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 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
@article{arxiv.1306.2281,
title = {A Kernel Test for Three-Variable Interactions},
author = {Dino Sejdinovic and Arthur Gretton and Wicher Bergsma},
journal= {arXiv preprint arXiv:1306.2281},
year = {2013}
}