Novel tools of statistical analysis via their algebraic properties

• Project/Area Number: 24700288
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Statistical science
• Research Institution: The Institute of Statistical Mathematics
• Principal Investigator: Kobayashi Kei 統計数理研究所, 大学共同利用機関等の部局等, 助教 (90465922)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 代数統計学 / 漸近統計学 / 情報幾何学 / 高次元データ解析 / 漸近的統計理論 / 計算機代数 / 幾何学的統計学 / 漸近理論 / 統計的推測 / 国際情報交換 / ベイズ統計学

Outline of Final Research Achievements

A class of novel algebraic estimators for algebraic models is proposed. We proposed an explicit method to compute the estimators and estimates by using computational algebraic methods. The estimators are defined by some lower-degree polynomial equations by holding some asymptotic statistical efficiency. This allows fast computation of the estimates. This research should be the first result evaluating and controlling trade-off between algebraic computation and statistical efficiency. Another result is a new permutation test for dendrograms by using their geometrical and algebraic structures. We tested difference between mental lexicons between groups of examinees by using the proposed method. The results of this research project have been published in several international conferences and journals.

Research Products

• [Int'l Joint Research] ロンドン・スクール・オブ・エコノミクス(英国)
• [Journal Article] 自律的語彙学習が英語心内辞書構造に与える影響 (2015)
  • Author(s): 折田充, 小林景, 村里泰昭, 神本忠光, 吉井誠, Richard S. Lavin, 相澤一美
  • Journal Title: 九州英語教育学会紀要 Volume: 43 Pages: 1-10
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] 日本人英語学習者の英語心内辞書の変容 (2015)
  • Author(s): 折田充, 小林景, 村里泰昭, 神本忠光, 吉井誠, Richard S. Lavin, 相澤一美
  • Journal Title: 熊本大学社会文化研究 Volume: 13 Pages: 15-30
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Statistical analysis via the curvature of data space (2015)
  • Author(s): Kei Kobayashi, Mitsuru Orita, Henry P. Wynn
  • Journal Title: BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING (MAXENT 2014), AIP Conf. Proc. Volume: 1641,97 Pages: 97-104
  • DOI: 10.1063/1.4905968
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] 日本人大学生の英語心内辞書の変容 (2015)
  • Author(s): 提出確認用 折田 充・小林 景・村里泰昭・神本忠光・吉井 誠・Richard S. Lavin・相澤一美
  • Journal Title: 熊本大学社会文化研究 Volume: 13 Pages: 15-30
  • NAID: 110009896119
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Computational algebraic methods in efficient estimation (2014)
  • Author(s): Kei Kobayashi, Henry P. Wynn,
  • Journal Title: Geometric Theory of Information (Signals and Communication Technology), Springer-Verlag Volume: - Pages: 119-140
  • DOI: 10.1007/978-3-319-05317-2_6
  • ISBN: 9783319053165, 9783319053172
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] 英語熟達度と心内辞書内の意味的クラスタリング構造の関係 (2014)
  • Author(s): 折田 充・小林 景・村里泰昭・相澤一美・吉井 誠・Lavin, R.
  • Journal Title: 九州英語教育学会紀要 Volume: 42 Pages: 1-10
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Computational algebraic methods in efficient estimation (2014)
  • Author(s): Kei Kobayashi and Henry P. Wynn
  • Journal Title: Geometric Theory of Information Volume: -
  • Peer Reviewed
• [Journal Article] Asymptotically efficient estimators for algebraic statistical manifolds (2013)
  • Author(s): Kei Kobayashi and Henry P. Wynn
  • Journal Title: Geometric Science of Information: Lecture Notes in Computer Science Volume: 8085 Pages: 721-728
  • DOI: 10.1007/978-3-642-40020-9_80
  • ISBN: 9783642400193, 9783642400209
  • Peer Reviewed
• [Journal Article] 日本語の心内辞書と英語の心内辞書－日本人英語学習者における日英語間で対応する訳語関係にある高頻度形容詞群の意味的クラスタリング構造 (2013)
  • Author(s): 折田充，小林景
  • Journal Title: 熊本大学社会文化 Volume: 11 Pages: 21-34
  • NAID: 110009595809
  • Peer Reviewed
• [Journal Article] 語彙サイズと心内辞書内の意味的クラスタリング構造の関係 (2013)
  • Author(s): 折田充, 小林景, 村里泰昭, 神本忠光, 吉井誠, Lavin, R.
  • Journal Title: KASELE Bulletin Volume: 41 Pages: 1-10
• [Journal Article] 日本語の心内辞書と英語の心内辞書―日本人英語学習者における日英語間で対応する訳語関係にある高頻度形容詞群の意味的クラスタリング構造 (2013)
  • Author(s): 折田充, 小林景
  • Journal Title: 熊本大学社会文化 Volume: 11
  • NAID: 110009595809
  • Peer Reviewed
• [Journal Article] 母語の心内辞書と第二言語の心内辞書―日本人英語 学習者における日英語間で訳語関係にある語彙項目群の構造 (2012)
  • Author(s): 折田充, 小林景
  • Journal Title: KASELE Bulletin Volume: 40 Pages: 1-10
  • Peer Reviewed
• [Presentation] Flattening the Density Gradient for Eliminating Spatial Centrality to Reduce Hubness (2016)
  • Author(s): Hara, K., Suzuki, I., Kobayashi, K. and Fukumizu, K. and Radovanovic, M.
  • Organizer: 30th Conference on Association for the Advancement of Artificial Intelligence (AAAI)
  • Place of Presentation: Phoenix, USA
  • Year and Date: 2016-02-15
  • Int'l Joint Research
• [Presentation] Geometry of dendrogram space and its application to mental lexicon analysis (2016)
  • Author(s): Kobayashi, K. and Orita, M.
  • Organizer: International Conference on Applied Physics and Mathematics (ICAPM 2016)
  • Place of Presentation: Singapore
  • Year and Date: 2016-01-14
  • Int'l Joint Research
• [Presentation] Reducing Hubness for Kernel Regression (2015)
  • Author(s): Hara, K., Suzuki, I., Kobayashi, K. and Fukumizu, K. and Radovanovic, M.
  • Organizer: SISAP2015
  • Place of Presentation: Glasgow
  • Year and Date: 2015-10-12
  • Int'l Joint Research
• [Presentation] A Discussion on Universality of Makespan in Flow Shop Scheduling Problem (2015)
  • Author(s): Shinzato, T., Kaku, I. and Kobayashi, K.
  • Organizer: 2015 Asian Conference of Management Science & Applications
  • Place of Presentation: Dalian, China
  • Year and Date: 2015-09-13
  • Int'l Joint Research
• [Presentation] 高次元データにおける近傍構造の指標と統計的解析 (2015)
  • Author(s): 小林景
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: 岡山大学
  • Year and Date: 2015-09-07
• [Presentation] Reducing Hubness: A Cause of Vulnerability in Recommender Systems (2015)
  • Author(s): Hara, K., Suzuki, I., Kobayashi, K. and Fukumizu, K
  • Organizer: 38th Annual ACM SIGIR Conference
  • Place of Presentation: Santiago de Chile
  • Year and Date: 2015-08-11
  • Int'l Joint Research
• [Presentation] Intrinsic and extrinsic means and curvature of metric cones (2015)
  • Author(s): Kobayashi, K. and Wynn, H.
  • Organizer: Algebraic Statistics 2015
  • Place of Presentation: Genoa
  • Year and Date: 2015-06-09
  • Int'l Joint Research
• [Presentation] Geodesic distances on data spaces: their computation and modification (2015)
  • Author(s): Kei Kobayashi
  • Organizer: ISI-ISM-ISSAS joint Conference 2015
  • Place of Presentation: Tokyo
  • Year and Date: 2015-04-02
  • Int'l Joint Research
• [Presentation] Localized Centering: Reducing Hubness in Large-Sample Data (2015)
  • Author(s): Hara, K., Suzuki, I., Shimbo, M., Kobayashi, K., Fukumizu, K. and Radovanovic, M.
  • Organizer: The Twenty-Ninth AAAI Conference on Artificial Intelligence (AAAI-15)
  • Place of Presentation: Austin, Texias
  • Year and Date: 2015-01-29
• [Presentation] 自律的語彙学習が英語心内辞書構造に与える影響 (2014)
  • Author(s): 折田 充・小林 景・村里泰昭・神本忠光・吉井 誠・Richard Lavin・相澤一美
  • Organizer: 第43回九州英語教育学会大分研究大会
  • Place of Presentation: 大分市 大分大学 旦野原キャンパス
  • Year and Date: 2014-12-06
• [Presentation] Statistical analysis via the curvature of data space (2014)
  • Author(s): Kei Kobayashi, Mitsuru Orita, Henry P. Wynn
  • Organizer: MaxEnt 2014
  • Place of Presentation: Amboise, France
  • Year and Date: 2014-09-22
• [Presentation] データ空間の曲率と距離変形を用いた解析手法 (2014)
  • Author(s): 小林景, Henry P. Wynn
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: 東京大学本郷キャンパス
  • Year and Date: 2014-09-14
• [Presentation] 日本人大学生の英語心内辞書の変容 (2014)
  • Author(s): 折田 充・小林 景・村里泰昭・神本忠光・吉井 誠・Richard S. Lavin・相澤一美
  • Organizer: 第40回全国英語教育学会徳島研究大会
  • Place of Presentation: 徳島市 徳島大学 常三島キャンパス
  • Year and Date: 2014-08-09
• [Presentation] The empirical geodesic graphs and their deformation for data analysis (2014)
  • Author(s): Kei Kobayashi, Henry P. Wynn,
  • Organizer: Australian Technology Park, Sydney, Australia
  • Place of Presentation: Australian Technology Park, Sydney, Australia
  • Year and Date: 2014-07-09
• [Presentation] The empirical geodesic graphs and a deformation of their metric (2014)
  • Author(s): Kobayashi, K. and Wynn, H
  • Organizer: Computational Algebraic Statistics, Theories and Applications (CASTA 2014)
  • Place of Presentation: Kyoto
• [Presentation] Hypothesis Testing for the Difference of Dendrograms (2014)
  • Author(s): Kobayashi, K.
  • Organizer: ISI-ISM-ISSAS Joint Conference 2014
  • Place of Presentation: ISI, Delhi
• [Presentation] Curvature of empirical metrics on a data space and its deformation (2014)
  • Author(s): Kobayashi, K.
  • Organizer: Workshop on Mathematical Approaches to Large-Dimensional Data Analysis
  • Place of Presentation: ISM, Tokyo
• [Presentation] An algebraic computation method for asymptotically efficient estimators (2013)
  • Author(s): Kei Kobayashi
  • Organizer: Joint Meeting of the IASC Satellite Conference and the 8th Conference of the Asian Regional Section of the IASC
  • Place of Presentation: Seoul
  • Invited
• [Presentation] Asymptotically Efficient Estimators for Algebraic Statistical Manifolds (2013)
  • Author(s): Kobayashi, K. and Wynn, H.
  • Organizer: First International Conference on Geometric Science of Information 2013
  • Place of Presentation: Ecole des Mines de Paris
• [Presentation] 木構造およびクラスター構造をもつデータの測地的解析手法 (2013)
  • Author(s): 小林景，折田充
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: 大阪大学
• [Presentation] 英語熟達度と心内辞書内の意味的クラスタリング構造の関係 (2013)
  • Author(s): 折田充, 小林景, 村里泰昭, 相澤一美, 吉井誠, Lavin, R.
  • Organizer: 第39回全国英語教育学会北海道研究大会
  • Place of Presentation: 北星学園大学
• [Presentation] DeRobertis Separation, Its Application to Bayesian Analysis and Generalization (2013)
  • Author(s): Kobayashi, K.
  • Organizer: ISI-ISM-ISSAS Joint Conference
  • Place of Presentation: Taipei
• [Presentation] DeRobertis分離度を用いた全変動距離の上界の改良 (2012)
  • Author(s): 小林景
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: 北海道大学
• [Presentation] 事後分布間のDeRobertis分離度の応用と拡張 (2012)
  • Author(s): 小林景
  • Organizer: 科研費研究集会「数理統計学の沃野」
  • Place of Presentation: 慶応大学矢上
• [Presentation] 英語心内辞書の木構造データ解析の新手法 (2012)
  • Author(s): 小林景, 折田充
  • Organizer: 日本行動計量学会
  • Place of Presentation: 新潟県立大学
• [Presentation] 母語の心内辞書と第二言語の心内辞書（３）―日英 語間で訳語関係にある高頻度形容詞群の意味的クラスタリング構造 (2012)
  • Author(s): 折田充, 小林景
  • Organizer: 第38 回全国英語教育学会愛知研究大会
  • Place of Presentation: 愛知学院大学
• [Presentation] 語彙サイズと心内辞書内の意味的クラスタリング構造の関係 (2012)
  • Author(s): 折田充, 小林景, 村里泰昭, 神本忠光, 吉井誠, Lavin, R.
  • Organizer: 九州英語教育学会
  • Place of Presentation: 長崎外国語大学
• [Presentation] Asymptotic estimation theory via algebraic computation (2012)
  • Author(s): Kobayashi, K. and Wynn, H.
  • Organizer: IMS-APRM
  • Place of Presentation: Tsukuba
• [Presentation] The best upper bound on total variation distance by DeRobertis separation (2012)
  • Author(s): Kobayashi, K.
  • Organizer: 8th World Congress in Probability and Statistics
  • Place of Presentation: Istanbul