2024 Fiscal Year Research-status Report
On Optimal Transport-based Statistical Measures for Graph Structured Data and Applications
| Project/Area Number |
23K16939
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| Research Institution | Hokkaido University |
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Principal Investigator |
NGUYEN DAIHAI 北海道大学, 情報科学研究院, 准教授 (50968401)
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| Project Period (FY) |
2023-04-01 – 2026-03-31
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| Keywords | proximal MCMC sampling / optimal transport / Bayesian inference |
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| Outline of Annual Research Achievements |
Our work has focused on generating structured data while effectively incorporating prior knowledge. To address this challenge, we formulated a general optimization problem involving the minimization of a composite objective function defined over probability distribution space. The objective consists of two components: one assumed to have a variational representation, and the other expressed in terms of the expectation operator of a possibly nonsmooth convex regularizer function, which represents the prior knowledge. We develope a general framework based on the optimal transport theory to minimize this objective. Furthermore, we also provide theoretical analyses and present experimental results to showcase the effectiveness of the proposed method.
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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
We have achieved promising results in generating structured data through distributional optimization, with our findings published in leading conferences and journals. Looking ahead, we aim to expand our research to encompass graph data and its diverse applications.
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| Strategy for Future Research Activity |
We plan to continue advancing optimal transport-based frameworks for solving distributional optimization problems, with a particular emphasis on applications in Bayesian inference and graph structured data.
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| Causes of Carryover |
We did not proceed with the travel or article purchases outlined in the original research plan. Instead, we plan to allocate the remaining funds toward travel for presentations at academic conferences this fiscal year.
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