Testing Independence Between Linear Combinations for Causal Discovery

Recently, regression based conditional independence (CI) tests have been employed to solve the problem of causal discovery. These methods provide an alternative way test for CI by transforming between residuals. Generally, it is nontrivial check when these residuals are linearly uncorrelated. With ability represent high-order moments, kernel-based usually used achieve this goal, but at a cost considerable time. In paper, we investigate two linear combinations under non-Gaussian structural equation model (SEM). We show that generally 1-st 4-th moments contain enough information infer whether or not they independent. The proposed method provides simpler more effective measure CIs, with only calculating input variables. When applied discovery, outperforms in terms both speed and accuracy. which validated extensive experiments.