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- W4293490003 abstract "We propose a new statistical model, the spiked transport model, which formalizes the assumption that two probability distributions differ only on a low-dimensional subspace. We study the minimax rate of estimation for the Wasserstein distance under this model and show that this low-dimensional structure can be exploited to avoid the curse of dimensionality. As a byproduct of our minimax analysis, we establish a lower bound showing that, in the absence of such structure, the plug-in estimator is nearly rate-optimal for estimating the Wasserstein distance in high dimension. We also give evidence for a statistical-computational gap and conjecture that any computationally efficient estimator is bound to suffer from the curse of dimensionality." @default.
- W4293490003 created "2022-08-29" @default.
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- W4293490003 date "2019-09-16" @default.
- W4293490003 modified "2023-09-27" @default.
- W4293490003 title "Estimation of Wasserstein distances in the Spiked Transport Model" @default.
- W4293490003 doi "https://doi.org/10.48550/arxiv.1909.07513" @default.
- W4293490003 hasPublicationYear "2019" @default.
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