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.

References in corpus (4)

• Brownian distance covariance
• Equivalence of distance-based and RKHS-based statistics in hypothesis testing
• Kernel-based Conditional Independence Test and Application in Causal Discovery
• Estimation of Rényi Entropy and Mutual Information Based on Generalized Nearest-Neighbor Graphs

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