  Constraint-based causal discovery (CCD) algorithms require fast and accurate
conditional independence (CI) testing. The Kernel Conditional Independence Test
(KCIT) is currently one of the most popular CI tests in the non-parametric
setting, but many investigators cannot use KCIT with large datasets because the
test scales cubicly with sample size. We therefore devise two relaxations
called the Randomized Conditional Independence Test (RCIT) and the Randomized
conditional Correlation Test (RCoT) which both approximate KCIT by utilizing
random Fourier features. In practice, both of the proposed tests scale linearly
with sample size and return accurate p-values much faster than KCIT in the
large sample size context. CCD algorithms run with RCIT or RCoT also return
graphs at least as accurate as the same algorithms run with KCIT but with large
reductions in run time.
