# Estimating 2-Sinkhorn Divergence between Gaussian Processes from Finite-Dimensional Marginals

arXiv: https://arxiv.org/abs/2102.03267 · HTML: https://mlsanity.com/paper/2102.03267/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 40 references that are in the map.
- First posted on arXiv 5 Feb 2021.

## Builds on (most cited first, 9 of 9)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem](https://mlsanity.com/paper/1905.11882/) (2019)
- [Entropy-Regularized 2-Wasserstein Distance between Gaussian Measures](https://mlsanity.com/paper/2006.03416/) (2020)
- [Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processes](https://mlsanity.com/paper/1801.01990/) (2018)
- [The statistical effect of entropic regularization in optimal transportation](https://mlsanity.com/paper/2006.05199/) (2020)
- [Bregman Divergences for Infinite Dimensional Covariance Matrices](https://mlsanity.com/paper/1403.4334/) (2014)
- [Optimal Transport losses and Sinkhorn algorithm with general convex regularization](https://mlsanity.com/paper/2007.00976/) (2020)
- [Entropic regularization of Wasserstein distance between infinite-dimensional Gaussian measures and Gaussian processes](https://mlsanity.com/paper/2011.07489/) (2020)

## Built on by (most cited first, 1 of 1)

- [Finite sample approximations of exact and entropic Wasserstein distances between covariance operators and Gaussian processes](https://mlsanity.com/paper/2104.12368/) (2021)

## Abstract (arXiv)

Optimal Transport (OT) has emerged as an important computational tool in machine learning and computer vision, providing a geometrical framework for studying probability measures. OT unfortunately suffers from the curse of dimensionality and requires regularization for practical computations, of which the entropic regularization is a popular choice, which can be 'unbiased', resulting in a Sinkhorn divergence. In this work, we study the convergence of estimating the 2-Sinkhorn divergence between Gaussian processes (GPs) using their finite-dimensional marginal distributions. We show almost sure convergence of the divergence when the marginals are sampled according to some base measure. Furthermore, we show that using n marginals the estimation error of the divergence scales in a dimension-free way as Oleft(ε^ -1n^-frac12right), where ε is the magnitude of entropic regularization.