分析について2016

    • Author(s)
      矢田和善, 青嶋 誠
    • Organizer
      日本数学会2016年度秋季総合分科会
    • Place of Presentation
      関西大学(大阪府吹田市)
    • Year and Date
      2016-09-18
    • Related Report
      2016 Annual Research Report
  • [Presentation] Reconstruction of a high-dimensional low-rank matrix2016

    • Author(s)
      矢田和善, 青嶋 誠
    • Organizer
      2016年度統計関連学会連合大会
    • Place of Presentation
      金沢大学(石川県金沢市)
    • Year and Date
      2016-09-07
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Effective Classifiers for High-Dimensional Non-Sparse Data2016

    • Author(s)
      Yata, K., Aoshima, M.
    • Organizer
      International Conference on Information Complexity and Statistical Modeling in High Dimensions with Applications
    • Place of Presentation
      Cappadocia (Turkey)
    • Year and Date
      2016-05-20
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Estimation of a signal matrix for high-dimensional data2016

    • Author(s)
      矢田和善,青嶋 誠
    • Organizer
      日本数学会2016年度年会
    • Place of Presentation
      筑波大学(茨城県つくば市)
    • Year and Date
      2016-03-19
    • Related Report
      2015 Research-status Report
  • [Presentation] Reconstruction of a signal matrix for high-dimensional data and its applications2016

    • Author(s)
      矢田和善,青嶋 誠
    • Organizer
      京都大学数理解析研究所RIMS研究集会「Statistical Inference on Divergence Measures and Its Related Topics」
    • Place of Presentation
      京都大学(京都府京都市)
    • Year and Date
      2016-03-07
    • Related Report
      2015 Research-status Report
  • [Presentation] 高次元データの統計数理2015

    • Author(s)
      青嶋 誠
    • Organizer
      筑波大学数理物質融合科学センター数理連携サロン
    • Place of Presentation
      筑波大学(茨城県つくば市)
    • Year and Date
      2015-12-02
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] 高次元小標本における第1主成分の漸近的性質と平均ベクトルの検定2015

    • Author(s)
      石井 晶,矢田和善,青嶋 誠
    • Organizer
      2015 年度統計関連学会連合大会
    • Place of Presentation
      岡山大学(岡山県岡山市)
    • Year and Date
      2015-09-08
    • Related Report
      2015 Research-status Report
  • [Presentation] Statistical Methods for Heterogeneous Data2015

    • Author(s)
      Aoshima, M.
    • Organizer
      ISNPS Meeting “Biosciences, Medicine, and novel Non-Parametric Methods”
    • Place of Presentation
      Graz (Austria)
    • Year and Date
      2015-07-15
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] PCA Consistency for High-Dimensional Multiclass Mixture Models and its Applications2015

    • Author(s)
      Yata, K., Aoshima, M.
    • Organizer
      ISNPS Meeting “Biosciences, Medicine, and novel Non-Parametric Methods”
    • Place of Presentation
      Graz (Austria)
    • Year and Date
      2015-07-13
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 高次元データにおける拡張クロスデータ行列法の漸近的性質とその応用について2015

    • Author(s)
      矢田和善, 青嶋 誠
    • Organizer
      日本数学会2015年度年会
    • Place of Presentation
      明治大学(東京都)
    • Year and Date
      2015-03-24
    • Related Report
      2014 Research-status Report
  • [Presentation] Extended cross-data-matrix methodology for high-dimensional data and its applications2015

    • Author(s)
      矢田和善, 青嶋 誠
    • Organizer
      京都大学数理解析研究所RIMS研究集会「New Advances in Statistical Inference and Its Related Topics」
    • Place of Presentation
      京都大学(京都府)
    • Year and Date
      2015-03-10
    • Related Report
      2014 Research-status Report
  • [Presentation] Reconstruction of a low-rank matrix for the power spiked model in high-dimensional settings2015

    • Author(s)
      村山 航, 矢田和善, 青嶋 誠
    • Organizer
      京都大学数理解析研究所RIMS研究集会「New Advances in Statistical Inference and Its Related Topics」
    • Place of Presentation
      京都大学(京都府)
    • Year and Date
      2015-03-09
    • Related Report
      2014 Research-status Report
  • [Presentation] 高次元混合分布におけるPCAとその応用2014

    • Author(s)
      矢田和善, 青嶋 誠
    • Organizer
      日本数学会2014年度秋季総合分科会
    • Place of Presentation
      広島大学(広島県)
    • Year and Date
      2014-09-28
    • Related Report
      2014 Research-status Report
  • [Presentation] 高次元小標本における共分散行列の同等性検定2014

    • Author(s)
      石井 晶, 矢田和善, 青嶋 誠
    • Organizer
      日本数学会2014年度秋季総合分科会
    • Place of Presentation
      広島大学(広島県)
    • Year and Date
      2014-09-28
    • Related Report
      2014 Research-status Report
  • [Presentation] 高次元データに対する特徴選択を用いた2次判別法について2014

    • Author(s)
      矢田和善, 青嶋 誠
    • Organizer
      2014年度統計関連学会連合大会
    • Place of Presentation
      東京大学(東京都)
    • Year and Date
      2014-09-14
    • Related Report
      2014 Research-status 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
      2016 Annual Research Report 2015 Research-status Report
  • [Remarks] 青嶋研究室ホームページ

    • URL

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

    • Related Report
      2014 Research-status Report
  • [Funded Workshop] International Symposium on Statistical Analysis for Large Complex Data2016

    • Place of Presentation
      筑波大学(茨城県つくば市)
    • Year and Date
      2016-11-21
    • Related Report
      2016 Annual Research Report

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Published: 2014-04-04   Modified: 2022-02-16  

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