• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Model selection and machine learning theory via large-scale random matrices

Research Project

Project/Area Number 20700258
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Statistical science
Research InstitutionThe Institute of Statistical Mathematics

Principal Investigator

KOBAYASHI Kei  統計数理研究所, 数理・推論研究系, 助教 (90465922)

Project Period (FY) 2008 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsカーネルグラム行列 / カーネルマシン / モデル選択 / 大規模ランダム行列
Research Abstract

Nystrom approximation method for kernel gram matrices reduces the rank of each matrix in two steps. In order to approximate those matrices efficiently, it is important to set an adequate reduction rate for each step and handle the tradeoff between accuracy of the approximation and cost of the computation. In this research program, we used methods of computational physics for analyzing large-scale random matrices and optimized the reduction rates. We checked experimentally that the proposed method attains high accuracy even with very low computational cost for real data of hand-written characters. We derived an upper bound for approximation error of Nystrom method and proved the statistical consistency. Moreover, the proposed method can be used not only for Nystrom method but also for other approximation methods including the sparse greedy approximation and the incomplete Cholesky decomposition. In parallel with this research, we studied commutative algebraic statistics and proposed a novel statistical estimator by applying the computational algebra to the asymptotic estimation theory. In addition, we proposed a statistical method to analyze dendrograms of mental lexicon, which is an example of models holding an algebraic structure.

Report

(6 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report   Self-evaluation Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (50 results)

All 2012 2011 2010 2009 2008

All Journal Article (13 results) (of which Peer Reviewed: 4 results) Presentation (37 results)

  • [Journal Article] 母語話者と第二言語話者の心内辞書-類語の混在する単語群における意味的クラスタリング構造-2012

    • Author(s)
      折田充,小林景
    • Journal Title

      熊本大学社会文化研究

      Volume: Vol.10 Pages: 17-30

    • Related Report
      2011 Final Research Report
  • [Journal Article] 心内辞書内の意味的クラスタリング構造-L1とL2の違いの指標となり得る語類の特定-2011

    • Author(s)
      折田充,小林景
    • Journal Title

      熊本大学社会文化研究

      Volume: 第9号 Pages: 19-37

    • NAID

      110008138849

    • Related Report
      2011 Final Research Report
  • [Journal Article] Effects of Intra-Lexical Features on the Completion Time of Sorting Tasks2011

    • Author(s)
      Orita, M. and Kobayashi, K.
    • Journal Title

      International Journal of Social and Cultural Studies

      Volume: Vol.4 Pages: 1-23

    • NAID

      110009613788

    • Related Report
      2011 Final Research Report
  • [Journal Article] DeRobertis分離度による全変動距離の上界2011

    • Author(s)
      小林景
    • Journal Title

      統計数理

      Volume: 59-2 Pages: 321-328

    • NAID

      40019180995

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Journal Article] 心内辞書内の意味的クラスタリング-高頻度英語形容詞における母語話者と第二言語話者の相違2011

    • Author(s)
      折田充,小林景
    • Journal Title

      九州英語教育学会紀要

      Volume: Vol.39 Pages: 1-11

    • Related Report
      2011 Final Research Report
  • [Journal Article] 心内辞書内の意味的クラスタリング-高頻度英語形容詞における母語話者と第二言語話者の相違2011

    • Author(s)
      折田充, 小林景
    • Journal Title

      九州英語教育学会紀要

      Volume: 39 Pages: 1-11

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Effects of Intra-Lexical Features on the Completion Time of Sorting Tasks2011

    • Author(s)
      Orita, Mitsuru, Kobayashi, Kei
    • Journal Title

      International Journal of Social and Cultural Studies

      Volume: 4 Pages: 1-23

    • NAID

      110009613788

    • Related Report
      2011 Annual Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 心内辞書内の意味的クラスタリング構造-L1とL2の違いの指標となり得る語類の特定-2011

    • Author(s)
      折田充, 小林景
    • Journal Title

      熊本大学社会文化研究 第9号

      Pages: 19-37

    • NAID

      110008138849

    • Related Report
      2010 Self-evaluation Report
  • [Journal Article] Effects of Intra-Lexical Features on the Completion Time of Sorting Tasks2011

    • Author(s)
      Orita, M., Kobayashi, K.
    • Journal Title

      International Journal of Social and Cultural Studies Vol.4

      Pages: 1-23

    • NAID

      110009613788

    • Related Report
      2010 Self-evaluation Report
  • [Journal Article] 心内辞書内の意味的クラスタリング構造-L1とL2の違いの指標となり得る語類の特定2011

    • Author(s)
      折田充, 小林景
    • Journal Title

      熊本大学社会文化研究

      Volume: 9 Pages: 19-37

    • NAID

      110008138849

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Bayesian shrinkage prediction for the regression problem2008

    • Author(s)
      Kobayashi, K. and Komaki, F.
    • Journal Title

      Journal of Multivariate Analysis

      Volume: 99(9) Pages: 1888-1905

    • Related Report
      2011 Final Research Report
  • [Journal Article] Bayesian shrinkage prediction for the regression problem2008

    • Author(s)
      Kobayashi, K., Komaki, F.
    • Journal Title

      Journal of Multivariate Analysis 99(9)

      Pages: 1888-1905

    • Related Report
      2010 Self-evaluation Report
  • [Journal Article] Bayesian shrinkage prediction for the regression problem2008

    • Author(s)
      Kobayashi, K. and Komaki, F.
    • Journal Title

      Journal of Multivariate Analysis 99

      Pages: 1888-1905

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Semantically Equivalent Lexical Items between L1 and L2 Mental Lexicons2012

    • Author(s)
      Orita, M. and Kobayashi, K.
    • Organizer
      22nd Vocabulary Acquisition Research Group Network Conference
    • Place of Presentation
      Swansea Univ
    • Year and Date
      2012-03-16
    • Related Report
      2011 Final Research Report
  • [Presentation] Semantically Equivalent Lexical Items between L1 and L2 Mental Lexicons2012

    • Author(s)
      Orita, Mitsuru, Kobayashi, Kei
    • Organizer
      22nd Vocabulary Acquisition Research Group Network Conference
    • Place of Presentation
      Swansea Univ.
    • Year and Date
      2012-03-16
    • Related Report
      2011 Annual Research Report
  • [Presentation] 計算機代数を用いた情報幾何学と漸近的推定理論2012

    • Author(s)
      小林景
    • Organizer
      情報論的学習理論と機械学習研究会(IBISML)
    • Place of Presentation
      統計数理研究所
    • Year and Date
      2012-03-13
    • Related Report
      2011 Final Research Report
  • [Presentation] 計算機代数を用いた情報幾何学と漸近的推定理論2012

    • Author(s)
      小林景
    • Organizer
      情報論的学習理論と機械学習研究会(IBISML)
    • Place of Presentation
      統計数理研究所(招待講演)
    • Year and Date
      2012-03-13
    • Related Report
      2011 Annual Research Report
  • [Presentation] Asymptotic efficiency of statistical estimators via algebraic computation and information geometry2012

    • Author(s)
      Kobayashi, K.
    • Organizer
      ISM-ISI-ISSAS Joint Conference
    • Place of Presentation
      統計数理研究
    • Year and Date
      2012-02-03
    • Related Report
      2011 Final Research Report
  • [Presentation] Asymptotic efficiency of statistical estimators via algebraic computation and information geometry2012

    • Author(s)
      Kobayashi, Kei
    • Organizer
      ISM-ISI-ISSAS Joint Conference
    • Place of Presentation
      統計数理研究所
    • Year and Date
      2012-02-03
    • Related Report
      2011 Annual Research Report
  • [Presentation] 計算機代数を用いた代数的統計モデルの推定理論2012

    • Author(s)
      小林景
    • Organizer
      研究集会「数理統計学と代数統計の新たな展開」
    • Place of Presentation
      つくば国際会議場,エポカルつくば
    • Year and Date
      2012-01-20
    • Related Report
      2011 Final Research Report
  • [Presentation] 計算機代数を用いた代数的統計モデルの推定理論2012

    • Author(s)
      小林景
    • Organizer
      研究集会「数理統計学と代数統計の新たな展開」
    • Place of Presentation
      つくば国際会議場エポカルつくば
    • Year and Date
      2012-01-20
    • Related Report
      2011 Annual Research Report
  • [Presentation] Using algebraic method in information geometry2012

    • Author(s)
      Kobayashi, K. and Wynn, H.
    • Organizer
      Information Geometry and its Applications III
    • Place of Presentation
      Leipzig
    • Related Report
      2011 Final Research Report
  • [Presentation] 母語の心内辞書と第二言語の心内辞書2011

    • Author(s)
      折田充,小林景
    • Organizer
      第40回九州英語教育学会
    • Place of Presentation
      宮崎県立看護大学
    • Year and Date
      2011-12-10
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] 計算機代数学を用いた漸近有効推定量の構成2011

    • Author(s)
      小林景
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      九州大学
    • Year and Date
      2011-09-05
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] 心内辞書内の意味的クラスタリング構造(3)-高頻度英語動詞における英語母語話者と日本人英語話者の相違2011

    • Author(s)
      折田充,小林景
    • Organizer
      第37回全国英語教育学会山形研究大会
    • Place of Presentation
      山形大学
    • Year and Date
      2011-08-21
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] Algebraic computations for asymptotically efficient estimators via information geometry2011

    • Author(s)
      Kobayashi, K. and Wynn, H.
    • Organizer
      Workshop on Geometric and Algebraic Statistics 3
    • Place of Presentation
      University of Warwick
    • Year and Date
      2011-04-07
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] Algebraic computations for asymptotically efficient estimators via information geometry2011

    • Author(s)
      Kobayashi, Kei, Wynn, Henry
    • Organizer
      WOGAS 3
    • Place of Presentation
      Warwick Univ.(招待講演)
    • Year and Date
      2011-04-07
    • Related Report
      2011 Annual Research Report
  • [Presentation] Semantic Clustering of High Frequency Nouns in L1 and L2 Mental Lexicons2011

    • Author(s)
      Orita, M. and Kobayashi, K.
    • Organizer
      Learners and Networks Conference 2011
    • Place of Presentation
      Swansea University
    • Year and Date
      2011-03-18
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] Semantic Clustering of High Frequency Nouns in L1 and L2 Mental Lexicons2011

    • Author(s)
      Orita, M., Kobayashi, K.
    • Organizer
      Learners and Networks Conference 2011
    • Place of Presentation
      Swansea University,イギリス
    • Year and Date
      2011-03-18
    • Related Report
      2010 Annual Research Report
  • [Presentation] 心内辞書内の意味的クラスタリング-母語話者と第二言語話者の相違2010

    • Author(s)
      折田充,小林景
    • Organizer
      第39回九州英語教育学会
    • Place of Presentation
      鹿児島大学
    • Year and Date
      2010-12-12
    • Related Report
      2011 Final Research Report 2010 Annual Research Report 2010 Self-evaluation Report
  • [Presentation] 心内辞書内のネットワーク構造-Sorting tasksを用いた母語話者と第二言語話者の違いの解明2010

    • Author(s)
      折田充,小林景
    • Organizer
      第54回熊本大学英文学会
    • Place of Presentation
      熊本大学
    • Year and Date
      2010-11-20
    • Related Report
      2011 Final Research Report 2010 Annual Research Report 2010 Self-evaluation Report
  • [Presentation] Difference in mental lexicon between native and non-native English speakers2010

    • Author(s)
      Kobayashi, K. and Orita, M.
    • Organizer
      73rd Annual Meeting of the Institute of Mathematical Statistics
    • Place of Presentation
      Gothenburg
    • Year and Date
      2010-08-13
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] Difference in mental lexicon between native and non-native English speakers2010

    • Author(s)
      Kobayashi, K., Orita, M.
    • Organizer
      73rd Annual Meeting of the Institute of Mathematical Statistics
    • Place of Presentation
      Gothenburg,スウェーデン
    • Year and Date
      2010-08-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] Effects of intra-lexical features on the completion time of sorting tasks2010

    • Author(s)
      折田充, 小林景
    • Organizer
      20th Vocabulary Acquisition Research Group Net work Conferenc
    • Place of Presentation
      Gregynog, UK
    • Year and Date
      2010-03-18
    • Related Report
      2009 Annual Research Report
  • [Presentation] Effects of intra-lexical Features on the completion time of sorting tasks2010

    • Author(s)
      Orita, M. and Kobayashi, K.
    • Organizer
      20th Vocabulary Acquisition Research Group Network Conference
    • Place of Presentation
      Gregynog
    • Year and Date
      2010-03-17
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] Shrinkage Bayesian prediction and its application to regression problems2010

    • Author(s)
      小林景
    • Organizer
      Queen Mary University Statistics Seminar
    • Place of Presentation
      Queen Mary University of London
    • Year and Date
      2010-03-04
    • Related Report
      2009 Annual Research Report
  • [Presentation] Using algebraic method in information geometry2010

    • Author(s)
      Kobayashi, K., Wynn, H.
    • Organizer
      Information Geometry and its Applications III
    • Place of Presentation
      Leipzig
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Using algebraic method in information geometry, Information Geometry and its Applications III2010

    • Author(s)
      Kobayashi, K., Wynn, H
    • Organizer
      Information Geometry and its Applications III
    • Place of Presentation
      Leipzig,ドイツ
    • Related Report
      2010 Annual Research Report
  • [Presentation] Predictors of L1 and L2 differences in lexical organisation2009

    • Author(s)
      Orita, M. and Kobayashi, K.
    • Organizer
      The 6th Vocabulary Acquisition Research Group Conference
    • Place of Presentation
      Tokyo
    • Year and Date
      2009-12-05
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] Predictors of L1 and L2 differences in lexical organisation2009

    • Author(s)
      折田充, 小林景
    • Organizer
      The 6th Vocabulary Acquisition Research Group Conference
    • Place of Presentation
      麗澤大学
    • Year and Date
      2009-12-05
    • Related Report
      2009 Annual Research Report
  • [Presentation] 日本人と英語母語話者との心内辞書構造の相違の統計的解析2009

    • Author(s)
      小林景,折田充
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      同志社大学,京田辺
    • Year and Date
      2009-09-09
    • Related Report
      2011 Final Research Report
  • [Presentation] 日本人と英語母語話者との心内辞書構造の相違の統計的解析2009

    • Author(s)
      小林景, 折田充
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      同志社大学, 京田辺
    • Year and Date
      2009-09-09
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] 日本人と英語母語話者との心内辞書構造の相違の統計的解析2009

    • Author(s)
      小林景, 折田充
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      京田辺
    • Year and Date
      2009-09-09
    • Related Report
      2009 Annual Research Report
  • [Presentation] Shrinkage Bayesian prediction and its application to regression problems2009

    • Author(s)
      Kobayashi, K.
    • Organizer
      Statistics Seminar
    • Place of Presentation
      Queen Mary Univ. of London
    • Year and Date
      2009-03-04
    • Related Report
      2011 Final Research Report
  • [Presentation] Shrinkage Bayesian prediction and its application to regression problems2009

    • Author(s)
      Kobayashi, K.
    • Organizer
      Statistics Seminar
    • Place of Presentation
      Queen Mary Univ.of London
    • Year and Date
      2009-03-04
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] 大規模行列固有値を用いたNystrom近似法の改良2008

    • Author(s)
      小林景
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      慶応義塾大学
    • Year and Date
      2008-09-09
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report 2008 Annual Research Report
  • [Presentation] Minimaxity of Stein-type Bayesian prediction for normal regression problem2008

    • Author(s)
      Kobayashi, K. and Komaki, F.
    • Organizer
      7th World Congress in Probability and Statistics
    • Place of Presentation
      Singapore
    • Year and Date
      2008-07-17
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report 2008 Annual Research Report
  • [Presentation] A Bayesian prediction for the Normal distributions with changeable covariances2008

    • Author(s)
      Kobayashi, K.
    • Organizer
      Joint Meeting of ISI, ISM and ISSAS
    • Place of Presentation
      Taipei
    • Year and Date
      2008-06-20
    • Related Report
      2011 Final Research Report
  • [Presentation] A Bayesian prediction for the Normal distributions with changeable covariances2008

    • Author(s)
      Kobayashi, K.
    • Organizer
      Joint Meeting of ISI
    • Place of Presentation
      ISM and ISSAS, Taipei
    • Year and Date
      2008-06-20
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] A Bayesian prediction for the Normal distributions with changeable covariances2008

    • Author(s)
      Kobayashi, K. and Komaki, F.
    • Organizer
      2008 Joint Meeting of ISI, ISM and ISSAS.
    • Place of Presentation
      Academia Sinica, Taipei
    • Year and Date
      2008-06-20
    • Related Report
      2008 Annual Research Report

URL: 

Published: 2008-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi