mlsanityData to 14 Oct 2026

Entropy Regularized Optimal Transport Independence Criterion

arXiv 2112.15265 ↗First posted 31 Dec 2021stat.ML cs.LGcited by 9

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Abstract (arXiv)

We introduce an independence criterion based on entropy regularized optimal transport. Our criterion can be used to test for independence between two samples. We establish non-asymptotic bounds for our test statistic and study its statistical behavior under both the null hypothesis and the alternative hypothesis. The theoretical results involve tools from U-process theory and optimal transport theory. We also offer a random feature type approximation for large-scale problems, as well as a differentiable program implementation for deep learning applications. We present experimental results on existing benchmarks for independence testing, illustrating the interest of the proposed criterion to capture both linear and nonlinear dependencies in synthetic data and real data.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 22 of its 68 references that are in the map. First posted on arXiv 31 Dec 2021.

Builds on

22 of 68 references.

References · 22

  1. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,316
  2. 2020Language-agnostic BERT Sentence Embeddingcited by 627
  3. 2017Learning Generative Models with Sinkhorn Divergencescited by 314
  4. 2013A survey of the Schr"odinger problem and some of its connections with optimal transportcited by 292
  5. 2016Stochastic Optimization for Large-scale Optimal Transportcited by 189
  6. 2015On Wasserstein Two Sample Testing and Related Families of Nonparametric Testscited by 166
  7. 2018Improving GANs Using Optimal Transportcited by 123
  8. 2018Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithmcited by 112
  9. 2019Statistical bounds for entropic optimal transport: sample complexity and the central limit theoremcited by 85
  10. 2021Self-Supervised Learning with Kernel Dependence Maximizationcited by 77
  11. 2019Wasserstein Dependency Measure for Representation Learningcited by 69
  12. 2013Regularized Discrete Optimal Transportcited by 54
10 more
  1. 2018On the Convergence and Robustness of Training GANs with Regularized Optimal Transportcited by 51
  2. 2018Convergence and Concentration of Empirical Measures under Wasserstein Distance in Unbounded Functional Spacescited by 41
  3. 2016Kernel-based Tests for Joint Independencecited by 40
  4. 2016Large-Scale Kernel Methods for Independence Testingcited by 32
  5. 2019Multivariate Rank-based Distribution-free Nonparametric Testing using Measure Transportationcited by 24
  6. 2020Linear Time Sinkhorn Divergences using Positive Featurescited by 17
  7. 2020The statistical effect of entropic regularization in optimal transportationcited by 14
  8. 2016An Adaptive Test of Independence with Analytic Kernel Embeddingscited by 13
  9. 2017Distance Metrics for Measuring Joint Dependence with Application to Causal Inferencecited by 7
  10. 2014A low variance consistent test of relative dependencycited by 1

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Cited by year

Citing papers per year: 2022: 2; 2023: 2; 2024: 2; 2025: 3.

9 papers.

  1. 2023Scalable Unbalanced Sobolev Transport for Measures on a Graphcited by 10
  2. 2024Generalized Sobolev Transport for Probability Measures on a Graphcited by 9
  3. 2023Optimal Transport for Measures with Noisy Tree Metriccited by 7
  4. 2024Tree-Sliced Wasserstein Distance: A Geometric Perspectivecited by 7
  5. 2025Distance-Based Tree-Sliced Wasserstein Distancecited by 4
  6. 2022Solving a Special Type of Optimal Transport Problem by a Modified Hungarian Algorithmcited by 3
  7. 2025Tree-Sliced Wasserstein Distance with Nonlinear Projectioncited by 3
  8. 2022Maximizing Conditional Independence for Unsupervised Domain Adaptationcited by 2
  9. 2025Partial Domain Adaptation via Importance Sampling-based Shift Correctioncited by 2