A Kernel Test for Three-Variable Interactions
Abstract
We introduce kernel nonparametric tests for Lancaster three-variable interaction and for total independence, using embeddings of signed measures into a reproducing kernel Hilbert space. The resulting test statistics are straightforward to compute, and are used in powerful three-variable interaction tests, which are consistent against all alternatives for a large family of reproducing kernels. We show the Lancaster test to be sensitive to cases where two independent causes individually have weak influence on a third dependent variable, but their combined effect has a strong influence. This makes the Lancaster test especially suited to finding structure in directed graphical models, where it outperforms competing nonparametric tests in detecting such V-structures.
Cite
Text
Sejdinovic et al. "A Kernel Test for Three-Variable Interactions." Neural Information Processing Systems, 2013.Markdown
[Sejdinovic et al. "A Kernel Test for Three-Variable Interactions." Neural Information Processing Systems, 2013.](https://mlanthology.org/neurips/2013/sejdinovic2013neurips-kernel/)BibTeX
@inproceedings{sejdinovic2013neurips-kernel,
title = {{A Kernel Test for Three-Variable Interactions}},
author = {Sejdinovic, Dino and Gretton, Arthur and Bergsma, Wicher},
booktitle = {Neural Information Processing Systems},
year = {2013},
pages = {1124-1132},
url = {https://mlanthology.org/neurips/2013/sejdinovic2013neurips-kernel/}
}