Causal Discovery with Latent Confounders Based on Higher-Order Cumulants

Ruichu Cai, Zhiyi Huang, Wei Chen, Zhifeng Hao, Kun Zhang
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:3380-3407, 2023.

Abstract

Causal discovery with latent confounders is an important but challenging task in many scientific areas. Despite the success of some overcomplete independent component analysis (OICA) based methods in certain domains, they are computationally expensive and can easily get stuck into local optima. We notice that interestingly, by making use of higher-order cumulants, there exists a closed-form solution to OICA in specific cases, e.g., when the mixing procedure follows the One-Latent-Component structure. In light of the power of the closed-form solution to OICA corresponding to the One-Latent-Component structure, we formulate a way to estimate the mixing matrix using the higher-order cumulants, and further propose the testable One-Latent-Component condition to identify the latent variables and determine causal orders. By iteratively removing the share identified latent components, we successfully extend the results on the One-Latent-Component structure to the Multi-Latent-Component structure and finally provide a practical and asymptotically correct algorithm to learn the causal structure with latent variables. Experimental results illustrate the asymptotic correctness and effectiveness of the proposed method.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-cai23a, title = {Causal Discovery with Latent Confounders Based on Higher-Order Cumulants}, author = {Cai, Ruichu and Huang, Zhiyi and Chen, Wei and Hao, Zhifeng and Zhang, Kun}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {3380--3407}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/cai23a/cai23a.pdf}, url = {https://proceedings.mlr.press/v202/cai23a.html}, abstract = {Causal discovery with latent confounders is an important but challenging task in many scientific areas. Despite the success of some overcomplete independent component analysis (OICA) based methods in certain domains, they are computationally expensive and can easily get stuck into local optima. We notice that interestingly, by making use of higher-order cumulants, there exists a closed-form solution to OICA in specific cases, e.g., when the mixing procedure follows the One-Latent-Component structure. In light of the power of the closed-form solution to OICA corresponding to the One-Latent-Component structure, we formulate a way to estimate the mixing matrix using the higher-order cumulants, and further propose the testable One-Latent-Component condition to identify the latent variables and determine causal orders. By iteratively removing the share identified latent components, we successfully extend the results on the One-Latent-Component structure to the Multi-Latent-Component structure and finally provide a practical and asymptotically correct algorithm to learn the causal structure with latent variables. Experimental results illustrate the asymptotic correctness and effectiveness of the proposed method.} }
Endnote
%0 Conference Paper %T Causal Discovery with Latent Confounders Based on Higher-Order Cumulants %A Ruichu Cai %A Zhiyi Huang %A Wei Chen %A Zhifeng Hao %A Kun Zhang %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-cai23a %I PMLR %P 3380--3407 %U https://proceedings.mlr.press/v202/cai23a.html %V 202 %X Causal discovery with latent confounders is an important but challenging task in many scientific areas. Despite the success of some overcomplete independent component analysis (OICA) based methods in certain domains, they are computationally expensive and can easily get stuck into local optima. We notice that interestingly, by making use of higher-order cumulants, there exists a closed-form solution to OICA in specific cases, e.g., when the mixing procedure follows the One-Latent-Component structure. In light of the power of the closed-form solution to OICA corresponding to the One-Latent-Component structure, we formulate a way to estimate the mixing matrix using the higher-order cumulants, and further propose the testable One-Latent-Component condition to identify the latent variables and determine causal orders. By iteratively removing the share identified latent components, we successfully extend the results on the One-Latent-Component structure to the Multi-Latent-Component structure and finally provide a practical and asymptotically correct algorithm to learn the causal structure with latent variables. Experimental results illustrate the asymptotic correctness and effectiveness of the proposed method.
APA
Cai, R., Huang, Z., Chen, W., Hao, Z. & Zhang, K.. (2023). Causal Discovery with Latent Confounders Based on Higher-Order Cumulants. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:3380-3407 Available from https://proceedings.mlr.press/v202/cai23a.html.

Related Material