A Study Of High-dimensional Causal Discovery Methods

Causal relationship is the fundamental relationship in the laws of nature.Causal discovery is a discipline evolved from statistics,which discovers causal relationship in real world.With the development of statistics and artificial intelligence(AI),causal discovery methods have evolved from low-dimensional to high-dimensional,from paradigm-free to paradigmatic,and from simple to complex data.Causal discovery analyses observed data to uncover causal relationships and infer fundamental laws of the real world.Therefore,the study of causal discovery is of great theoretical and practical significance.This paper focuses on two key problems existing in causal discovery,those are 1)the inefficiency of kernel-based conditional independence methods,2)it is difficult for causal discovery methods to solve high-dimensional problems.To solve these problems,two methods are proposed in this paper,the main contributions are summarized as follow:A causal discovery algorithm based on the partial correlation test is proposed to address the problem of low accuracy and efficiency of the kernel-based CI test method in high dimensionality.Firstly,the computational complexity of CI test and the sensitivity of data set dimensionality to CI test are reduced by introducing partial correlation test.Secondly,the method is combined with a constraint-based approach to enable fast causal discovery.The algorithm has a higher causal discovery accuracy as well as shorter running time than comparable algorithms.A causal decomposition algorithm based on spectral clustering is proposed to solve the problem of low efficiency and accuracy of high-dimensional causal discovery.Specifically,a causal decomposition method(CDSC)is devised and proved to find optimal subsets in the sense of the cut ratio without breaking the connectivity of the subsets.In contrast to previous recursive methods,this causal decomposition method allows arbitrary partitioning of the original variable set.Extensive experiments demonstrate that the proposed algorithm can discover causality quickly and efficiently.