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/}
}