Entropy Regularized Optimal Transport Independence Criterion

Lang Liu, Soumik Pal, Zaid Harchaoui
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:11247-11279, 2022.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-liu22h, title = { Entropy Regularized Optimal Transport Independence Criterion }, author = {Liu, Lang and Pal, Soumik and Harchaoui, Zaid}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {11247--11279}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/liu22h/liu22h.pdf}, url = {https://proceedings.mlr.press/v151/liu22h.html}, abstract = { 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. } }
Endnote
%0 Conference Paper %T Entropy Regularized Optimal Transport Independence Criterion %A Lang Liu %A Soumik Pal %A Zaid Harchaoui %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-liu22h %I PMLR %P 11247--11279 %U https://proceedings.mlr.press/v151/liu22h.html %V 151 %X 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.
APA
Liu, L., Pal, S. & Harchaoui, Z.. (2022). Entropy Regularized Optimal Transport Independence Criterion . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:11247-11279 Available from https://proceedings.mlr.press/v151/liu22h.html.

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