2014 Fiscal Year Annual Research Report
Fast Optimal Transport and Applications to Inference and Simulation in Large Scale Statistical Machine Learning
| Project/Area Number |
26700002
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| Research Institution | Kyoto University |
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Principal Investigator |
CUTURI Marco 京都大学, 情報学研究科, 准教授 (80597344)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | optimal transport / medical imaging / graphics / optimization |
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| Outline of Annual Research Achievements |
We have proposed over the past year several important results related to the fast computation of Wasserstein distances and their direct application to statistics, computation, and machine learning.
Our flagship contribution is a paper accepted at ACM SIGGRAPH 2015. ACM SIGGRAPH 2015 is the most competitive venue in the whole field of computer science. In that contribution, we lay out a novel approach to carry out optimal transport on meshes of more than 1 million points. This approach can serve as a blueprint to apply optimal transport in other challenging settings.
Our second important contribution is a publication in the SIAM Journal on Scientific Computing. That publication provides the mathematical tools needed to support our application to graphics in SIGGRAPH, and provides an elegant and surprisingly simple way to compute barycenters in the Wasserstein space.
Our third contribution is an application to medical imaging, which allows for an intelligent averaging of cortical activation maps. We will present these results in the IPMI (Information Processing in Medical Imaging) conference.
Combined, our first year in this project has been extremely productive. We have also organized (one year ahead of the planned schedule) a workshop at the NIPS workshop on optimal transport, which was a success, with more than 60 attendees and prestigious speakers.
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| Current Status of Research Progress |
Current Status of Research Progress
1: Research has progressed more than it was originally planned.
Reason
The excellence of our list of publications this year is the reason we believe we are progressing more smoothly than initially planned. We have 2 journal papers (ACM Transactions in Graphics/Siggraph , SIAM Journal on Scientific Computing) in tops venues, and a conference proceeding in a very competitive medical imaging conference (IPMI). In addition to this we have held a workshop on this topic during the NIPS conference (we were planning to do so much later in the course of this project).
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| Strategy for Future Research Activity |
Our plans for future work include
- domain dependent approximations, to speed up computations;
- methodological innovation grounded on our increased computational abilities: this will cover as a whole any introduction of the Wasserstein distance in parameter estimation for statistical models and/or dimensionality reduction (Wasserstein PCA, Wasserstein dictionary learning etc...)
- consideration of specific application domains such as natural language processing and computer vision
We are confident that we can add even more value to this project by exploring all these low hanging fruits.
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| Causes of Carryover |
Our project has just started, and we have initial funds to buy hardware and carry out important travel to write papers with collaborators and give talks at important, specialized venues in both the fields of optimal transport and that of statistics/machine learning.
We need to continue these important collaborations and, to a lesser extent, invest further in hardware to be able to fulfill our goals.
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| Expenditure Plan for Carryover Budget |
Our plan is to continue our collaborations by working closely with Justin Solomon (Stanford University), Gabriel Peyre (Dauphine University), Jean-David Benamou (INRIA) who are our main collaborators at this time. We have several new ideas in this field and need to concretize them. Our second usage plan will be to help and support my collaborators at Kyoto University, mostly students, so that they can present their work in the most prestigious conference venues.
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