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Consideration on singularities in learning theory by complex and real analysis

Research Project

Project/Area Number 23540224
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionNihon University

Principal Investigator

AOYAGI Miki  日本大学, 理工学部, 准教授 (90338434)

Project Period (FY) 2011-04-28 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords学習係数 / 特異点解消 / log canonical threshold / 学習理論
Outline of Final Research Achievements

The purpose of a learning system is to estimate an unknown true density function that generates the data. Recently, the WAIC model selection method, which is a generalized AIC, has been considered for estimating a probability function from data in a singular learning system. The learning coefficient in Bayesian estimation serves to measure the learning efficiency, and has an important role in the WAIC method. Mathematically, the learning coefficient is the log canonical threshold of the relative entropy. In this study we consider learning coefficients and several theorems for our results.

Report

(7 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (14 results)

All 2017 2016 2015 2014 2013 2012 Other

All Journal Article (9 results) (of which Peer Reviewed: 6 results,  Acknowledgement Compliant: 3 results) Presentation (5 results) (of which Int'l Joint Research: 1 results,  Invited: 2 results)

  • [Journal Article] Learning coefficients and reproducing true probability functions in learning systems2017

    • Author(s)
      Miki Aoyagi
    • Journal Title

      New Trends in Analysis and Interdisciplinary Applications, Trends in Mathematics

      Volume: 10 Pages: 347-353

    • DOI

      10.1007/978-3-319-48812-7_44

    • ISBN
      9783319488103, 9783319488127
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] ベイズ推定とギブズ推定2016

    • Author(s)
      岡田憲相, 青柳美輝
    • Journal Title

      日本大学理工学部学術講演会予稿集

      Volume: 60 Pages: 1200-1201

    • Related Report
      2016 Annual Research Report
  • [Journal Article] 学習理論と学習係数2015

    • Author(s)
      青柳美輝 岡田憲相
    • Journal Title

      数理解析研究所講究録, 再生核の応用についての総合的な研究

      Volume: 1980 Pages: 220-233

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Learning coefficients and reproducing true probability functions in learning systems2015

    • Author(s)
      Miki Aoyagi
    • Journal Title

      The tenth ISAAC Congress

      Volume: 10

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] 学習理論における特異性と特異点解消について2014

    • Author(s)
      高村京輔 青柳美輝
    • Journal Title

      日本大学理工学部学術講演会

      Volume: 58 Pages: 1307-1308

    • Related Report
      2014 Research-status Report
  • [Journal Article] 学習理論における特異性の超関数を使った解析について2014

    • Author(s)
      高橋
    • Journal Title

      日本大学理工学部学術講演会

      Volume: 58 Pages: 1311-1312

    • Related Report
      2014 Research-status Report
  • [Journal Article] Learning coefficient in Bayesian estimation of restricted Boltzmann machine2013

    • Author(s)
      Miki Aoyagi
    • Journal Title

      Journal of Algebraic Statistics

      Volume: 4 Pages: 30-57

    • Related Report
      2013 Research-status Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Consideration on Singularities in Learning Theory and the Learning Coefficient2013

    • Author(s)
      Miki Aoyagi
    • Journal Title

      Entropy

      Volume: 15 Issue: 9 Pages: 3714-3733

    • DOI

      10.3390/e15093714

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Learning coefficient of generalization error in Bayesian estimation and Vandermonde matrix type singularity2012

    • Author(s)
      Miki Aoyagi and Kenji Nagata
    • Journal Title

      Neural Computation

      Volume: 24, Issue 6

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] ベイズ推定とギブズ推定2017

    • Author(s)
      岡田憲相, 青柳美輝
    • Organizer
      日本大学理工学部学術講演会
    • Place of Presentation
      日本大学理工学部(東京都千代田区)
    • Related Report
      2016 Annual Research Report
  • [Presentation] 学習理論と学習係数2015

    • Author(s)
      青柳美輝 岡田憲相
    • Organizer
      RIMS Symposium, 再生核の応用についての総合的な研究
    • Place of Presentation
      数理解析研究所(京都府・京都市)
    • Year and Date
      2015-10-07
    • Related Report
      2015 Research-status Report
  • [Presentation] Learning coefficients and reproducing true probability functions in learning systems2015

    • Author(s)
      Miki Aoyagi
    • Organizer
      The tenth ISAAC Congress
    • Place of Presentation
      Macau, China
    • Year and Date
      2015-08-03
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Learning coefficient and singular fluctuation in statistical learning theory2012

    • Author(s)
      Miki Aoyagi
    • Organizer
      Algebraic Statistics in the Alleghenies
    • Place of Presentation
      The Pennsylvania State University
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Consideration on singularities in learning theory and real log canonical threshold

    • Author(s)
      Miki Aoyagi
    • Organizer
      Singular learning theory: connecting algebraic geometry and model selection in statistics(招待講演)
    • Place of Presentation
      AIM Research Conference Center (ARCC), Palo Alto, USA
    • Related Report
      2011 Research-status Report

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

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