Additive noise model structure learning based on rank correlation

To examine the structural learning of the additive noise model in causal discovery, a new algorithm, i.e., RCB (Rank-Correlation-Based), is proposed in combination with the method of Rank Correlation. This algorithm can effectively process multivariate linear Gaussian, non-Gaussian and multivariate nonlinear non-Gaussian data. In this article we have made three contributions. First, it is proven that rank correlation can be used as the criterion of the independence test. Second, through a series of experiments, the optimal threshold of rank correlation is found to select the potential neighbors of the target node. Thus, the RCB algorithm greatly reduces the search space and achieves good time performance. The third contribution is the improvement of the RCB algorithm in combination with the hypothesis testing method, and the RCS (Rank-Correlation-Statistics) algorithm is proposed to solve the theoretical basis for the threshold selection. Compared with the existing technology on 7 networks, the RCS algorithm is superior to existing algorithms in terms of both accuracy and time performance. In addition, simulations show that the RCS algorithm can achieve a good time performance and accuracy on low-dimensional large samples, high-dimensional large samples and real data.