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- W4387687946 abstract "We consider structured approximation of measures in Wasserstein space $W_p(mathbb{R}^d)$ for $pin[1,infty)$ by discrete and piecewise constant measures based on a scaled Voronoi partition of $mathbb{R}^d$. We show that if a full rank lattice $Lambda$ is scaled by a factor of $hin(0,1]$, then approximation of a measure based on the Voronoi partition of $hLambda$ is $O(h)$ regardless of $d$ or $p$. We then use a covering argument to show that $N$-term approximations of compactly supported measures is $O(N^{-frac1d})$ which matches known rates for optimal quantizers and empirical measure approximation in most instances. Finally, we extend these results to noncompactly supported measures with sufficient decay." @default.
- W4387687946 created "2023-10-17" @default.
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- W4387687946 date "2023-10-13" @default.
- W4387687946 modified "2023-10-18" @default.
- W4387687946 title "Lattice Approximations in Wasserstein Space" @default.
- W4387687946 doi "https://doi.org/10.48550/arxiv.2310.09149" @default.
- W4387687946 hasPublicationYear "2023" @default.
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