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- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.25 No.4
- 발행연도
- 2021.12
- 수록면
- 162 - 172 (11page)
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초록· 키워드
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This paper proposes stochastic methods to find an approximate solution for the L²-Wasserstein least squares problem of Gaussian measures. The variable for the problem is in a set of positive definite matrices. The first proposed stochastic method is a type of classical stochastic gradient methods combined with projection and the second one is a type of variance reduced methods with projection. Their global convergence are analyzed by using the framework of proximal stochastic gradient methods. The convergence of the classical stochastic gradient method combined with projection is established by using diminishing learning rate rule in which the learning rate decreases as the epoch increases but that of the variance reduced method with projection can be established by using constant learning rate. The numerical results show that the present algorithms with a proper learning rate outperforms a gradient projection method.
목차
ABSTRACT
1. INTRODUCTION
2. LIPSCHITZ CONTINUITY AND GRADIENT PROJECTION METHOD
3. STOCHASTIC GRADIENT (PROJECTION) METHOD
4. NUMERICAL EXPERIMENTS
5. CONCLUSION
REFERENCES
참고문헌 (16)
참고문헌 신청
C. R. Givens / 1984 / A class of wasserstein metrics for probability distributions / Mich. Math. J 31:231~240
금상호 / 2019 / Gradient projection methods for the $n$-coupling problem / 대한수학회지 56(4):1001~1016
M. Agueh / 2011 / Barycenters in the wasserstein space / SIAM J. Math. Anal 43:904~924
Y. -H. Kim / 2015 / Multi-marginal optimal transport on Riemannian manifolds / Amer. J. Math 137:1045~1060
B. Pass / 2012 / The local structure of optimal measures in the multi-marginal optimal transportation problem / Calc. Var. Partial Differential Equations 43:529~536
금상호 / 2019 / Gradient projection methods for the $n$-coupling problem / 대한수학회지 56(4):1001~1016
M. Agueh / 2011 / Barycenters in the wasserstein space / SIAM J. Math. Anal 43:904~924
Y. -H. Kim / 2015 / Multi-marginal optimal transport on Riemannian manifolds / Amer. J. Math 137:1045~1060
B. Pass / 2012 / The local structure of optimal measures in the multi-marginal optimal transportation problem / Calc. Var. Partial Differential Equations 43:529~536
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