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Thery and methods for high dimensional data analysis with internal structure

Research Project

Project/Area Number 26280009
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field Statistical science
Research InstitutionThe Institute of Statistical Mathematics

Principal Investigator

Fukumizu Kenji  統計数理研究所, 数理・推論研究系, 教授 (60311362)

Co-Investigator(Kenkyū-buntansha) 鈴木 大慈  東京大学, 大学院情報理工学系研究科, 准教授 (60551372)
小林 景  慶應義塾大学, 理工学部(矢上), 准教授 (90465922)
Project Period (FY) 2014-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥12,350,000 (Direct Cost: ¥9,500,000、Indirect Cost: ¥2,850,000)
Fiscal Year 2018: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2017: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2016: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2015: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2014: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Keywords統計数学 / データ解析 / 高次元 / アルゴリズム / 統計的学習理論 / 高次元データ / 機械学習
Outline of Final Research Achievements

The hub phenomenon has been analysed as an example of special properties of high-dimensional data, and a method of resolving hubs has been proposed. Methods of data analysis have been proposed for non-Euclidean data such as trees and points with skewed distance measures. Additionally, for a new method of density estimation of high-dimensional data, a kernel methods for constructing infinite dimensional exponential families has been proposed, and its estmation has been discussed.

Academic Significance and Societal Importance of the Research Achievements

ビッグデータ時代になり高次元で複雑なデータを扱う必要性が高まったが,そのようなデータの性質や解析法の関して,理論的な知見や有効な方法が成果として得られた.今後,さまざまな分野に現れる高次元データを扱う際にこれらの成果が貢献できると考える.

Report

(6 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Annual Research Report
  • 2016 Annual Research Report
  • 2015 Annual Research Report
  • 2014 Annual Research Report

Research Products

(50 results)

All 2020 2018 2017 2016 2015 2014 Other

All Int'l Joint Research (8 results) Journal Article (21 results) (of which Int'l Joint Research: 8 results,  Peer Reviewed: 21 results,  Open Access: 16 results,  Acknowledgement Compliant: 3 results) Presentation (18 results) (of which Int'l Joint Research: 2 results,  Invited: 10 results) Remarks (3 results)

  • [Int'l Joint Research] University of Oxford/Imperial College London(英国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Carnegie Mellon University(米国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] University College London/Oxford University(英国)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Pennsylvania State University(米国)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Mahidol University(タイ)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] University of Kentucky/, North Dakota State University,(米国)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] University of Novi Sad(Serbia)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] Pennsylvania State University(米国)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Empirical geodesic graphs and CAT(k) metrics for data analysis2020

    • Author(s)
      Kei Kobayashi and Henry P. Wynn
    • Journal Title

      Statistics and Computing

      Volume: 2019 Feb. Pages: 1-18

    • DOI

      10.1007/s11222-019-09855-3

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Post Selection Inference with Incomplete Maximum Mean Discrepancy Estimator2018

    • Author(s)
      Makoto Yamada, Denny Wu, Yao-Hung Hubert Tsai, Hirofumi Ohta, Ruslan Salakhutdinov, Ichiro Takeuchi, Kenji Fukumizu
    • Journal Title

      Proceedings of the 7th Seventh International Conference on Learning Representations

      Volume: 7 Pages: 1-16

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Variational Learning on Aggregate Outputs with Gaussian Processes2018

    • Author(s)
      Ho Chung Law, Dino Sejdinovic, Ewan Cameron, Tim Lucas, Seth Flaxman, Katherine Battle, Kenji Fukumizu
    • Journal Title

      Advances in Neural Information Processing Systems

      Volume: 31

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Fast learning rate of non-sparse multiple kernel learning and optimal regularization strategies2018

    • Author(s)
      Suzuki Taiji
    • Journal Title

      Journal of Multivariate Analysis

      Volume: 12 Pages: 2141-2192

    • DOI

      10.1214/18-ejs1399

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Short-term local weather forecast using dense weather station by deep neural network2018

    • Author(s)
      Yonekura Kazuo、Hattori Hitoshi、Suzuki Taiji
    • Journal Title

      Proceedings of 2018 IEEE International Conference on Big Data (Big Data)

      Volume: 1 Pages: 10-13

    • DOI

      10.1109/bigdata.2018.8622195

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Sample Efficient Stochastic Gradient Iterative Hard Thresholding Method for Stochastic Sparse Linear Regression with Limited Attribute Observation2018

    • Author(s)
      Tomoya Murata, and Taiji Suzuki
    • Journal Title

      Advances in Neural Information Processing Systems

      Volume: 31

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Adam Induces Implicit Weight Sparsity in Rectifier Neural Networks2018

    • Author(s)
      Atsushi Yaguchi, Taiji Suzuki, Wataru Asano, Shuhei Nitta, Yukinobu Sakata, Akiyuki Tanizawa
    • Journal Title

      Proceedings of Machine Learning Research AISTATS2018,

      Volume: * Pages: 17-20

    • DOI

      10.1109/icmla.2018.00054

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Post Selection Inference with Kernels2018

    • Author(s)
      Makoto Yamada, Yuta Umezu, Kenji Fukumizu, and Ichiro Takeuchi
    • Journal Title

      Proceedings of Machine Learning Research: AISTATS 2018

      Volume: 84 Pages: 152-160

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Kernel Mean Embedding of Distributions: A Review and Beyond2017

    • Author(s)
      Krikamol Muandet, Kenji Fukumizu, Bharath K. Sriperumbudur, Bernhard Schoelkopf
    • Journal Title

      Foundations and Trends? in Machine Learning

      Volume: 10 Pages: 1-141

    • DOI

      10.1561/2200000060

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Density Estimation in Infinite Dimensional Exponential Families2017

    • Author(s)
      Bharath Sriperumbudur, Kenji Fukumizu, Arthur Gretton, Aapo Hyvarinen, Revant Kumar
    • Journal Title

      Journal of Machine Learning Research

      Volume: 18(57) Pages: 1-59

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Multilocus phylogenetic analysis with gene tree clustering2017

    • Author(s)
      Ruriko Yoshida, Kenji Fukumizu, Chrysafis Vogiatzis
    • Journal Title

      Annals of Operations Research

      Volume: 印刷中

    • DOI

      10.1007/s10479-017-2456-9

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] A Characterization of Minimum Spanning Tree-like Metric Spaces2017

    • Author(s)
      Hayamizu, M., Endo, H. and Fukumizu, K.
    • Journal Title

      IEEE/ACM Transactions on Computational Biology and Bioinformatics

      Volume: 99 Pages: 1-1

    • DOI

      10.1109/tcbb.2016.2550431

    • Related Report
      2016 Annual Research Report 2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Unsupervised Group Matching with Application to Cross-lingual Topic Matching without Alignment Information2016

    • Author(s)
      Iwata, T., Kanagawa, M., Hirao, T. and Fukumizu, K.
    • Journal Title

      Data Mining and Knowledge Discovery

      Volume: 2016 Pages: 1-19

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Flattening the Density Gradient for Eliminating Spatial Centrality to Reduce Hubness2016

    • Author(s)
      Hara, K., Suzuki, I., Kobayashi, K., Fukumizu, K. and Radovanovic, M.
    • Journal Title

      Proc. 30th AAAI Conference on Artificial Intelligence

      Volume: 1 Pages: 1659-1665

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] System Identification and Parameter Estimation in Mathematical Medicine: Examples Demonstrated for Prostate Cancer2016

    • Author(s)
      Yoshito Hirata, Kai Morino, Taiji Suzuki, Qian Guo, Hiroshi Fukuhara, and Kazuyuki Aihara
    • Journal Title

      Quantitative Biology

      Volume: 4(1) Pages: 13-19

    • DOI

      10.1007/s40484-016-0059-0

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Stochastic Alternating Direction Method of Multipliers for Structured Regularization2015

    • Author(s)
      Taiji Suzuki
    • Journal Title

      Journal of Japan Society of Computational Statistics

      Volume: 28 Pages: 105-124

    • NAID

      130005434004

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Localized Centering: Reducing Hubness in Large-Sample Data2015

    • Author(s)
      K. Hara, I. Suzuki, M. Shimbo, K. Kobayashi, K. Fukumizu, and M. Radomanovic
    • Journal Title

      Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence

      Volume: 1 Pages: 2645-2651

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] A Consistent Method for Graph Based Anomaly Localization2015

    • Author(s)
      Satoshi Hara, Tetsuro Morimura, Toshihiro Takahashi, Hiroki Yanagisawa, Taiji Suzuki
    • Journal Title

      JMLR Workshop and Conference Proceedings

      Volume: 38

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Support Consistency of Direct Sparse-Change Learning in Markov Networks2015

    • Author(s)
      Song Liu, Taiji Suzuki, and Masashi Sugiyama
    • Journal Title

      Proceedigs of the Twenty-Ninth AAAI Conference on Artificial Intelligence (AAAI2015)

      Volume: 1 Pages: 2785-2791

    • NAID

      110009971454

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] 凸最適化に基づくテンソル分解2014

    • Author(s)
      冨岡亮太,鈴木大慈,林浩平,鹿島久嗣
    • Journal Title

      応用数理

      Volume: 24 Pages: 16-23

    • NAID

      110009900559

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stochastic Dual Coordinate Ascent with Alternating Direction Method of Multipliers2014

    • Author(s)
      Taiji Suzuki
    • Journal Title

      JMLR Workshop and Conference Proceedings

      Volume: 32 Pages: 736-744

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Presentation] Element-wise shrinkage of positive correlation matrices for increasing sparsity2018

    • Author(s)
      Kei Kobayashi, Henry P. Wynn
    • Organizer
      2018 IMS Annual Meeting on Probability and Statistics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Monotone shrinkage of correlation matrices for sparsity2018

    • Author(s)
      Kei Kobayashi
    • Organizer
      統計関連学会連合大会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 2次元アニメーション制作における中割り自動化のためのベクタ形式画像の対応づけ2018

    • Author(s)
      童 祺俊,小林 景
    • Organizer
      統計関連学会連合大会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 無限隠れマルコフモデルによるバスケットボールの戦術分析2018

    • Author(s)
      竹原 大翼,小林 景
    • Organizer
      統計関連学会連合大会
    • Related Report
      2018 Annual Research Report
  • [Presentation] MHアルゴリズムによる分散共分散行列のグラフ推定とその応用2018

    • Author(s)
      夏 悠寧,小林 景
    • Organizer
      統計関連学会連合大会
    • Related Report
      2018 Annual Research Report
  • [Presentation] カーネル法に基づく疎な言語表現のための高速計算可能な共起尺度2018

    • Author(s)
      横井祥, 小林 颯介, 福水健次, 乾 健太郎
    • Organizer
      2018年度 人工知能学会全国大会(第32回)
    • Related Report
      2018 Annual Research Report
  • [Presentation] 教師ありクラスタマッチングとその隕石-小惑星分類体系への応用2018

    • Author(s)
      福水健次
    • Organizer
      日本分類学会第37回大会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 統計・機械学習における確率的最適化2018

    • Author(s)
      鈴木大慈
    • Organizer
      統計数理研究所公開講座
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 深層学習の統計的学習理論:カーネル法とウェーブレット解析による視点2018

    • Author(s)
      鈴木大慈
    • Organizer
      第3回統計・機械学習若手シンポジウム「統計・機械学習の交わりと拡がり」
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 機械学習における構造を利用した確率的最適化技法2018

    • Author(s)
      鈴木大慈
    • Organizer
      2018年電子情報通信学会基礎・境界ソサイエティ大会大会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 機械学習の現状と深層学習の数理2018

    • Author(s)
      鈴木大慈
    • Organizer
      山形大学データサイエンス推進室キックオフミーティング
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] カーネル法に基づく疎な言語表現のための共起尺度2018

    • Author(s)
      横井祥, 小林颯介 , 福水健次, 乾健太郎
    • Organizer
      言語処理学会第24回年次大会
    • Related Report
      2017 Annual Research Report
  • [Presentation] データ構造を解明する機械学習アプローチ --グラフ構造、幾何構造--2017

    • Author(s)
      福水健次
    • Organizer
      第3回WIRPワークショップ
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Local minima and saddle points in hierarchical structure of neural networks2017

    • Author(s)
      Kenji Fukumizu
    • Organizer
      Deep Learning: Theory, Algorithms, and Applications
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 低ランクテンソル推定におけるベイズ推定量の性質2015

    • Author(s)
      鈴木大慈
    • Organizer
      第9回日本統計学会春季集会
    • Place of Presentation
      東京
    • Year and Date
      2015-03-08
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] スパース推定概観:モデル・理論・応用2014

    • Author(s)
      鈴木大慈
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      東京
    • Year and Date
      2014-09-13 – 2014-09-16
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Risk Bounds of Convex and Bayes Tensor Estimators: Near Optimal Rate without Strong Convexity2014

    • Author(s)
      Taiji Suzuki
    • Organizer
      International Workshop on Spatial and Temporal Modeling from Statistical, Machine Learning and Engineering perspectives (STM2014)
    • Place of Presentation
      東京
    • Year and Date
      2014-07-28 – 2014-07-29
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Stochastic Dual Coordinate Ascent with ADMM2014

    • Author(s)
      Taiji Suzuki
    • Organizer
      SIAM Conference on Optimization (SIAM-OPT2014)
    • Place of Presentation
      San Diego, USA
    • Year and Date
      2014-05-19 – 2014-05-22
    • Related Report
      2014 Annual Research Report
  • [Remarks]

    • URL

      http://www.ism.ac.jp/~fukumizu/

    • Related Report
      2017 Annual Research Report
  • [Remarks] http://www.ism.ac.jp/~fukumizu/

    • Related Report
      2016 Annual Research Report
  • [Remarks]

    • URL

      http://www.ism.ac.jp/~fukumizu/

    • Related Report
      2015 Annual Research Report

URL: 

Published: 2014-04-04   Modified: 2022-02-22  

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