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Fast Optimal Transport and Applications to Inference and Simulation in Large Scale Statistical Machine Learning

Research Project

Project/Area Number 26700002
Research Category

Grant-in-Aid for Young Scientists (A)

Allocation TypePartial Multi-year Fund
Research Field Statistical science
Research InstitutionKyoto University

Principal Investigator

CUTURI Marco  京都大学, 情報学研究科, 准教授 (80597344)

Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥25,090,000 (Direct Cost: ¥19,300,000、Indirect Cost: ¥5,790,000)
Fiscal Year 2016: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2015: ¥6,240,000 (Direct Cost: ¥4,800,000、Indirect Cost: ¥1,440,000)
Fiscal Year 2014: ¥13,780,000 (Direct Cost: ¥10,600,000、Indirect Cost: ¥3,180,000)
Keywords最適輸送理論 / 機械学習 / 最適化 / グラフィックス / 統計学 / 統計的機械学習 / optimal transport / medical imaging / graphics / optimization
Outline of Final Research Achievements

This funding was used to push forward the idea that optimal transport could be used numerically to solve real life problems using a regularization approach. We have demonstrated over the course of this project that these ideas were feasible, and have shown their applicability to a very wide range of applications, ranging from graphics and medical imaging to graphics and machine learning. These ideas were presented in top conferences and journals.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Annual Research Report
  • 2014 Annual Research Report
  • Research Products

    (23 results)

All 2016 2015 2014 Other

All Int'l Joint Research (2 results) Journal Article (11 results) (of which Int'l Joint Research: 8 results,  Peer Reviewed: 11 results,  Open Access: 10 results,  Acknowledgement Compliant: 8 results) Presentation (8 results) (of which Invited: 8 results) Patent(Industrial Property Rights) (2 results) (of which Overseas: 1 results)

  • [Int'l Joint Research] Universite Paris Dauphine/INRIA(France)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] Stanford/MIT/Pixar(米国)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Stochastic Optimization for Large-scale Optimal Transport2016

    • Author(s)
      A. Genevay, M. Cuturi, G. Peyre, F. Bach
    • Journal Title

      Advances in Neural Information Processing Systems

      Volume: 29

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Wasserstein Training of Restricted Boltzmann Machines2016

    • Author(s)
      G. Montavon, K.-R. Muller, M. Cuturi
    • Journal Title

      Advances in Neural Information Processing Systems

      Volume: 29

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Gromov-Wasserstein Averaging of Kernel and Distance Matrices2016

    • Author(s)
      G. Peyre, M. Cuturi, J. Solomon
    • Journal Title

      JMLR W&CP ICML'16

      Volume: 48 Pages: 2664-2672

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Wasserstein Barycentric Coordinates: Histogram Regression Using Optimal Transport2016

    • Author(s)
      Nicolas Bonneel, G. Peyre, M. Cuturi
    • Journal Title

      ACM Transactions on Graphics (Proceedings of SIGGRAPH 2016)

      Volume: 35 (4) Issue: 4 Pages: 1-10

    • DOI

      10.1145/2897824.2925918

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] A Smoothed Dual Approach for Variational Wasserstein Problems2016

    • Author(s)
      Marco Cuturi, Gabriel Peyre
    • Journal Title

      SIAM Journal on Imaging Sciences

      Volume: 9 (1) Issue: 1 Pages: 320-343

    • DOI

      10.1137/15m1032600

    • Related Report
      2016 Annual Research Report 2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Iterative Bregman Projections for Regularized Transportation Problems2015

    • Author(s)
      Jean-David Benamou, Guillaume Carlier, Marco Cuturi, Luca Nenna, Gabriel Peyre
    • Journal Title

      SIAM Journal on Scientific Computing

      Volume: 37 (2) Issue: 2 Pages: 1111-1138

    • DOI

      10.1137/141000439

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Principal Geodesic Analysis for Probability Measures under the Optimal Transport Metric2015

    • Author(s)
      Vivien Seguy, Marco Cuturi
    • Journal Title

      Advances in Neural Information Processing Systems 28 (NIPS 2015)

      Volume: 1 Pages: 3294-3302

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Convolutional Wasserstein Distances: Efficient Optimal Transportation on Geometric Domains2015

    • Author(s)
      Justin Solomon, Fernando de Goes, Gabriel Peyre, Marco Cuturi, Adrian Butscher, Andy Nguyen, Tao Du, Leonidas J. Guibas
    • Journal Title

      Proc. 42nd International Conference and Exhibition on Computer Graphics and Interactive Techniques (SIGGRAPH2015), ACM Transactions on Graphics

      Volume: 34 (4) Issue: 4 Pages: 1-11

    • DOI

      10.1145/2766963

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Convolutional Wasserstein Distances: Efficient Optimal Transportation on Geometric Domains2015

    • Author(s)
      J. Solomon, F. de Goes, G. Peyre, M. Cuturi, A. Butscher, A. Nguyen, T. Du, L. Guibas.
    • Journal Title

      ACM Transactions on Graphics / SIGGRAPH

      Volume: 未定

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Iterative Bregman Projections for Regularized Transportation Problems2015

    • Author(s)
      J.D. Benamou, G. Carlier, M. Cuturi, L. Nenna, G. Peyre,
    • Journal Title

      SIAM Journal on Scientific Computing

      Volume: 未定

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Fast Optimal Transport Averaging of Neuroimaging Data2015

    • Author(s)
      A. Gramfort, G. Peyre, M. Cuturi
    • Journal Title

      Springer LNCS, Information Processing in Medical Imaging

      Volume: 未定

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Presentation] New Approaches to Learn with Probability Measures using Fast Optimal Transport2015

    • Author(s)
      M. Cuturi
    • Organizer
      IBIS 2015 Workshop
    • Place of Presentation
      茨城県つくば市つくば国際会議場
    • Year and Date
      2015-11-25
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] New Approaches to Learn with Probability Measures using Fast Optimal Transport2015

    • Author(s)
      M. Cuturi
    • Organizer
      Workshop on Learning, IMS NUS, Singapore
    • Place of Presentation
      Institute for Mathematical Sciences, National University of Singapore, Singapore
    • Year and Date
      2015-11-18
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] New Approaches to Learn with Probability Measures using Fast Optimal Transport2015

    • Author(s)
      M. Cuturi
    • Organizer
      Workshop on Optimization in machine learning, vision and image processing
    • Place of Presentation
      Universite Paul Sabatier, Toulouse, France
    • Year and Date
      2015-10-07
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Fast Optimal Transport on GPGPUs2015

    • Author(s)
      M. Cuturi
    • Organizer
      GTC Japan 2015 テクニカルセッション
    • Place of Presentation
      東京都港区 虎ノ門ヒルズフォーラム
    • Year and Date
      2015-09-18
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] An overview of Wasserstein barycenter algorithms2015

    • Author(s)
      M. Cuturi
    • Organizer
      New Trends in Optimal Transport
    • Place of Presentation
      Bonn, Germany
    • Year and Date
      2015-03-02 – 2015-03-06
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Optimal Transport with Entropy Regularization: Pros and Cons2015

    • Author(s)
      M. Cuturi
    • Organizer
      Advances in Numerical Optimal Transportation, Banff
    • Place of Presentation
      Banff, Canada
    • Year and Date
      2015-02-15 – 2015-02-20
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] The Wasserstein Barycenter Problem2015

    • Author(s)
      M. Cuturi
    • Organizer
      Optimization and Statistical Learning
    • Place of Presentation
      Les Houches, France
    • Year and Date
      2015-01-12 – 2015-02-16
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] The Wasserstein Barycenter Problem2014

    • Author(s)
      M. Cuturi
    • Organizer
      Foundations of Computational Mathematics (FoCM 2014)
    • Place of Presentation
      Montevideo, Uruguay
    • Year and Date
      2014-12-18 – 2014-12-20
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Patent(Industrial Property Rights)] Method to Compute the Barycenter of a Set of Histograms2015

    • Inventor(s)
      Marco Cuturi
    • Industrial Property Rights Holder
      Marco Cuturi
    • Industrial Property Rights Type
      特許
    • Filing Date
      2015-04-14
    • Related Report
      2015 Annual Research Report
    • Overseas
  • [Patent(Industrial Property Rights)] Method to Compute the Barycenter of A Set of Histograms2014

    • Inventor(s)
      M. Cuturi
    • Industrial Property Rights Holder
      M. Cuturi
    • Industrial Property Rights Type
      特許
    • Filing Date
      2014-04-16
    • Related Report
      2014 Annual Research Report

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Published: 2014-04-04   Modified: 2022-01-27  

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