Kernel-based Conditional Independence Test and Application in Causal Discovery
This addresses a key bottleneck in Bayesian network learning and causal discovery for researchers and practitioners, offering an incremental improvement over existing methods.
The authors tackled the problem of conditional independence testing for continuous variables, which is challenging due to the curse of dimensionality, by proposing a Kernel-based Conditional Independence test (KCI-test) that outperforms other methods, especially with large conditioning sets or small sample sizes.
Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly challenging. We propose a Kernel-based Conditional Independence test (KCI-test), by constructing an appropriate test statistic and deriving its asymptotic distribution under the null hypothesis of conditional independence. The proposed method is computationally efficient and easy to implement. Experimental results show that it outperforms other methods, especially when the conditioning set is large or the sample size is not very large, in which case other methods encounter difficulties.