Estimation of Wasserstein distances in the Spiked Transport Model

Jonathan Niles-Weed, Philippe Rigollet

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)2663-2688
Number of pages26
Issue number4
StatePublished - Nov 2022


  • Wasserstein distance
  • high-dimensional statistics
  • optimal transport

ASJC Scopus subject areas

  • Statistics and Probability


Dive into the research topics of 'Estimation of Wasserstein distances in the Spiked Transport Model'. Together they form a unique fingerprint.

Cite this