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Activity Number: 141 - Minimax Theory for High-Dimensional Models
Type: Invited
Date/Time: Tuesday, August 4, 2020 : 10:00 AM to 11:50 AM
Sponsor: IMS
Abstract #309274
Title: Estimation of Wasserstein Distances in the Spiked Transport Model
Author(s): Jonathan Niles-Weed* and Philippe Rigollet
Companies: New York University and Massachusetts Institute of Technology
Keywords: Wasserstein distance; Optimal transport
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.


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