Abstract
LiNGAM has been successfully applied to casual inferences of some real world problems. Nevertheless, basic LiNGAM assumes that there is no latent confounder of the observed variables, which may not hold as the confounding effect is quite common in the real world. Causal discovery for LiNGAM in the presence of latent confounders is a more significant and challenging problem. In this paper, we propose a cumulant-based approach to the pairwise causal discovery for LiNGAM in the presence of latent confounders. The method assumes that the latent confounder is Gaussian distributed and statistically independent of the disturbances. We give a theoretical proof that in the presence of latent Gaussian confounders, the causal direction of the observed variables is identifiable under the mild condition that the disturbances are both super-gaussian or sub-gaussian. Experiments on synthesis data and real world data have been conducted to show the effectiveness of our proposed method.
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References
Pearl, J.: Causality: models, reasoning, and inference. Cambridge Univ. Pr. (2000)
Spirtes, P., Glymour, C.N., Scheines, R.: Causation, prediction, and search. The MIT Press (2000)
Shimizu, S., Hoyer, P.O., Hyvärinen, A., Kerminen, A.: A linear non-gaussian acyclic model for causal discovery. The Journal of Machine Learning Research 7, 2003–2030 (2006)
Sogawa, Y., Shimizu, S., Hyvärinen, A., Washio, T., Shimamura, T., Imoto, S.: Discovery of Exogenous Variables in Data with More Variables Than Observations. In: Diamantaras, K., Duch, W., Iliadis, L.S. (eds.) ICANN 2010. LNCS, vol. 6352, pp. 67–76. Springer, Heidelberg (2010)
Comon, P.: Independent component analysis, a new concept? Signal Processing 36(3), 287–314 (1994)
Hyvärinen, A., Oja, E.: Independent component analysis: algorithms and applications. Neural Networks 13(4-5), 411–430 (2000)
Shimizu, S., Inazumi, T., Sogawa, Y., Hyvärinen, A., Kawahara, Y., Washio, T., Hoyer, P.O., Bollen, K.: Directlingam: A direct method for learning a linear non-gaussian structural equation model. Journal of Machine Learning Research 12, 1225–1248 (2011)
Hyvärinen, A.: Pairwise measures of causal direction in linear non-gaussian acyclic models. In: JMLR Workshop and Conference Proceedings (Proc. 2nd Asian Conference on Machine Learning, ACML 2010), vol. 13, pp. 1–16 (2010)
Hoyer, P.O., Shimizu, S., Kerminen, A.J.: Estimation of linear, non-gaussian causal models in the presence of confounding latent variables. Arxiv preprint cs/0603038 (2006)
Janzing, D., Peters, J., Mooij, J., Schölkopf, B.: Identifying confounders using additive noise models. In: Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence, pp. 249–257. AUAI Press (2009)
Kawahara, Y., Bollen, K., Shimizu, S., Washio, T.: Grouplingam: Linear non-gaussian acyclic models for sets of variables. Arxiv preprint arXiv:1006.5041 (2010)
Daniušis, P., Janzing, D., Mooij, J., Zscheischler, J., Steudel, B., Zhang, K., Schölkopf, B.: Inferring deterministic causal relations. In: Proceedings of the Twenty-Sixth Annual Conference on Uncertainty in Artificial Intelligence (UAI 2010), pp. 143–150. AUAI Press, Corvallis (2010)
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Chen, Z., Chan, L. (2012). Causal Discovery for Linear Non-Gaussian Acyclic Models in the Presence of Latent Gaussian Confounders. In: Theis, F., Cichocki, A., Yeredor, A., Zibulevsky, M. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2012. Lecture Notes in Computer Science, vol 7191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28551-6_3
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DOI: https://doi.org/10.1007/978-3-642-28551-6_3
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