An Adaptive Test of Independence with Analytic Kernel Embeddings

Wittawat Jitkrittum, Zoltán Szabó, Arthur Gretton
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:1742-1751, 2017.

Abstract

A new computationally efficient dependence measure, and an adaptive statistical test of independence, are proposed. The dependence measure is the difference between analytic embeddings of the joint distribution and the product of the marginals, evaluated at a finite set of locations (features). These features are chosen so as to maximize a lower bound on the test power, resulting in a test that is data-efficient, and that runs in linear time (with respect to the sample size n). The optimized features can be interpreted as evidence to reject the null hypothesis, indicating regions in the joint domain where the joint distribution and the product of the marginals differ most. Consistency of the independence test is established, for an appropriate choice of features. In real-world benchmarks, independence tests using the optimized features perform comparably to the state-of-the-art quadratic-time HSIC test, and outperform competing O(n) and O(n log n) tests.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-jitkrittum17a, title = {An Adaptive Test of Independence with Analytic Kernel Embeddings}, author = {Wittawat Jitkrittum and Zolt{\'a}n Szab{\'o} and Arthur Gretton}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {1742--1751}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/jitkrittum17a/jitkrittum17a.pdf}, url = {https://proceedings.mlr.press/v70/jitkrittum17a.html}, abstract = {A new computationally efficient dependence measure, and an adaptive statistical test of independence, are proposed. The dependence measure is the difference between analytic embeddings of the joint distribution and the product of the marginals, evaluated at a finite set of locations (features). These features are chosen so as to maximize a lower bound on the test power, resulting in a test that is data-efficient, and that runs in linear time (with respect to the sample size n). The optimized features can be interpreted as evidence to reject the null hypothesis, indicating regions in the joint domain where the joint distribution and the product of the marginals differ most. Consistency of the independence test is established, for an appropriate choice of features. In real-world benchmarks, independence tests using the optimized features perform comparably to the state-of-the-art quadratic-time HSIC test, and outperform competing O(n) and O(n log n) tests.} }
Endnote
%0 Conference Paper %T An Adaptive Test of Independence with Analytic Kernel Embeddings %A Wittawat Jitkrittum %A Zoltán Szabó %A Arthur Gretton %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-jitkrittum17a %I PMLR %P 1742--1751 %U https://proceedings.mlr.press/v70/jitkrittum17a.html %V 70 %X A new computationally efficient dependence measure, and an adaptive statistical test of independence, are proposed. The dependence measure is the difference between analytic embeddings of the joint distribution and the product of the marginals, evaluated at a finite set of locations (features). These features are chosen so as to maximize a lower bound on the test power, resulting in a test that is data-efficient, and that runs in linear time (with respect to the sample size n). The optimized features can be interpreted as evidence to reject the null hypothesis, indicating regions in the joint domain where the joint distribution and the product of the marginals differ most. Consistency of the independence test is established, for an appropriate choice of features. In real-world benchmarks, independence tests using the optimized features perform comparably to the state-of-the-art quadratic-time HSIC test, and outperform competing O(n) and O(n log n) tests.
APA
Jitkrittum, W., Szabó, Z. & Gretton, A.. (2017). An Adaptive Test of Independence with Analytic Kernel Embeddings. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:1742-1751 Available from https://proceedings.mlr.press/v70/jitkrittum17a.html.

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