Conditional independence testing based on a nearest-neighbor estimator of conditional mutual information
This work addresses a fundamental challenge in causal discovery for researchers dealing with complex data dependencies, though it is incremental as it builds on existing nearest-neighbor and permutation methods.
The authors tackled the problem of conditional independence testing for continuous data with nonlinear and high-dimensional dependencies by developing a fully non-parametric test based on conditional mutual information and a local permutation scheme, which reliably simulates null distributions even for small sample sizes and outperforms kernel-based tests in calibration and power for non-smooth densities.
Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data based on conditional mutual information combined with a local permutation scheme is presented. Through a nearest neighbor approach, the test efficiently adapts also to non-smooth distributions due to strongly nonlinear dependencies. Numerical experiments demonstrate that the test reliably simulates the null distribution even for small sample sizes and with high-dimensional conditioning sets. The test is better calibrated than kernel-based tests utilizing an analytical approximation of the null distribution, especially for non-smooth densities, and reaches the same or higher power levels. Combining the local permutation scheme with the kernel tests leads to better calibration, but suffers in power. For smaller sample sizes and lower dimensions, the test is faster than random fourier feature-based kernel tests if the permutation scheme is (embarrassingly) parallelized, but the runtime increases more sharply with sample size and dimensionality. Thus, more theoretical research to analytically approximate the null distribution and speed up the estimation for larger sample sizes is desirable.