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Construction and evaluation of non-Gaussian spatio-temporal models through the use of gradient maps

Research Project

Project/Area Number 19700258
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Statistical science
Research InstitutionThe University of Tokyo

Principal Investigator

SEI Tomonari  The University of Tokyo, 大学院・情報理工学系研究科, 助教 (20401242)

Project Period (FY) 2007 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥3,920,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥720,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥800,000 (Direct Cost: ¥800,000)
Keywords勾配写像 / 凸最適化問題 / 輸送問題 / 方向統計学 / 時空間モデル / 凸関数 / 非ガウスモデル / グラフィカルモデリング / 多変量解析 / 不等分散性
Research Abstract

For data in the form of function of time and space, we proposed a statistical model to extract complex structures behind the data. We used the gradient map as a special transformation. In particular, we apply a sparse estimation method, which is an analogy of recently developed methodology in machine learning theory. Furthermore, we generalize our models to those of directional data. We also clarify a theoretical merit of our models from the viewpoint of loss of estimation.

Report

(6 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report   Self-evaluation Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (35 results)

All 2011 2010 2009 2008 2007 Other

All Journal Article (13 results) (of which Peer Reviewed: 11 results) Presentation (18 results) Remarks (4 results)

  • [Journal Article] Efron's curvature of the structural gradient model2011

    • Author(s)
      Sei, T.
    • Journal Title

      Journal of the Japan Statistical Society accepted.

    • NAID

      10029335253

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A Jacobian inequality for gradient maps on the sphere and its application to directional statistics2011

    • Author(s)
      Sei, T.
    • Journal Title

      Communications in Statistics-Theory and Methods accepted.

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A Jacobian inequality for gradient maps on the sphere and its application to directional statistics2011

    • Author(s)
      Sei, T.
    • Journal Title

      Communications in Statistics-Theory and Methods

      Volume: (印刷中(掲載予定))

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Efron's curvature of the structural gradient model2011

    • Author(s)
      Sei, T.
    • Journal Title

      Journal of the Japan Statistical Society

      Volume: (印刷中(掲載予定))

    • NAID

      10029335253

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A structural model on a hypercube represented by optimal transport2010

    • Author(s)
      Sei, T.
    • Journal Title

      Statistica Sinica accepted.

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A structural model on a hypercube represented by optimal transport2010

    • Author(s)
      Sei, T
    • Journal Title

      Statistica Sinica (掲載決定)

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Gradient modeling for multivariate quantitative data2009

    • Author(s)
      Sei, T.
    • Journal Title

      Annals of the Institute of Statistical Mathematics accepted.

    • NAID

      40019008506

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Gradient modeling for multivariate quantitative data2009

    • Author(s)
      Sei, T
    • Journal Title

      Annals of the Institute of Statistical Mathematics (掲載決定)

    • NAID

      40019008506

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Perturbation method for determining the group of invariance of hierarchical models2009

    • Author(s)
      Sei, T., Aoki, S., Takemura, A.
    • Journal Title

      Advances in Applied Mathematics 43

      Pages: 375-389

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Jacobian inequality for gradient maps on the sphere and its application to directional statistics2009

    • Author(s)
      Sei, T.
    • Journal Title

      Technical Report METR2009-23 1

      Pages: 1-20

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Information geometry of small diffusions2008

    • Author(s)
      Tomonari Sei and Fumiyasu Komaki
    • Journal Title

      Statistical Inference for Stochastic Processes 11

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Gradient modeling for multivariate analysis2008

    • Author(s)
      Tomonari Sei
    • Journal Title

      Proceedings of The Pyrenees International Workshop SPO 2007 1

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A structural model on a hypercube represented by optimal transport2008

    • Author(s)
      Tomonari Sei
    • Journal Title

      Technical Report METR2009-03 1

    • Related Report
      2008 Annual Research Report
  • [Presentation] Structural gradient model for time series2010

    • Author(s)
      Sei, T.
    • Organizer
      The International Symposium on Statistical Analysis of Spatio-Temporal Data
    • Place of Presentation
      Kamakura, Japan.
    • Year and Date
      2010-11-06
    • Related Report
      2010 Final Research Report
  • [Presentation] Structural gradient model for time series2010

    • Author(s)
      Sei, T.
    • Organizer
      The International Symposium on Statistical Analysis of Spatio-Temporal Data
    • Place of Presentation
      鎌倉
    • Year and Date
      2010-11-06
    • Related Report
      2010 Annual Research Report
  • [Presentation] 時系列解析のための構造的勾配モデル2010

    • Author(s)
      清智也
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2010-09-06
    • Related Report
      2010 Final Research Report
  • [Presentation] Optimal transportation and statistics2010

    • Author(s)
      Sei, T.
    • Organizer
      BIRS 5-day Workshop-Optimal transportation and applications
    • Place of Presentation
      Banff, Canada.
    • Year and Date
      2010-04-21
    • Related Report
      2010 Final Research Report
  • [Presentation] 勾配写像で表される球面分布族とその性質2009

    • Author(s)
      清智也
    • Organizer
      研究集会「高次元データの統計学-理論・方法論・関連分野への応用-」
    • Place of Presentation
      筑波大学
    • Year and Date
      2009-12-15
    • Related Report
      2010 Final Research Report
  • [Presentation] Spherical distributions defined by gradient maps2009

    • Author(s)
      Sei, T.
    • Organizer
      Directional, asymptotic, differential-geometric statistics and related area
    • Place of Presentation
      Osaka, Japan.
    • Year and Date
      2009-11-06
    • Related Report
      2010 Final Research Report
  • [Presentation] 球面上の勾配写像で表される分布族2009

    • Author(s)
      清智也
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      同志社大学
    • Year and Date
      2009-09-08
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Presentation] 球面上の勾配写像で表される分布族2009

    • Author(s)
      清智也
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      同志社大学, 京都
    • Year and Date
      2009-09-08
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] 凸関数のフーリエ級数表示と勾配モデル2008

    • Author(s)
      清智也
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      慶應義塾大学
    • Year and Date
      2008-09-10
    • Related Report
      2010 Final Research Report
  • [Presentation] 凸関数のフーリエ級数表示と勾配モデル2008

    • Author(s)
      清智也
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      慶應義塾大学, 神奈川
    • Year and Date
      2008-09-10
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] 凸関数のフーリエ級数表示と勾配モデル2008

    • Author(s)
      清智也
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      慶應義塾大学(神奈川)
    • Year and Date
      2008-09-10
    • Related Report
      2008 Annual Research Report
  • [Presentation] 構造的勾配モデルの許容領域について2008

    • Author(s)
      清 智也
    • Organizer
      京都大学数理解析研究所研究会「Statistical Analysis of Various Models」
    • Place of Presentation
      京都
    • Year and Date
      2008-03-11
    • Related Report
      2007 Annual Research Report
  • [Presentation] Gradient modeling for multivariate analysis2007

    • Author(s)
      Sei, T.
    • Organizer
      The Pyrenees International Workshop on Statistics, Probability and Operations Research (SPO 2007)
    • Place of Presentation
      Jaca, Spain.
    • Year and Date
      2007-09-12
    • Related Report
      2010 Final Research Report
  • [Presentation] Gradient modeling for multivariate analysis2007

    • Author(s)
      清 智也
    • Organizer
      The Pyrenees International Workshop on Statistics, Probability and Operations Research
    • Place of Presentation
      Jaca, Spain
    • Year and Date
      2007-09-12
    • Related Report
      2007 Annual Research Report
  • [Presentation] Brenier写像を利用した近似的グラフィカルモデリング2007

    • Author(s)
      清智也
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      神戸大学
    • Year and Date
      2007-09-08
    • Related Report
      2010 Final Research Report
  • [Presentation] Brenier写像を利用した近似的グラフィカルモデリング2007

    • Author(s)
      清智也
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      神戸大学, 神戸
    • Year and Date
      2007-09-08
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Brenier写像を利用した近似的グラフィカルモデリング2007

    • Author(s)
      清 智也
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      神戸
    • Year and Date
      2007-09-08
    • Related Report
      2007 Annual Research Report
  • [Presentation] Gradient modeling for multivariate analysis2007

    • Author(s)
      Sei, T
    • Organizer
      The Pyrenees International Workshop on Statistics, Probability and Operations Research (SPO 2007)
    • Place of Presentation
      Jaca, Spain
    • Related Report
      2009 Self-evaluation Report
  • [Remarks] ホームページ等

    • Related Report
      2010 Final Research Report
  • [Remarks]

    • URL

      http://www.stat.t.u-tokyo.ac.jp/~sei/cv-sei-j.html

    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://www.stat.t.u-tokyo.acjp/~sei/cv-sei-j.html

    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://www.stat.t.u-tokyo.ac.jp/~sei/cv-sei-j.html

    • Related Report
      2007 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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