2022 Fiscal Year Annual Research Report
Machine learning and statistical methhods on infinite-dimensional manifolds
| Project/Area Number |
20H04250
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| Research Institution | Institute of Physical and Chemical Research |
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Principal Investigator |
Ha QuangMinh 国立研究開発法人理化学研究所, 革新知能統合研究センター, ユニットリーダー (90868928)
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| Project Period (FY) |
2020-04-01 – 2023-03-31
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| Keywords | Gaussian measures / Gaussian processes / Optimal transport / Divergences / Entropic regularization |
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| Outline of Annual Research Achievements |
We have obtained the following:
(i) Convergence analysis which shows theoretical guarantees for finite-dimensional approximations of the regularized Kullback-Leibler and Renyi divergences in the reproducing kernel Hilbert space and Gaussian process settings. The sample complexities are dimension-independent in all cases.
(ii) Limit theorems for the entropic Wasserstein distance between infinite-dimensional Gaussian measures.
We have proved many theoretical results under different assumptions.
(iii) We have obtained some preliminary numerical results using the previous theoretical results for Functional Data classification in the Gaussian process setting.
Our results are the first in the literature in the setting of infinite-dimensional Gaussian measures and Gaussian processes. These results are expected to form a crucial part in the mathematical foundations for subsequent work on Gaussian process methods in machine learning.
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| Research Progress Status |
令和4年度が最終年度であるため、記入しない。
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| Strategy for Future Research Activity |
令和4年度が最終年度であるため、記入しない。
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