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Estimation of Stationary Optimal Transport Plans

arXiv 2107.11858 ↗First posted 25 Jul 2021math.ST math.DS stat.MLcited by 0

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Abstract (arXiv)

We study optimal transport for stationary stochastic processes taking values in finite spaces. In order to reflect the stationarity of the underlying processes, we restrict attention to stationary couplings, also known as joinings. The resulting optimal joining problem captures differences in the long run average behavior of the processes of interest. We introduce estimators of both optimal joinings and the optimal joining cost, and we establish consistency of the estimators under mild conditions. Furthermore, under stronger mixing assumptions we establish finite-sample error rates for the estimated optimal joining cost that extend the best known results in the iid case. Finally, we extend the consistency and rate analysis to an entropy-penalized version of the optimal joining problem.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 31 of its 107 references that are in the map. First posted on arXiv 25 Jul 2021.

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31 of 107 references.

References · 31

  1. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,316
  2. 2018Computational Optimal Transportcited by 780
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  4. 2017Wasserstein Auto-Encoderscited by 373
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  6. 2018Statistical Aspects of Wasserstein Distancescited by 203
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  8. 2018Optimal Transport for structured data with application on graphscited by 172
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  11. 2018Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithmcited by 112
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19 more
  1. 2019Statistical bounds for entropic optimal transport: sample complexity and the central limit theoremcited by 85
  2. 2019On Efficient Optimal Transport: An Analysis of Greedy and Accelerated Mirror Descent Algorithmscited by 62
  3. 2021Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projectionscited by 53
  4. 2017Multilevel Clustering via Wasserstein Meanscited by 49
  5. 2019An Optimal Transport approach for the Schr"odinger bridge problem and convergence of Sinkhorn algorithmcited by 38
  6. 2020Wasserstein Regressioncited by 35
  7. 2019Approximate Bayesian computation with the Wasserstein distancecited by 34
  8. 2021Entropic Optimal Transport: Convergence of Potentialscited by 31
  9. 2018Semi-dual Regularized Optimal Transportcited by 26
  10. 2016Inference for Empirical Wasserstein Distances on Finite Spacescited by 21
  11. 2021Entropic Optimal Transport: Geometry and Large Deviationscited by 20
  12. 2018Wasserstein regularization for sparse multi-task regressioncited by 18
  13. 2020The statistical effect of entropic regularization in optimal transportationcited by 14
  14. 2017Co-clustering through Optimal Transportcited by 13
  15. 2016Optimal spectral transportation with application to music transcriptioncited by 12
  16. 2018Variational Wasserstein Clusteringcited by 11
  17. 2019Optimal Transport Based Change Point Detection and Time Series Segment Clusteringcited by 8
  18. 2020Optimal Transport for Stationary Markov Chains via Policy Iterationcited by 8
  19. 2013Entropy, Pressure and Duality for Gibbs plans in Ergodic Transportcited by 1

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