Kobayashi, Kei

写真a

Affiliation

Faculty of Science and Technology, Department of Mathematics (Yagami)

Position

Professor
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Other Affiliation 【 Display / hide 】

  • The Institute of Statistical Mathematics, Research Center for Statistical Machine Learning, Visiting Associate Professor

  • RIKEN, Center for Advanced Intelligence Project, Visiting researcher

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Career 【 Display / hide 】

  • 2002.04
    -
    2005.03

    JSPS, Research Fellowships for Doctor Course Student

  • 2005.04
    -
    2007.07

    JSPS, Research Fellowships for Postdoctoral Fellows

  • 2007.08
    -
    2016.03

    The Institute of Statistical Mathematics, Department of Mathematical Analysis and Statistical Inference, Assistant Professor

  • 2014.10
    -
    2018.03

    JST PRESTO, Research director (concurrent post)

  • 2016.04
    -
    Present

    Keio University, Faculty of Science and Technology, Associate Professor

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Academic Background 【 Display / hide 】

  • 1996.04
    -
    2000.03

    The University of Tokyo, Bachelor of Engineering, Department of Mathematical Engineering and Instrumental Physics

  • 2000.04
    -
    2002.03

    University of Tokyo, Department of Mathematical Engineering and Instrumental Physics, Master of Engineering

  • 2002.04
    -
    2005.03

    University of Tokyo, Graduate School of Information Science and Technology, Doctor of Information Science and Technology

  • 2002.04
    -
    2005.03

    The University of Tokyo, Graduate School of Information Science and Technology

    Graduate School, Completed, Doctoral course

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Academic Degrees 【 Display / hide 】

  • PhD(Information Science and Technology), The University of Tokyo, Dissertation, 2005.03

    Bayesian theory for kernel machines and network models

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Research Areas 【 Display / hide 】

  • Informatics / Statistical science

  • Informatics / Statistical science

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Research Keywords 【 Display / hide 】

  • Theoretical Statistics

  • Geometrical Statistics

  • Bayesian Prediction Theory

  • Algebraic Statistics

  • Mathematical Statistics

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Books 【 Display / hide 】

  • 統計学実践ワークブック

    青木敏，伊藤陽一，岩崎学，紙屋英彦，黒住英司，小林景，佐井至道，清水泰隆，鈴木大慈，清智也，寒 水孝司，竹村彰通，中西寛子，橋口博樹，原尚幸，日野英逸，姫野哲人，松浦峻，山田秀，汪金芳, 東京図書, 2020.05,  Page： 330

    Scope: 第８章「統計的推定の基礎」執筆および編集委員

  • 機械学習 ─データを読み解くアルゴリズムの技法─

    ピーター フラッハ (著), 竹村 彰通 (監修, 翻訳), 田中 研太郎 (翻訳), 小林 景 (翻訳), 兵頭 昌 (翻訳), 片山 翔太 (翻訳), 山本 倫生 (翻訳), 吉田 拓真 (翻訳), 林 賢一 (翻訳), 松井 秀俊 (翻訳), 小泉 和之 (翻訳), 永井 勇 (翻訳), 朝倉書店, 2017.04

    Scope: １章「機械学習の三大要素」

  • 現代統計学

    美添泰人，足立浩平，鹿島久嗣，姫野哲人，大屋幸輔，鎌谷研吾，小林 景, 日本評論社, 2017.03

    Scope: １１章「統計における最適化」

  • 基礎講座：現代統計学 統計における最適化(2)

    小林 景, 統計数理研究所, 2015.12

  • 基礎講座：現代統計学 統計における最適化(1)

    小林 景, 統計数理研究所, 2015.11

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Papers 【 Display / hide 】

  • Representing Hierarchical Structured Data Using Cone Embedding

    Takehara D., Kobayashi K.

    Mathematics (Mathematics)  11 ( 10 )  2023.05

    　View Summary

    Extracting hierarchical structure in graph data is becoming an important problem in fields such as natural language processing and developmental biology. Hierarchical structures can be extracted by embedding methods in non-Euclidean spaces, such as Poincaré embedding and Lorentz embedding, and it is now possible to learn efficient embedding by taking advantage of the structure of these spaces. In this study, we propose embedding into another type of metric space called a metric cone by learning an only one-dimensional coordinate variable added to the original vector space or a pre-trained embedding space. This allows for the extraction of hierarchical information while maintaining the properties of the pre-trained embedding. The metric cone is a one-dimensional extension of the original metric space and has the advantage that the curvature of the space can be easily adjusted by a parameter even when the coordinates of the original space are fixed. Through an extensive empirical evaluation we have corroborated the effectiveness of the proposed cone embedding model. In the case of randomly generated trees, cone embedding demonstrated superior performance in extracting hierarchical structures compared to existing techniques, particularly in high-dimensional settings. For WordNet embeddings, cone embedding exhibited a noteworthy correlation between the extracted hierarchical structures and human evaluation outcomes.

  • Entropy-regularized optimal transport on multivariate normal and q-normal distributions

    Tong, Q., Kobayashi, K.

    Entropy (Entropy)  23 ( 2 ) 302 - 20 2021

    Research paper (scientific journal), Accepted

    　View Summary

    The distance and divergence of the probability measures play a central role in statistics, machine learning, and many other related fields. The Wasserstein distance has received much attention in recent years because of its distinctions from other distances or divergences. Although computing the Wasserstein distance is costly, entropy-regularized optimal transport was proposed to computationally efficiently approximate the Wasserstein distance. The purpose of this study is to understand the theoretical aspect of entropy-regularized optimal transport. In this paper, we focus on entropy-regularized optimal transport on multivariate normal distributions and q-normal distributions. We obtain the explicit form of the entropy-regularized optimal transport cost on multivariate normal and q-normal distributions; this provides a perspective to understand the effect of entropy regularization, which was previously known only experimentally. Furthermore, we obtain the entropy-regularized Kantorovich estimator for the probability measure that satisfies certain conditions. We also demonstrate how the Wasserstein distance, optimal coupling, geometric structure, and statistical efficiency are affected by entropy regularization in some experiments. In particular, our results about the explicit form of the optimal coupling of the Tsallis entropy-regularized optimal transport on multivariate q-normal distributions and the entropy-regularized Kantorovich estimator are novel and will become the first step towards the understanding of a more general setting.

  • 語彙サイズの異なる大学生の英語心内辞書

    折田 充, 村里泰昭, 小林 景, 吉井 誠, Richard Lavin, 相澤一美, 神本忠光

    熊本大学英語英文学 63.64   207 - 222 2021

    Research paper (bulletin of university, research institution), Accepted

  • Empirical geodesic graphs and CAT(k) metrics for data analysis

    Kei Kobayashi, Henry P. Wynn

    Statistics and Computing (Spriger)  30 ( 1 ) 1 - 18 2020

    Research paper (scientific journal), Joint Work, Accepted,  ISSN  1573-1375

    　View Summary

    A methodology is developed for data analysis based on empirically constructed geodesic metric spaces. For a probability distribution, the length along a path between two points can be defined as the amount of probability mass accumulated along the path. The geodesic, then, is the shortest such path and defines a geodesic metric. Such metrics are transformed in a number of ways to produce parametrised families of geodesic metric spaces, empirical versions of which allow computation of intrinsic means and associated measures of dispersion. These reveal properties of the data, based on geometry, such as those that are difficult to see from the raw Euclidean distances. Examples of application include clustering and classification. For certain parameter ranges, the spaces become CAT(0) spaces and the intrinsic means are unique. In one case, a minimal spanning tree of a graph based on the data becomes CAT(0). In another, a so-called “metric cone” construction allows extension to CAT(k) spaces. It is shown how to empirically tune the parameters of the metrics, making it possible to apply them to a number of real cases.

  • 心内辞書内の単語の結びつき方―英単語学習プログラムへの取り組み前

    折田充, 村里泰昭, 小林景, 神本忠光, 相澤一美, Richard S. Lavin, 吉井誠

    KASELE BULLETIN 468   9 - 18 2020

    Research paper (bulletin of university, research institution), Accepted

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Reviews, Commentaries, etc. 【 Display / hide 】

  • 多様体学習とデータ空間の幾何学

    KOBAYASHI Kei

    数理解析研究所講究録「統計的モデリングと予測理論のための統合的数理研究」 2057   1 - 11 2017

    Article, review, commentary, editorial, etc. (bulletin of university, research institution)

  • The Development of the L2 Mental Lexicon : A Case of Japanese College EFL Learners

    Orita Mitsuru, Kobayashi Kei, Murasato Yasuaki, Kamimoto Tadamitsu, Yoshii Makoto, Lavin Richard S., Aizawa Kazumi

    Kumamto University studies in social and cultural sciences (Kumamoto University)   ( 13 ) 15 - 30 2015

    ISSN  1348-530X

    　View Summary

    This study addresses the question as to whether the English mental lexicon Japanese college EFL learners have built can develop into a more elaborated structure within a 15-week period of general English education. A free sorting task on a set of 50 high-frequency English verbs was given to 30 first-year college students (NNS) of intermediate low English proficiency in the 2nd ("PRE") and 14th ("POST") weeks. The task was also given to 30 native speakers of English (NS). A pair-wise comparison of the distance matrices of the sorting task results by means of permutation tests showed that the dendrograms of PRE and POST were not statistically significantly different from each other at the 5% significance level (p=0.8509), disclosing that the English mental lexicon NNS have shaped does not easily develop into a more intricately organized structure. The analysis also revealed that both the dendrograms of PRE and NS and those of POST and NS were statistically significantly different from each other at the 5% significance level (p=0.0003). This indicates that the organization of the English mental lexicon of Japanese EFL learners is distinctively different from that of their NS counterparts.That is, the NNS English mental lexicon cannot readily be approximated into the NS English mental lexicon. Furthermore, the examination of the degrees of similarity between lexical items confirmed that the NNS English mental lexicon contains a statistically significantly larger number of hazy, vague lexical links than the NS mental lexicon does.

  • 英語心内辞書の木構造データ解析の新手法(特別セッション 数理統計学の展開とその応用)

    小林 景, 折田 充

    日本行動計量学会大会発表論文抄録集 (日本行動計量学会)  40   101 - 104 2012.09

  • Crystal Voronoi Diagram and Its Applications (Algorithm Engineering as a New Paradigm)

    Kobayashi Kei, Sugihara Kokichi

    RIMS Kokyuroku (Kyoto University)  1185   109 - 119 2001.01

    ISSN  1880-2818

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Presentations 【 Display / hide 】

  • 行列式点過程によるグラフサンプリング

    鴨志田陸，小林景

    第26回情報論的学習理論ワークショップ (IBIS2023), 

    2023.10
    , 

    Poster presentation

  • 欠測データに対する機械学習モデルの判断根拠可視化

    風呂井啓人，小林景

    第26回情報論的学習理論ワークショップ (IBIS2023), 

    2023.10
    , 

    Poster presentation

  • DDPMにおけるノイズ分布についての考察

    海老澤優，小林景

    第26回情報論的学習理論ワークショップ (IBIS2023), 

    2023.10
    , 

    Poster presentation

  • Statistical Analysis with Geodesics and Curvature in Data Space

    Kobayashi, K. and Wynn, H.

    10th International Congress on Industrial and Applied Mathematics (ICIAM2023), 

    2023.08
    , 

    Oral presentation (general)

  • Novel geometric methods for data analysis focusing on curvature and geodesics in data space

    Kobayashi, Kei

    Boston-Keio-Tsinghua Wokshop 2023 (Boston University USA) , 

    2023.06
    , 

    Oral presentation (general)

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Research Projects of Competitive Funds, etc. 【 Display / hide 】

  • データ空間上の測地距離およびその変換に着目した統計解析

    2022.04
    -
    2025.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, 基盤研究(C), Principal investigator

  • データに潜在する曲率情報に着目した統計解析手法の開発

    2019.04
    -
    2022.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Principal investigator

    　View Summary

    研究初年度である本年度は，新しいプロジェクトの立ち上げのための研究環境の整備および研究ネットワークの構築を行いつつ，研究により得られた成果の国際会議での発表および学術誌における論文出版を行った．具体的には，まず曲率CAT(k)に着目した距離変換と統計解析手法とその理論についての論文を，統計学および計算機理論の一流学術誌であるStatistics and Computingに出版し，国際会議(32nd European Meeting of Statisticians) において発表した．さらに，超球面上のデータに関する幾何学的なアイデアに基づき，相関係数行列を正定値行列のまま疎行列化するための新手法を提案し，その妥当性の理論的な評価を行った．その結果は統計関連学会連合大会において発表した．一方，データ空間や潜在変数の空間の幾何学を用いた統計理論を，深層学習や自然言語処理の手法に応用した新しい研究を開始し，複数の進展がみられた．そのうちのいくつかについて得られた結果を共著のarXivプレプリント２篇としてまとめ，一部は査読付き国際会議(SafeAI, AAAI-19 Workshop)において発表した．さらに，共同研究者であるHenry Wynn（London School of Economics教授）のもとを訪問し，特に「グラフのリッチ曲率を用いたデータ解析」，「周期的構造をもつデータの幾何学的な特徴量抽出」という２つの研究テーマについて研究討論を行い，今後の研究方針を確定することが出来た．

  • 語彙知識の構造化を促進するウェブ教材の完成とネイティブ度診断テストの開発

    2019.04
    -
    2022.03

    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), Coinvestigator(s)

    　View Summary

    大学生がオンラインで取り組める、単語の理解を確実にすることから始める、心内辞書（メンタルレキシコン）内の単語のまとまりである「単語クラスター」構造化のための自学語彙学習プログラム Word Cluster Master Program (WCMP) 形容詞版の開発を1つ目の目的とした。これまでに開発を終えている動詞版および名詞版の成果を踏まえて開発に着手した。
    なお、WCMP で目指す「学習クラスター」習得のための学習プログラムのメニューは、形容詞版においても、「提示」（動画：①コア語とクラスター語の関係把握、②目標語を使った英文ペアの確認）→「自己診断」（関連する意味の単語を選ぶ）→「学習」（単語を聞き取る、タイプ入力するなど４つ）→「強化」（意味の上で関連する語群に分ける）の７つで構成することとした。
    初年度は、全12ユニット（各ユニットは４ないし５つの「学習クラスター」から構成）のうち、前半の6ユニットのスクリプト作成、そしてデジタル化まで終了し、実証研究を実施した（収集したデータ解析は、2年目に予定）。
    併せて、もう一つの研究目的である、学習者それぞれの心内辞書内で英単語群がどの程度構造化されているのか、一人ひとりを診断し結果を学習者にフィードバックするツールである「ネイティブ度診断テスト」の開発に取り組んだ。初年度は、WordNET（プリンストン大学）で公開されているsynset（同意語を中心とする単語クラスター）、およびこれまでに行った基礎研究に基づき、診断テストのための英単語を選定した。名詞版・動詞版・形容詞版、それぞれ4つのユニットから各1つの「学習クラスター」を選び、各テストを合計24語の英単語で構成することとした。

  • スマートデバイスで取り組める語彙知識のネットワーク化を促進する自学教材の開発

    2016.04
    -
    2018.03

    科研費基盤研究(C), No Setting

  • データ空間の幾何学的特徴を活用する解析手法と統計理論

    2014.10
    -
    2018.03

    JST, Precursory Research for Embryonic Science and Technology, Kei Kobayashi, Principal investigator

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Courses Taught 【 Display / hide 】

  • SPECIAL EXERCISE IN MATHEMATICAL SCIENCE

    2024

  • SEMINAR IN STATISTICAL SCIENCES

    2024

  • OFF-CAMPUS WORK-STUDY PROGRAM

    2024

  • MATHEMATICAL STATISTICS 2

    2024

  • MATHEMATICAL STATISTICS 1 AND ITS EXERCISE

    2024

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Courses Previously Taught 【 Display / hide 】

  • データ解析同演習

    Keio University

    2018.04
    -
    2019.03
    , 

    Autumn Semester

  • 統計科学輪講

    Keio University

    2018.04
    -
    2019.03
    , 

    Autumn Semester

  • 数理統計学第２

    Keio University

    2018.04
    -
    2019.03
    , 

    Autumn Semester

  • 数理統計学第１同演習

    Keio University

    2018.04
    -
    2019.03
    , 

    Spring Semester

  • 数学２A

    Keio University

    2018.04
    -
    2019.03
    , 

    Spring Semester

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Memberships in Academic Societies 【 Display / hide 】

  • 日本統計学会

    　

  • 日本数学会

    　

  • The Institute of Mathematical Statistics

    　
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Committee Experiences 【 Display / hide 】

  • 2021.10
    -
    Present

    Co-editor, Annals of Institute of Statistical Mathematics

  • 2020.04
    -
    2022.03

    統計検定 準１級 副委員長, 統計検定

  • 2019.07
    -
    2021.09

    Associate Editor, Annals of Institute of Statistical Mathematics

  • 2019.06
    -
    2021.09

    Associate Editor, Annals of the Institute of Statistical Mathematics (AISM)

  • 2019.04
    -
    2020.03

    統計検定 準１級 委員長, 統計検定

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