A Kernel Test for Three-Variable Interactions
By Dino Sejdinovic, Arthur Gretton, Wicher P. Bergsma. 2013
42 citations recorded by the source corpus.
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.
Subfields: Artificial Intelligence, Statistics and Probability
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Bernhard Schölkopf
- Arthur Gretton
- Bharath K. Sriperumbudur
- Kenji Fukumizu
- Krikamol Muandet
- Dino Sejdinovic
- Jan Peters
- David Lopez-Paz
In Statistics and Probability
- Bernhard Schölkopf
- Arthur Gretton
- Bharath K. Sriperumbudur
- Kenji Fukumizu
- Dino Sejdinovic
- Krikamol Muandet
- Jan Peters
- Kacper P. Chwialkowski
Citations in the corpus
- Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “Bounliphone et al. (2015) constructs a consistent test for relative dependency which—unlike the Lancaster test of Sejdinovic et al. (2013a)—measures dependency between a source variable and two candidate target variables.”
- Kernel‐based tests for joint independence (2016, methodology): “Although the dHSIC test statistic was briefly mentioned by Sejdinovic et al. (2013), the derivation of the general results about asymptotic distributions (theorem 2 and theorem 3 in Section 3.1) as well as the mathematically rigorous treatment of the permutation test and the bootstrap test are…”
- A Wild Bootstrap for Degenerate Kernel Tests (2014, methodology): “This degeneracy is common to many kernel statistics when the null hypothesis holds [15, 17, 24].”
- A low variance consistent test of relative dependency (2014, background): “This test does not address the issue of finding which connections are strongest, however.”
- Large-scale kernel methods for independence testing (2016, background): “Moreover, [30] (Theorem 5 and 6) provides another elegant proof in the context of three-variable interaction testing from [32].”