Causal Discovery of Linear Non-Gaussian Acyclic Model with Small Samples

Linear non-Gaussian Acyclic Model (LiNGAM) is a well-known model for causal discovery from observational data. Existing estimation methods are usually based on infinite sample theory and often fail to obtain an ideal result in the small samples. However, it is commonplace to encounter non-Gaussian data with small or medium sample sizes in practice. In this paper, we propose a Minimal Set-based LiNGAM algorithm (MiS-LiNGAM) to address the LiNGAM with small samples. MiS-LiNGAM is a two-phase and greedy search algorithm. Specifically, in the first phase, we find the skeleton of the network using the regression-based conditional independence test, which helps us reduce the complexity in finding the minimal LiNGAM set of the second phase. Further, this independence test we applied guarantees the reliability when the number of conditioning variables increases. In the second phase, we give an efficient method to iteratively select the minimal LiNGAM set with the skeleton and learn the causal network. We also present the corresponding theoretical derivation. The experimental results on simulated networks and real networks are presented to demonstrate the efficacy of our method.