Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery
This work addresses a computational bottleneck for researchers using non-parametric causal discovery on large datasets, though it is incremental as it builds on existing kernel-based methods.
The authors tackled the problem of slow conditional independence testing in causal discovery by developing two fast approximations, RCIT and RCoT, which scale linearly with sample size and achieve comparable accuracy to the standard KCIT test.
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.