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Theory and Applications of Density Ratio

Research Project

Project/Area Number 24500340
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Statistical science
Research InstitutionNagoya University

Principal Investigator

Kanamori Takafumi  名古屋大学, 情報科学研究科, 教授 (60334546)

Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥5,330,000 (Direct Cost: ¥4,100,000、Indirect Cost: ¥1,230,000)
Fiscal Year 2014: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords数理統計学 / 機械学習 / 統計学 / 統計的学習理論 / ロバスト統計
Outline of Final Research Achievements

Density ratio is defined as the ratio of two probability densities. That is very useful when two distinct data domains are compared. Important applications of the density ratio includes regression analysis and classification problems under covariate shift, statistical test, and dimension reduction. In this study, we developed methods to improve the statistical accuracy and computational efficiency of density ratio estimation. Moreover, we studied the relation between density ration and statistical divergences which is regarded as a discrepancy measure between two probability distributions. Statistical usefulness of the divergence is considered from the view point of the density ratio.

Report

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

    (50 results)

All 2015 2014 2013 2012 2011

All Journal Article (18 results) (of which Peer Reviewed: 18 results,  Acknowledgement Compliant: 1 results,  Open Access: 4 results) Presentation (28 results) (of which Int'l Joint Research: 2 results,  Invited: 2 results) Book (4 results)

  • [Journal Article] Robust Estimation under Heavy Contamination using Unnormalized Models2015

    • Author(s)
      Takafumi Kanamori, Hironori Fujisawa
    • Journal Title

      Biometrika

      Volume: 102 Pages: 559-572

    • NAID

      110009971452

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Extended Robust Support Vector Machine Based on Financial Risk Minimization2014

    • Author(s)
      A. Takeda, S. Fujiwara, T. Kanamori
    • Journal Title

      Neural Computation

      Volume: 26 Issue: 11 Pages: 2541-2569

    • DOI

      10.1162/neco_a_00647

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Affine Invariant Divergences associated with Proper Composite Scoring Rules and their Applications2014

    • Author(s)
      T. Kanamori and H. Fujisawa,
    • Journal Title

      Bernoulli

      Volume: 20 Pages: 2278-2304

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Numerical Study of Learning Algorithms on Stiefel Manifold2014

    • Author(s)
      Takafumi Kanamori, Akiko Takeda
    • Journal Title

      Computational Management Science

      Volume: 11 Issue: 4 Pages: 319-340

    • DOI

      10.1007/s10287-013-0181-7

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Constrained Least-Squares Density-Difference Estimation2014

    • Author(s)
      T. D. Nguyen, M. C. du Plessis, T. Kanamori, M. Sugiyama
    • Journal Title

      IEICE Transactions on Information and Systems

      Volume: E97-D Pages: 1822-1829

    • NAID

      130004519278

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Statistical Analysis of Distance Estimators with Density Differences and Density Ratios2014

    • Author(s)
      T. Kanamori and M. Sugiyama
    • Journal Title

      Entropy

      Volume: 16 Issue: 2 Pages: 921-942

    • DOI

      10.3390/e16020921

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] A Bregman Extension of quasi-Newton updates II: Analysis of Robustness Properties2013

    • Author(s)
      Takafumi Kanamori and Atsumi Ohara
    • Journal Title

      Journal of Computational and Applied Mathematics

      Volume: 253 Pages: 104-122

    • DOI

      10.1016/j.cam.2013.04.005

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Density-difference estimation2013

    • Author(s)
      M. Sugiyama, T. Suzuki, T. Kanamori, M. C. du Plessis, S. Liu, and I. Takeuchi
    • Journal Title

      Neural Computation

      Volume: 25 Issue: 10 Pages: 2734-2775

    • DOI

      10.1162/neco_a_00492

    • NAID

      110009588474

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Conjugate Relation between Loss Functions and Uncertainty Sets in Classification Problems2013

    • Author(s)
      T. Kanamori, A. Takeda, T. Suzuki
    • Journal Title

      Journal of Machine Learning Research

      Volume: 14 Pages: 1461-1504

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Direct Divergence Approximation between Probability Distributions and its Applications in Machine Learning.2013

    • Author(s)
      Sugiyama, M., Liu, S., du Plessis, M. C., Yamanaka, M., Yamad a, M., Suzuki, T., & Kanamori, T.
    • Journal Title

      Journal of Computing Science and Engineering

      Volume: Vol.7no.2 Issue: 2 Pages: 99-111

    • DOI

      10.5626/jcse.2013.7.2.99

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Relative Density-Ratio Estimation for Robust Distribution Comparison2013

    • Author(s)
      Makoto Yamada, Taiji Suzuki, Takafumi Kanamori, Hirotaka Hachiya, and Masashi Sugiyama
    • Journal Title

      Neural Computation

      Volume: 25 Issue: 5 Pages: 1324-1370

    • DOI

      10.1162/neco_a_00442

    • NAID

      10031099905

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Semi-Supervised Learning with Density-Ratio Estimation2013

    • Author(s)
      M. Kawakita, T. Kanamori
    • Journal Title

      Machine Learning

      Volume: 91 Issue: 2 Pages: 189-209

    • DOI

      10.1007/s10994-013-5329-8

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Statistical Models and Learning Algorithms for Ordinal Regression Problems2013

    • Author(s)
      T. Kanamori
    • Journal Title

      Information Fusion

      Volume: 14 Issue: 2 Pages: 199-207

    • DOI

      10.1016/j.inffus.2012.05.006

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Improving LogitBoost with Prior Knowledge2013

    • Author(s)
      T. Kanamori, T. Takenouchi
    • Journal Title

      Information Fusion

      Volume: 14 Issue: 2 Pages: 208-219

    • DOI

      10.1016/j.inffus.2011.11.004

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] A Unified Classification Model Based on Robust Optimization2013

    • Author(s)
      Akiko Takeda, Hiroyuki Mitsugi, and Takafumi Kanamori
    • Journal Title

      Neural Computation

      Volume: 25 Issue: 3 Pages: 759-804

    • DOI

      10.1162/neco_a_00412

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Computational complexity of kernel-based density-ratio estimation: A condition number analysis2013

    • Author(s)
      Takafumi Kanamori, Taiji Suzuki, and Masashi Sugiyama
    • Journal Title

      Machine Learning

      Volume: 90 Issue: 3 Pages: 431-460

    • DOI

      10.1007/s10994-012-5323-6

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] A Bregman Extension of quasi-Newton updates I: An Information Geometrical framework2013

    • Author(s)
      Takafumi Kanamori and Atsumi Ohara
    • Journal Title

      Optimization Methods and Software

      Volume: 28 Issue: 1 Pages: 96-123

    • DOI

      10.1080/10556788.2011.613073

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Density ratio matching under the Bregman divergence: A unified framework of density ratio estimation2011

    • Author(s)
      Masashi Sugiyama, Taiji Suzuki, and Takafumi Kanamori
    • Journal Title

      Annals of the Institute of Statistical Mathematics

      Volume: 11 Issue: 5 Pages: 1-36

    • DOI

      10.1007/s10463-011-0343-8

    • NAID

      40019382740

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] Robust regression using unnormalized model under heterogeneous contamination2015

    • Author(s)
      Hironori Fujisawa, Takafumi Kanamori
    • Organizer
      International Conference of the ERCIM WG on Computational and Methodological Statistics
    • Place of Presentation
      London, UK
    • Year and Date
      2015-12-12
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Empirical Localization of Homogeneous Divergences on Discrete Sample Spaces2015

    • Author(s)
      Takashi Takenouchi, Takafumi Kanamori
    • Organizer
      The Neural Information Processing Systems
    • Place of Presentation
      Montreal, Canada
    • Year and Date
      2015-12-09
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Robustification of Learning Algorithms using Hinge-loss2015

    • Author(s)
      金森 敬文,藤原 秀平, 武田朗子
    • Organizer
      情報論的学習理論ワークショップ
    • Place of Presentation
      筑波
    • Year and Date
      2015-11-26
    • Related Report
      2015 Annual Research Report
  • [Presentation] 同次ダイバージェンスとその応用2015

    • Author(s)
      竹之内高志,金森 敬文
    • Organizer
      情報論的学習理論ワークショップ
    • Place of Presentation
      筑波
    • Year and Date
      2015-11-26
    • Related Report
      2015 Annual Research Report
  • [Presentation] 斉次ダイバージェンスとその応用2015

    • Author(s)
      金森 敬文
    • Organizer
      RIMS共同研究「量子統計モデリングの基盤構築」
    • Place of Presentation
      京都
    • Year and Date
      2015-11-12
    • Related Report
      2015 Annual Research Report
  • [Presentation] 非凸最適化に基づく機械学習アルゴリズムのロバストネス2015

    • Author(s)
      金森 敬文,藤原 秀平, 武田朗子
    • Organizer
      日本オペレーションズ・リサーチ学会 RAMPシンポジウム
    • Place of Presentation
      静岡
    • Year and Date
      2015-10-15
    • Related Report
      2015 Annual Research Report
  • [Presentation] 擬球スコアとその周辺2015

    • Author(s)
      金森 敬文
    • Organizer
      研究集会「大規模統計モデリングと計算統計II」
    • Place of Presentation
      東京
    • Year and Date
      2015-09-26
    • Related Report
      2015 Annual Research Report
  • [Presentation] Robustness of Machine Learning Algorithms using Non-Convex Loss Functions2015

    • Author(s)
      金森 敬文,藤原 秀平, 武田朗子
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      岡山
    • Year and Date
      2015-09-08
    • Related Report
      2015 Annual Research Report
  • [Presentation] Robust Estimation under Heavy Contamination using Unnormalized Models2015

    • Author(s)
      金森 敬文,藤澤洋徳
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      岡山
    • Year and Date
      2015-09-08
    • Related Report
      2015 Annual Research Report
  • [Presentation] 準ニュートン法のブレグマン拡張と疎なヘッセ行列の更新則2015

    • Author(s)
      金森 敬文
    • Organizer
      RIMS共同研究「デザイン・符号・グラフおよびその周辺」
    • Place of Presentation
      京都
    • Year and Date
      2015-07-09
    • Related Report
      2015 Annual Research Report
  • [Presentation] Legendre Transformation in Machine Learning2014

    • Author(s)
      T. Kanamori
    • Organizer
      Workshop: Information Geometry for Machine Learning
    • Place of Presentation
      RIKEN, Saitama, Japan
    • Year and Date
      2014-12-03 – 2014-12-05
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 規格化されていないモデルを用いたロバスト推定2014

    • Author(s)
      金森敬文
    • Organizer
      統計多様体の諸分野への応用
    • Place of Presentation
      京都大学数理解析研究所共同研究
    • Year and Date
      2014-11-19 – 2014-11-21
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Breakdown Point of Robust Support Vector Machine2014

    • Author(s)
      Takafumi Kanamori, Fujiwara Shuhei, Akiko Takeda
    • Organizer
      第17回情報論的学習理論ワークショップ(IBIS2014)
    • Place of Presentation
      名古屋大学
    • Year and Date
      2014-11-17 – 2014-11-19
    • Related Report
      2014 Research-status Report
  • [Presentation] Robust Estimation under Heavy Contamination using Unnormalized Models2014

    • Author(s)
      Takafumi Kanamori, Hironori Fujisawa,
    • Organizer
      第17回情報論的学習理論ワークショップ(IBIS2014)
    • Place of Presentation
      名古屋大学
    • Year and Date
      2014-11-17 – 2014-11-19
    • Related Report
      2014 Research-status Report
  • [Presentation] Parallel Distributed Block Coordinate Descent Methods based on Pairwise Comparison Oracle,2014

    • Author(s)
      Kota Matsui, Wataru Kumagai, Takafumi Kanamori,
    • Organizer
      第17回情報論的学習理論ワークショップ(IBIS2014)
    • Place of Presentation
      名古屋大学
    • Year and Date
      2014-11-17 – 2014-11-19
    • Related Report
      2014 Research-status Report
  • [Presentation] ロバストサポートベクターマシンの拡張に対する DC アルゴリズムの適用,2014

    • Author(s)
      藤原秀平, 武田朗子, 金森敬文,
    • Organizer
      第17回情報論的学習理論ワークショップ(IBIS2014)
    • Place of Presentation
      名古屋大学
    • Year and Date
      2014-11-17 – 2014-11-19
    • Related Report
      2014 Research-status Report
  • [Presentation] Affine Invariant Divergences and their Applications,2014

    • Author(s)
      T. Kanamori, H. Fujisawa,
    • Organizer
      The 3rd Institute of Mathematical Statistics, Asia Pacific Rim Meeting,
    • Place of Presentation
      Taipei
    • Year and Date
      2014-06-30 – 2014-07-03
    • Related Report
      2014 Research-status Report
  • [Presentation] A comparison-based derivative free optimization algorithm and its query complexity2014

    • Author(s)
      松井孝太, 熊谷 亘, 金森 敬文
    • Organizer
      東海ファシィ研究会
    • Place of Presentation
      愛知県知多郡南知多町日間賀島字永峰18 日間賀島公民館
    • Related Report
      2013 Research-status Report
  • [Presentation] ヘルダー不等式とスケール不変ダイバージェンス2014

    • Author(s)
      金森敬文
    • Organizer
      研究所短期共同研究,統計多様体の幾何学の新展開
    • Place of Presentation
      京都大学 数理解析研究所
    • Related Report
      2013 Research-status Report
  • [Presentation] アファイン不変な統計的ダイバージェンスとその応用2013

    • Author(s)
      金森敬文,藤澤洋徳
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      大阪大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Constrained Least-Squares Density-Difference Estimation2013

    • Author(s)
      Nguyen Tuan Duong, Marthinus Christoffel du Plessis, Takafumi Kanamori, Masashi Sugiyama
    • Organizer
      情報論的学習理論と機械学習研究会
    • Place of Presentation
      名古屋工業大学
    • Related Report
      2012 Research-status Report
  • [Presentation] A Conjugate Property between Loss Functions and Uncertainty Sets in Classification Problems,2012

    • Author(s)
      Kanamori, T., Takeda, A., Suzuki, T.
    • Organizer
      25th International Conference on Learning Theory(COLT)
    • Place of Presentation
      Edinburgh, Scotland
    • Related Report
      2012 Research-status Report
  • [Presentation] A Unified Robust Classification Model2012

    • Author(s)
      Takeda, A., Mitsugi, H., Kanamori, T.
    • Organizer
      29th International Conference on Machine Learning(ICML)
    • Place of Presentation
      Edinburgh, Scotland
    • Related Report
      2012 Research-status Report
  • [Presentation] f-divergence estimation and two-sample test under semi-parametric density ratio models.2012

    • Author(s)
      Kanamori T., Suzuki, T., Sugiyama, M.
    • Organizer
      The 2nd Institute of Mathematical Statistics, Asia Pacific Rim Meeting (IMS-APRM)
    • Place of Presentation
      Tsukuba,Japan
    • Related Report
      2012 Research-status Report
  • [Presentation] Robust optimization-based classification method.2012

    • Author(s)
      Takeda A. Kanamori T., Mitsugi H.
    • Organizer
      The 21st International Symposium on Mathematical Programming(ISMP)
    • Place of Presentation
      Berlin, Germany
    • Related Report
      2012 Research-status Report
  • [Presentation] Density-Difference Estimation.2012

    • Author(s)
      Sugiyama M., Kanamori T., Suzuki T., Plessis M., Liu S., Takeuchi I.
    • Organizer
      The Neural Information Processing Systems(NIPS)
    • Place of Presentation
      Nevada, USA
    • Related Report
      2012 Research-status Report
  • [Presentation] Non-Convex Optimization on Stiefel Manifold and Applications to Machine Learning,2012

    • Author(s)
      Kanamori T., Takeda A.
    • Organizer
      The 19th International Conference on Neural Information Processing(ICONIP)
    • Place of Presentation
      Doha, Qatar
    • Related Report
      2012 Research-status Report
  • [Presentation] 2値判別における損失関数と不確実性集合の共役性,2012

    • Author(s)
      金森敬文, 武田朗子, 鈴木大慈
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      北海道大学
    • Related Report
      2012 Research-status Report
  • [Book] 統計的学習理論2015

    • Author(s)
      金森敬文
    • Total Pages
      189
    • Publisher
      講談社
    • Related Report
      2015 Annual Research Report
  • [Book] 統計的学習の基礎 —データマイニング・推論・予測—2014

    • Author(s)
      Trevor Hastie 他
    • Total Pages
      47
    • Publisher
      共立出版
    • Related Report
      2014 Research-status Report
  • [Book] モンテカルロ法ハンドブック2014

    • Author(s)
      伏見正則 他
    • Total Pages
      9
    • Publisher
      朝倉書店
    • Related Report
      2014 Research-status Report
  • [Book] 応用数理ハンドブック,2013

    • Author(s)
      薩摩順吉・大石進一・杉原正顕(編)
    • Publisher
      朝倉書店
    • Related Report
      2013 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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