Non-parametric threshold for smoothed empirical Wasserstein distance
Consider an empirical measure P𝑛 induced by 𝑛 iid samples from a 𝑑-dimensional 𝐾-subgaussian distribution P. We show that when 𝐾 < 𝜎, the Wasserstein distance 𝑊₂² (Pₙ*𝒩(0, 𝜎² 𝐼 subscript 𝑑), P*𝒩 (0, 𝜎² 𝐼 subscript 𝑑)) converges at the parametric rate 𝑂(1/𝑛), and when 𝐾 > 𝜎, there exists a 𝐾-su...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2022
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| Online Access: | https://hdl.handle.net/1721.1/143344 https://orcid.org/0000-0002-0687-445X |