Abstract
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.
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Notes
- 1.
Matlab package available at https://www.cs.helsinki.fi/u/ahyvarin/code/pwcausal/, Here, we adopt mxnt (maximum entropy approximations) to estimate the likelihood ratios in the Pairwise-LiNGAM algorithm.
- 2.
Matlab package available at https://sites.google.com/site/sshimizu06/Dlingamcode.
- 3.
Matlab package available at https://sites.google.com/site/sshimizu06/lingam.
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Acknowledgement
This work was supported in part by the NSFC-Guangdong Joint Fund under Grant U1501254, in part by the Natural Science Foundation of China under Grant 61876043 and Grant 61472089, in part by the Natural Science Foundation of Guangdong under Grant 2014A030306004 and Grant 2014A030308008, in part by the Science and Technology Planning Project of Guangdong under Grant 2013B051000076, Grant 2015B010108006, and Grant 2015B010131015, in part by the Guangdong High-Level Personnel of Special Support Pro- gram under Grant 2015TQ01X140, in part by the Pearl River S&T Nova Program of Guangzhou under Grant 201610010101, and in part by the Science and Technology Planning Project of Guangzhou under Grant 201902010058.
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Xie, F., Cai, R., Zeng, Y., Hao, Z. (2019). Causal Discovery of Linear Non-Gaussian Acyclic Model with Small Samples. In: Cui, Z., Pan, J., Zhang, S., Xiao, L., Yang, J. (eds) Intelligence Science and Big Data Engineering. Big Data and Machine Learning. IScIDE 2019. Lecture Notes in Computer Science(), vol 11936. Springer, Cham. https://doi.org/10.1007/978-3-030-36204-1_32
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