Optimal estimation of linear non-Gaussian structure equation models

Sunmin Oh, Seungsu Han, Gunwoong Park
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:748-756, 2025.

Abstract

Much of science involves discovering and modeling causal relationships in nature. Significant progress has been made in developing statistical methods for representing and identifying causal knowledge from data using Linear Non-Gaussian Acyclic Models (LiNGAMs). Despite successes in learning LiNGAMs across various sample settings, the optimal sample complexity for high-dimensional LiNGAMs remains unexplored. This study establishes the optimal sample complexity for learning the structure of LiNGAMs under a sub-Gaussianity assumption. Specifically, it introduces a structure recovery algorithm using distance covariance that achieves the optimal sample complexity, $n = \Theta(d_{in} \log \frac{p}{d_{in}})$, without assuming faithfulness or a known indegree. The theoretical findings and superiority of the proposed algorithm compared to existing algorithms are validated through numerical experiments and real data analysis.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-oh25a, title = {Optimal estimation of linear non-Gaussian structure equation models}, author = {Oh, Sunmin and Han, Seungsu and Park, Gunwoong}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {748--756}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/oh25a/oh25a.pdf}, url = {https://proceedings.mlr.press/v258/oh25a.html}, abstract = {Much of science involves discovering and modeling causal relationships in nature. Significant progress has been made in developing statistical methods for representing and identifying causal knowledge from data using Linear Non-Gaussian Acyclic Models (LiNGAMs). Despite successes in learning LiNGAMs across various sample settings, the optimal sample complexity for high-dimensional LiNGAMs remains unexplored. This study establishes the optimal sample complexity for learning the structure of LiNGAMs under a sub-Gaussianity assumption. Specifically, it introduces a structure recovery algorithm using distance covariance that achieves the optimal sample complexity, $n = \Theta(d_{in} \log \frac{p}{d_{in}})$, without assuming faithfulness or a known indegree. The theoretical findings and superiority of the proposed algorithm compared to existing algorithms are validated through numerical experiments and real data analysis.} }
Endnote
%0 Conference Paper %T Optimal estimation of linear non-Gaussian structure equation models %A Sunmin Oh %A Seungsu Han %A Gunwoong Park %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-oh25a %I PMLR %P 748--756 %U https://proceedings.mlr.press/v258/oh25a.html %V 258 %X Much of science involves discovering and modeling causal relationships in nature. Significant progress has been made in developing statistical methods for representing and identifying causal knowledge from data using Linear Non-Gaussian Acyclic Models (LiNGAMs). Despite successes in learning LiNGAMs across various sample settings, the optimal sample complexity for high-dimensional LiNGAMs remains unexplored. This study establishes the optimal sample complexity for learning the structure of LiNGAMs under a sub-Gaussianity assumption. Specifically, it introduces a structure recovery algorithm using distance covariance that achieves the optimal sample complexity, $n = \Theta(d_{in} \log \frac{p}{d_{in}})$, without assuming faithfulness or a known indegree. The theoretical findings and superiority of the proposed algorithm compared to existing algorithms are validated through numerical experiments and real data analysis.
APA
Oh, S., Han, S. & Park, G.. (2025). Optimal estimation of linear non-Gaussian structure equation models. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:748-756 Available from https://proceedings.mlr.press/v258/oh25a.html.

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