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高次元多変量データにおけるモデル選択規準の一致性

Research Project

Project/Area Number 18J12123
Research Category

Grant-in-Aid for JSPS Fellows

Allocation TypeSingle-year Grants
Section国内
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionHiroshima University

Principal Investigator

小田 凌也  広島大学, 情報科学部, 特任助教

Project Period (FY) 2018-04-25 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2019: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2018: ¥800,000 (Direct Cost: ¥800,000)
Keywords変数選択 / 多変量解析 / 高次元 / 高次元一致性 / 多変量線形回帰モデル / 正準判別分析モデル / 統計数学
Outline of Annual Research Achievements

複数の予測対象である変数(目的変数)とそれらに影響を与えると考えられる変数(説明変数)の関係を記述する多変量線形回帰モデルにおいて, 説明変数を選択するための様々な変数選択法が提案されている. 特に, 一致性をもつ変数選択法は有限標本下でも真のモデルを選択する確率が高いことが期待され, これまで標本数のみを無限大とする大標本漸近枠組みの下で様々な変数選択法の一致性が評価されてきた.
近年では, 標本数のみでなく目的変数ベクトルの次元数もしくは説明変数ベクトルの次元数も大きな高次元データを扱う重要性が高まっている. しかし, 大標本漸近枠組みを用いて一致性を評価した変数選択法は, 高次元データに対して真のモデルを選択する確率が低くなる可能性がある. さらに, これまでに提案されている変数選択法の多くは, 目的変数ベクトルの次元数は標本数よりも小さくないと使用することができず, 一致性を評価する際に真のモデルにおける誤差ベクトルに正規性が仮定されている.
そこで本研究では, 目的変数ベクトルの次元数は標本数よりも大きくても使用できるようリッジ型変数選択規準を用いた変数選択法に着目した. さらに, 一致性を保証する際, 真のモデルにおける誤差ベクトルに正規性は仮定せず, 標本数は必ず無限大, 目的変数ベクトルの次元数は標本数を超えて無限大でも固定でもよい, 説明変数ベクトルの次元数は標本数未満の下で無限大でも固定でもよいという大標本高次元漸近枠組みを用いた. 非正規性と大標本高次元漸近枠組みの両方の下で一致性をもつ変数選択法はこれまでに存在しなかった. 本提案手法は非正規性の下でも標本数がある程度大きければ次元数の大小に関わらず真のモデルを選択する確率が高いことが期待できる.

Research Progress Status

令和元年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

令和元年度が最終年度であるため、記入しない。

Report

(2 results)
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • Research Products

    (22 results)

All 2020 2019 2018 Other

All Int'l Joint Research (1 results) Journal Article (11 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 6 results,  Open Access: 6 results) Presentation (10 results) (of which Int'l Joint Research: 2 results,  Invited: 1 results)

  • [Int'l Joint Research] スウェーデン農業科学大学/リンショーピング大学(スウェーデン)

    • Related Report
      2018 Annual Research Report
  • [Journal Article] A consistent variable selection method in high-dimensional canonical discriminant analysis2020

    • Author(s)
      Oda Ryoya、Suzuki Yuya、Yanagihara Hirokazu、Fujikoshi Yasunori
    • Journal Title

      Journal of Multivariate Analysis

      Volume: 175 Pages: 104561-104561

    • DOI

      10.1016/j.jmva.2019.104561

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A high-dimensional bias-corrected AIC for selecting response variables in multivariate calibration2020

    • Author(s)
      Oda Ryoya、Mima Yoshie、Yanagihara Hirokazu、Fujikoshi Yasunori
    • Journal Title

      Communications in Statistics - Theory and Methods

      Volume: - Issue: 14 Pages: 1-24

    • DOI

      10.1080/03610926.2019.1705978

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A fast and consistent variable selection method for high-dimensional multivariate linear regression with a large number of explanatory variables2020

    • Author(s)
      Oda Ryoya、Yanagihara Hirokazu
    • Journal Title

      Electronic Journal of Statistics

      Volume: 14 Issue: 1 Pages: 1386-1412

    • DOI

      10.1214/20-ejs1701

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Consistent variable selection criteria in multivariate linear regression even when dimension exceeds sample size2020

    • Author(s)
      Oda Ryoya
    • Journal Title

      Hiroshima Mathematical Journal

      Volume: (in press)

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Strong Consistency of Log-Likelihood-Based Information Criterion in High-Dimensional Canonical Correlation Analysis2019

    • Author(s)
      Oda Ryoya、Yanagihara Hirokazu、Fujikoshi Yasunori
    • Journal Title

      Sankhya A

      Volume: - Issue: 1 Pages: 109-127

    • DOI

      10.1007/s13171-019-00174-3

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A fast and consistent variable selection method for high-dimensional multivariate linear regression with a large number of explanatory variables2019

    • Author(s)
      Oda, R., Yanagihara, Y.
    • Journal Title

      Hiroshima Statistical Research Group Technical Report

      Volume: TR19-01

    • Related Report
      2018 Annual Research Report
    • Open Access
  • [Journal Article] Strong consistency of log-likelihood-based information criterion in high-dimensional canonical correlation analysis2019

    • Author(s)
      Oda, R., Yanagihara, H., Fujikoshi, Y.
    • Journal Title

      Hiroshima Statistical Research Group Technical Report

      Volume: TR19-02

    • Related Report
      2018 Annual Research Report
    • Open Access
  • [Journal Article] Growth curve model with bilinear random coefficients2019

    • Author(s)
      Imori, S., von Rosen, D., Oda, R.
    • Journal Title

      Hiroshima Statistical Research Group Technical Report

      Volume: TR19-03

    • Related Report
      2018 Annual Research Report
    • Open Access / Int'l Joint Research
  • [Journal Article] A consistent variable selection method in high-dimensional canonical discriminant analysis2019

    • Author(s)
      Oda, R., Suzuki, Y., Yanagihara, H., Fujikoshi, Y.
    • Journal Title

      Hiroshima Statistical Research Group Technical Report

      Volume: TR19-04

    • Related Report
      2018 Annual Research Report
    • Open Access
  • [Journal Article] Asymptotic null and non-null distributions of test statistics for redundancy in high-dimensional canonical correlation analysis2018

    • Author(s)
      Oda Ryoya、Yanagihara Hirokazu、Fujikoshi Yasunori
    • Journal Title

      Random Matrices: Theory and Applications

      Volume: 08 Issue: 01 Pages: 1950001-1950001

    • DOI

      10.1142/s2010326319500011

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A high-dimensional bias-corrected AIC for selecting response variables in multivariate calibration2018

    • Author(s)
      Oda, R., Mima, Y., Yanagihara, H., Fujikoshi, Y.
    • Journal Title

      Hiroshima Statistical Research Group Technical Report

      Volume: TR18-10

    • Related Report
      2018 Annual Research Report
    • Open Access
  • [Presentation] Consistency of variable selection criteria in high-dimensional multiple responses linear regression2020

    • Author(s)
      小田凌也
    • Organizer
      広島大学金曜セミナー
    • Related Report
      2019 Annual Research Report
  • [Presentation] 高次元多変量モデルにおける非正規下での変数選択法の一致性2019

    • Author(s)
      小田凌也, 栁原宏和
    • Organizer
      2019年度 統計関連学会連合大会
    • Related Report
      2019 Annual Research Report
  • [Presentation] 多変量線形回帰におけるリッジ型標本共分散行列を用いた変数選択規準の一致性2019

    • Author(s)
      小田凌也, 栁原宏和
    • Organizer
      統計サマーセミナー2019
    • Related Report
      2019 Annual Research Report
  • [Presentation] 多変量線形回帰における Adaptive Group Lasso 型罰則付き推定法2019

    • Author(s)
      小田凌也, 栁原宏和
    • Organizer
      日本行動計量学会岡山地域部会第71回研究会
    • Related Report
      2018 Annual Research Report
  • [Presentation] A consistent variable selection method in the high-dimensional multiple responses linear regression2018

    • Author(s)
      Oda, R., Yanagihara, H.
    • Organizer
      The 5th Institute of Mathematical Statistics Asia Pacific Rim Meeting
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 多変量線形回帰における Group Lasso 型罰則項を用いた推定法2018

    • Author(s)
      小田凌也, 栁原宏和
    • Organizer
      統計サマーセミナー2018
    • Related Report
      2018 Annual Research Report
  • [Presentation] Group Lasso 型罰則項を伴う重み付き残差平方和の最小化に基づく多変量線形回帰モデルの推定2018

    • Author(s)
      小田凌也, 栁原宏和
    • Organizer
      2018年度統計関連学会連合大会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 正準判別分析における一致性を持つ高次元変数の選択法2018

    • Author(s)
      鈴木裕也, 小田凌也, 栁原宏和, 藤越康祝
    • Organizer
      2018年度統計関連学会連合大会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Sparse Group Lasso を用いた GMANOVA モデルの変数選択2018

    • Author(s)
      永井勇, 小田凌也, 栁原宏和
    • Organizer
      2018年度統計関連学会連合大会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Growth curve model with bilinear random coefficient2018

    • Author(s)
      Imori, S., von Rosen, D., Oda, R.
    • Organizer
      CMStatistics 2018
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited

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Published: 2018-05-01   Modified: 2024-03-26  

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