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Mathematics > Probability
Title: Sharp bounds for max-sliced Wasserstein distances
(Submitted on 1 Mar 2024 (v1), last revised 3 Apr 2024 (this version, v5))
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 $\mu$ on a Euclidean space and its symmetrized empirical distribution in terms of the operator norm of the covariance matrix of $\mu$ and the diameter of the support of $\mu$.
Submission history
From: March Boedihardjo [view email][v1] Fri, 1 Mar 2024 16:55:10 GMT (10kb)
[v2] Thu, 14 Mar 2024 17:58:35 GMT (18kb)
[v3] Thu, 28 Mar 2024 17:57:18 GMT (18kb)
[v4] Tue, 2 Apr 2024 16:56:01 GMT (18kb)
[v5] Wed, 3 Apr 2024 20:10:07 GMT (18kb)
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