# Estimation of Stationary Optimal Transport Plans

arXiv: https://arxiv.org/abs/2107.11858 · HTML: https://mlsanity.com/paper/2107.11858/

## 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.

## Builds on (most cited first, 30 of 31)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [Learning with a Wasserstein Loss](https://mlsanity.com/paper/1506.05439/) (2015)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [Gromov-Wasserstein Learning for Graph Matching and Node Embedding](https://mlsanity.com/paper/1901.06003/) (2019)
- [Large-Scale Optimal Transport and Mapping Estimation](https://mlsanity.com/paper/1711.02283/) (2017)
- [Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm](https://mlsanity.com/paper/1802.04367/) (2018)
- [Scalable Gromov-Wasserstein Learning for Graph Partitioning and Matching](https://mlsanity.com/paper/1905.07645/) (2019)
- [Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem](https://mlsanity.com/paper/1905.11882/) (2019)
- [On Efficient Optimal Transport: An Analysis of Greedy and Accelerated Mirror Descent Algorithms](https://mlsanity.com/paper/1901.06482/) (2019)
- [Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projections](https://mlsanity.com/paper/2107.01718/) (2021)
- [Multilevel Clustering via Wasserstein Means](https://mlsanity.com/paper/1706.03883/) (2017)
- [An Optimal Transport approach for the Schr"odinger bridge problem and convergence of Sinkhorn algorithm](https://mlsanity.com/paper/1911.06850/) (2019)
- [Wasserstein Regression](https://mlsanity.com/paper/2006.09660/) (2020)
- [Approximate Bayesian computation with the Wasserstein distance](https://mlsanity.com/paper/1905.03747/) (2019)
- [Entropic Optimal Transport: Convergence of Potentials](https://mlsanity.com/paper/2104.11720/) (2021)
- [Semi-dual Regularized Optimal Transport](https://mlsanity.com/paper/1811.05527/) (2018)
- [Inference for Empirical Wasserstein Distances on Finite Spaces](https://mlsanity.com/paper/1610.03287/) (2016)
- [Entropic Optimal Transport: Geometry and Large Deviations](https://mlsanity.com/paper/2102.04397/) (2021)
- [Wasserstein regularization for sparse multi-task regression](https://mlsanity.com/paper/1805.07833/) (2018)
- [The statistical effect of entropic regularization in optimal transportation](https://mlsanity.com/paper/2006.05199/) (2020)
- [Co-clustering through Optimal Transport](https://mlsanity.com/paper/1705.06189/) (2017)
- [Optimal spectral transportation with application to music transcription](https://mlsanity.com/paper/1609.09799/) (2016)
- [Variational Wasserstein Clustering](https://mlsanity.com/paper/1806.09045/) (2018)
- [Optimal Transport Based Change Point Detection and Time Series Segment Clustering](https://mlsanity.com/paper/1911.01325/) (2019)
- [Optimal Transport for Stationary Markov Chains via Policy Iteration](https://mlsanity.com/paper/2006.07998/) (2020)

## 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.