mlsanityData to 7 Oct 2026

Gaussian Processes on Distributions based on Regularized Optimal Transport

arXiv 2210.06574 ↗First posted 12 Oct 2022stat.ML cs.LGcited by 6

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Abstract (arXiv)

We present a novel kernel over the space of probability measures based on the dual formulation of optimal regularized transport. We propose an Hilbertian embedding of the space of probabilities using their Sinkhorn potentials, which are solutions of the dual entropic relaxed optimal transport between the probabilities and a reference measure U. We prove that this construction enables to obtain a valid kernel, by using the Hilbert norms. We prove that the kernel enjoys theoretical properties such as universality and some invariances, while still being computationally feasible. Moreover we provide theoretical guarantees on the behaviour of a Gaussian process based on this kernel. The empirical performances are compared with other traditional choices of kernels for processes indexed on distributions.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 19 of its 61 references that are in the map. First posted on arXiv 12 Oct 2022.

Builds on

19 of 61 references.

References · 19

  1. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  2. 2018Computational Optimal Transportcited by 765
  3. 2017Learning Generative Models with Sinkhorn Divergencescited by 310
  4. 2017Near-linear time approximation algorithms for optimal transport via Sinkhorn iterationcited by 219
  5. 2021Efficient and Modular Implicit Differentiationcited by 199
  6. 2018Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithmcited by 111
  7. 2022Optimal Transport Tools (OTT): A JAX Toolbox for all things Wassersteincited by 96
  8. 2019Statistical bounds for entropic optimal transport: sample complexity and the central limit theoremcited by 85
  9. 2015Sliced Wasserstein Kernels for Probability Distributionscited by 64
  10. 2017Sliced Wasserstein Distance for Learning Gaussian Mixture Modelscited by 59
  11. 2014Learning Theory for Distribution Regressioncited by 48
  12. 2020Linear Optimal Transport Embedding: Provable Wasserstein classification for certain rigid transformations and perturbationscited by 37
7 more
  1. 2022A Unified Framework for Implicit Sinkhorn Differentiationcited by 28
  2. 2013Distribution-Free Distribution Regressioncited by 21
  3. 2016A supermartingale approach to Gaussian process based sequential design of experimentscited by 20
  4. 2022Distribution Regression with Sliced Wasserstein Kernelscited by 18
  5. 2022An improved central limit theorem and fast convergence rates for entropic transportation costscited by 18
  6. 2017A Gaussian Process Regression Model for Distribution Inputscited by 12
  7. 2022Nonparametric Multiple-Output Center-Outward Quantile Regressioncited by 11

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 2; 2025: 1; 2026: 1.

6 papers.

  1. 2024Gaussian process regression with Sliced Wasserstein Weisfeiler-Lehman graph kernelscited by 7
  2. 2023Vecchia Gaussian Process Ensembles on Internal Representations of Deep Neural Networkscited by 3
  3. 2023Improved learning theory for kernel distribution regression with two-stage samplingcited by 1
  4. 2024Learning signals defined on graphs with optimal transport and Gaussian process regressioncited by 1
  5. 2025Families of Optimal Transport Kernels for Cell Complexescited by 0
  6. 2026Inducing Permutation Invariant Priors in Bayesian Optimization for Carbon Capture and Storage Applicationscited by 0