A Kernel Test for Three-Variable Interactions
This provides a tool for researchers in statistics and machine learning to identify complex dependencies in data, though it is incremental as it builds on existing kernel methods for interaction testing.
The paper tackles the problem of detecting three-variable interactions in data, particularly for directed graphical models, by introducing kernel nonparametric tests for Lancaster interaction and total independence, and shows that these tests outperform competing methods in detecting V-structures where combined effects are strong.
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.