# Entropy Regularized Optimal Transport Independence Criterion

arXiv: https://arxiv.org/abs/2112.15265 · HTML: https://mlsanity.com/paper/2112.15265/

## 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 (most cited first, 22 of 22)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Language-agnostic BERT Sentence Embedding](https://mlsanity.com/paper/2007.01852/) (2020)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests](https://mlsanity.com/paper/1509.02237/) (2015)
- [Improving GANs Using Optimal Transport](https://mlsanity.com/paper/1803.05573/) (2018)
- [Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm](https://mlsanity.com/paper/1802.04367/) (2018)
- [Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem](https://mlsanity.com/paper/1905.11882/) (2019)
- [Self-Supervised Learning with Kernel Dependence Maximization](https://mlsanity.com/paper/2106.08320/) (2021)
- [Wasserstein Dependency Measure for Representation Learning](https://mlsanity.com/paper/1903.11780/) (2019)
- [Regularized Discrete Optimal Transport](https://mlsanity.com/paper/1307.5551/) (2013)
- [On the Convergence and Robustness of Training GANs with Regularized Optimal Transport](https://mlsanity.com/paper/1802.08249/) (2018)
- [Convergence and Concentration of Empirical Measures under Wasserstein Distance in Unbounded Functional Spaces](https://mlsanity.com/paper/1804.10556/) (2018)
- [Kernel-based Tests for Joint Independence](https://mlsanity.com/paper/1603.00285/) (2016)
- [Large-Scale Kernel Methods for Independence Testing](https://mlsanity.com/paper/1606.07892/) (2016)
- [Multivariate Rank-based Distribution-free Nonparametric Testing using Measure Transportation](https://mlsanity.com/paper/1909.08733/) (2019)
- [Linear Time Sinkhorn Divergences using Positive Features](https://mlsanity.com/paper/2006.07057/) (2020)
- [The statistical effect of entropic regularization in optimal transportation](https://mlsanity.com/paper/2006.05199/) (2020)
- [An Adaptive Test of Independence with Analytic Kernel Embeddings](https://mlsanity.com/paper/1610.04782/) (2016)
- [Distance Metrics for Measuring Joint Dependence with Application to Causal Inference](https://mlsanity.com/paper/1711.09179/) (2017)
- [A low variance consistent test of relative dependency](https://mlsanity.com/paper/1406.3852/) (2014)

## Built on by (most cited first, 9 of 9)

- [Scalable Unbalanced Sobolev Transport for Measures on a Graph](https://mlsanity.com/paper/2302.12498/) (2023)
- [Generalized Sobolev Transport for Probability Measures on a Graph](https://mlsanity.com/paper/2402.04516/) (2024)
- [Optimal Transport for Measures with Noisy Tree Metric](https://mlsanity.com/paper/2310.13653/) (2023)
- [Tree-Sliced Wasserstein Distance: A Geometric Perspective](https://mlsanity.com/paper/2406.13725/) (2024)
- [Distance-Based Tree-Sliced Wasserstein Distance](https://mlsanity.com/paper/2503.11050/) (2025)
- [Solving a Special Type of Optimal Transport Problem by a Modified Hungarian Algorithm](https://mlsanity.com/paper/2210.16645/) (2022)
- [Tree-Sliced Wasserstein Distance with Nonlinear Projection](https://mlsanity.com/paper/2505.00968/) (2025)
- [Maximizing Conditional Independence for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2203.03212/) (2022)
- [Partial Domain Adaptation via Importance Sampling-based Shift Correction](https://mlsanity.com/paper/2507.20191/) (2025)

## 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.