A Unified Data Representation Learning for Non-parametric Two-sample Testing

Xunye Tian, Liuhua Peng, Zhijian Zhou, Mingming Gong, Arthur Gretton, Feng Liu
Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, PMLR 286:4165-4184, 2025.

Abstract

Learning effective data representations has been crucial in non-parametric two-sample testing. Common approaches will first split data into training and test sets and then learn data representations purely on the training set. However, recent theoretical studies have shown that, as long as the sample indexes are not used during the learning process, the whole data can be used to learn data representations, meanwhile ensuring control of Type-I errors. The above fact motivates us to use the test set (but without sample indexes) to facilitate the data representation learning in the testing. To this end, we propose a representation-learning two-sample testing (RL-TST) framework. RL-TST first performs purely self-supervised representation learning on the entire dataset to capture inherent representations (IRs) that reflect the underlying data manifold. A discriminative model is then trained on these IRs to learn discriminative representations (DRs), enabling the framework to leverage both the rich structural information from IRs and the discriminative power of DRs. Extensive experiments demonstrate that RL-TST outperforms representative approaches by simultaneously using data manifold information in the test set and enhancing test power via finding the DRs with the training set.

Cite this Paper

BibTeX
@InProceedings{pmlr-v286-tian25a, title = {A Unified Data Representation Learning for Non-parametric Two-sample Testing}, author = {Tian, Xunye and Peng, Liuhua and Zhou, Zhijian and Gong, Mingming and Gretton, Arthur and Liu, Feng}, booktitle = {Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence}, pages = {4165--4184}, year = {2025}, editor = {Chiappa, Silvia and Magliacane, Sara}, volume = {286}, series = {Proceedings of Machine Learning Research}, month = {21--25 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v286/main/assets/tian25a/tian25a.pdf}, url = {https://proceedings.mlr.press/v286/tian25a.html}, abstract = {Learning effective data representations has been crucial in non-parametric two-sample testing. Common approaches will first split data into training and test sets and then learn data representations purely on the training set. However, recent theoretical studies have shown that, as long as the sample indexes are not used during the learning process, the whole data can be used to learn data representations, meanwhile ensuring control of Type-I errors. The above fact motivates us to use the test set (but without sample indexes) to facilitate the data representation learning in the testing. To this end, we propose a representation-learning two-sample testing (RL-TST) framework. RL-TST first performs purely self-supervised representation learning on the entire dataset to capture inherent representations (IRs) that reflect the underlying data manifold. A discriminative model is then trained on these IRs to learn discriminative representations (DRs), enabling the framework to leverage both the rich structural information from IRs and the discriminative power of DRs. Extensive experiments demonstrate that RL-TST outperforms representative approaches by simultaneously using data manifold information in the test set and enhancing test power via finding the DRs with the training set.} }
Endnote
%0 Conference Paper %T A Unified Data Representation Learning for Non-parametric Two-sample Testing %A Xunye Tian %A Liuhua Peng %A Zhijian Zhou %A Mingming Gong %A Arthur Gretton %A Feng Liu %B Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2025 %E Silvia Chiappa %E Sara Magliacane %F pmlr-v286-tian25a %I PMLR %P 4165--4184 %U https://proceedings.mlr.press/v286/tian25a.html %V 286 %X Learning effective data representations has been crucial in non-parametric two-sample testing. Common approaches will first split data into training and test sets and then learn data representations purely on the training set. However, recent theoretical studies have shown that, as long as the sample indexes are not used during the learning process, the whole data can be used to learn data representations, meanwhile ensuring control of Type-I errors. The above fact motivates us to use the test set (but without sample indexes) to facilitate the data representation learning in the testing. To this end, we propose a representation-learning two-sample testing (RL-TST) framework. RL-TST first performs purely self-supervised representation learning on the entire dataset to capture inherent representations (IRs) that reflect the underlying data manifold. A discriminative model is then trained on these IRs to learn discriminative representations (DRs), enabling the framework to leverage both the rich structural information from IRs and the discriminative power of DRs. Extensive experiments demonstrate that RL-TST outperforms representative approaches by simultaneously using data manifold information in the test set and enhancing test power via finding the DRs with the training set.
APA
Tian, X., Peng, L., Zhou, Z., Gong, M., Gretton, A. & Liu, F.. (2025). A Unified Data Representation Learning for Non-parametric Two-sample Testing. Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 286:4165-4184 Available from https://proceedings.mlr.press/v286/tian25a.html.

Related Material