A Permutation-Based Kernel Conditional Independence Test
Gary Doran, Krikamol Muandet, Kun Zhang, Bernhard Schoelkopf
Determining conditional independence (CI) re-
lationships between random variables is a chal-
lenging but important task for problems such as
Bayesian network learning and causal discovery.
We propose a new kernel CI test that uses a sin-
gle, learned permutation to convert the CI test
problem into an easier two-sample test problem.
The learned permutation leaves the joint distri-
bution unchanged if and only if the null hypoth-
esis of CI holds. Then, a kernel two-sample test,
which has been studied extensively in prior work,
can be applied to a permuted and an unpermuted
sample to test for CI. We demonstrate that the
test (1) easily allows the incorporation of prior
knowledge during the permutation step, (2) has
power competitive with state-of-the-art kernel CI
tests, and (3) accurately estimates the null distri-
bution of the test statistic, even as the dimension-
ality of the conditioning variable grows.
PDF Link: /papers/14/p132-doran.pdf
AUTHOR = "Gary Doran
and Krikamol Muandet and Kun Zhang and Bernhard Schoelkopf",
TITLE = "A Permutation-Based Kernel Conditional Independence Test",
BOOKTITLE = "Proceedings of the Thirtieth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-14)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2014",
PAGES = "132--141"