Sharp Bounds for Max-sliced Wasserstein Distances.
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| Title: | Sharp Bounds for Max-sliced Wasserstein Distances. |
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| Authors: | Boedihardjo, March T.1 (AUTHOR) boedihar@msu.edu |
| Source: | Foundations of Computational Mathematics. Apr2026, Vol. 26 Issue 2, p747-778. 32p. |
| Subjects: | Probability measures, Hilbert space, Data distribution, Covariance matrices, Banach spaces, Matrix norms |
| Abstract: | We obtain essentially matching upper and lower bounds for the expected max-sliced 1-Wasserstein distance between a probability measure on a separable Hilbert space and its empirical distribution from n samples. By proving a Banach space version of this result, we also obtain an upper bound, that is sharp up to a log factor, for the expected max-sliced 2-Wasserstein distance between a symmetric probability measure μ on a Euclidean space and its symmetrized empirical distribution in terms of the operator norm of the covariance matrix of μ and the diameter of the support of μ. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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