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Sharp Bounds for Max-sliced Wasserstein Distances.

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Title: Sharp Bounds for Max-sliced Wasserstein Distances.
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]
Copyright of Foundations of Computational Mathematics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: 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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  Data: <i>Copyright of Foundations of Computational Mathematics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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