Kernel-based conditional independence test and application in causal discovery

Conditional independence testing is an im-portant problem, especially in Bayesian net-work learning and causal discovery. Due to the curse of dimensionality, testing for condi-tional 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 dis-tribution under the null hypothesis of condi-tional independence. The proposed method is computationally efficient and easy to im-plement. 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.