Learning Deep Kernels for Non-Parametric Two-Sample Tests

Feng Liu, Wenkai Xu, Jie Lu, Guangquan Zhang, Arthur Gretton, Danica J. Sutherland
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:6316-6326, 2020.

Abstract

We propose a class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test power. These tests adapt to variations in distribution smoothness and shape over space, and are especially suited to high dimensions and complex data. By contrast, the simpler kernels used in prior kernel testing work are spatially homogeneous, and adaptive only in lengthscale. We explain how this scheme includes popular classifier-based two-sample tests as a special case, but improves on them in general. We provide the first proof of consistency for the proposed adaptation method, which applies both to kernels on deep features and to simpler radial basis kernels or multiple kernel learning. In experiments, we establish the superior performance of our deep kernels in hypothesis testing on benchmark and real-world data. The code of our deep-kernel-based two-sample tests is available at github.com/fengliu90/DK-for-TST.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-liu20m, title = {Learning Deep Kernels for Non-Parametric Two-Sample Tests}, author = {Liu, Feng and Xu, Wenkai and Lu, Jie and Zhang, Guangquan and Gretton, Arthur and Sutherland, Danica J.}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {6316--6326}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/liu20m/liu20m.pdf}, url = {https://proceedings.mlr.press/v119/liu20m.html}, abstract = {We propose a class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test power. These tests adapt to variations in distribution smoothness and shape over space, and are especially suited to high dimensions and complex data. By contrast, the simpler kernels used in prior kernel testing work are spatially homogeneous, and adaptive only in lengthscale. We explain how this scheme includes popular classifier-based two-sample tests as a special case, but improves on them in general. We provide the first proof of consistency for the proposed adaptation method, which applies both to kernels on deep features and to simpler radial basis kernels or multiple kernel learning. In experiments, we establish the superior performance of our deep kernels in hypothesis testing on benchmark and real-world data. The code of our deep-kernel-based two-sample tests is available at github.com/fengliu90/DK-for-TST.} }
Endnote
%0 Conference Paper %T Learning Deep Kernels for Non-Parametric Two-Sample Tests %A Feng Liu %A Wenkai Xu %A Jie Lu %A Guangquan Zhang %A Arthur Gretton %A Danica J. Sutherland %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-liu20m %I PMLR %P 6316--6326 %U https://proceedings.mlr.press/v119/liu20m.html %V 119 %X We propose a class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test power. These tests adapt to variations in distribution smoothness and shape over space, and are especially suited to high dimensions and complex data. By contrast, the simpler kernels used in prior kernel testing work are spatially homogeneous, and adaptive only in lengthscale. We explain how this scheme includes popular classifier-based two-sample tests as a special case, but improves on them in general. We provide the first proof of consistency for the proposed adaptation method, which applies both to kernels on deep features and to simpler radial basis kernels or multiple kernel learning. In experiments, we establish the superior performance of our deep kernels in hypothesis testing on benchmark and real-world data. The code of our deep-kernel-based two-sample tests is available at github.com/fengliu90/DK-for-TST.
APA
Liu, F., Xu, W., Lu, J., Zhang, G., Gretton, A. & Sutherland, D.J.. (2020). Learning Deep Kernels for Non-Parametric Two-Sample Tests. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:6316-6326 Available from https://proceedings.mlr.press/v119/liu20m.html.

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