An Efficient Maximal Ancestral Graph Listing Algorithm

Tian-Zuo Wang, Wen-Bo Du, Zhi-Hua Zhou
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:50353-50378, 2024.

Abstract

Maximal ancestral graph (MAG) is a prevalent graphical model to characterize causal relations in the presence of latent variables including latent confounders and selection variables. Given observational data, only a Markov equivalence class (MEC) of MAGs is identifiable if without some additional assumptions. Due to this fact, MAG listing, listing all the MAGs in the MEC, is usually demanded in many downstream tasks. To the best of our knowledge, there are no relevant methods for MAG listing other than brute force in the literature. In this paper, we propose the first brute-force-free MAG listing method, by determining the local structures of each vertex recursively. We provide the graphical characterization for each valid local transformation of a vertex, and present sound and complete rules to incorporate the valid local transformation in the presence of latent confounders and selection variables. Based on these components, our method can efficiently output all the MAGs in the MEC with no redundance, that is, every intermediate graph in the recursive process is necessary for the MAG listing task. The empirical analysis demonstrates the superiority of our proposed method on efficiency and effectiveness.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-wang24o, title = {An Efficient Maximal Ancestral Graph Listing Algorithm}, author = {Wang, Tian-Zuo and Du, Wen-Bo and Zhou, Zhi-Hua}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {50353--50378}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/wang24o/wang24o.pdf}, url = {https://proceedings.mlr.press/v235/wang24o.html}, abstract = {Maximal ancestral graph (MAG) is a prevalent graphical model to characterize causal relations in the presence of latent variables including latent confounders and selection variables. Given observational data, only a Markov equivalence class (MEC) of MAGs is identifiable if without some additional assumptions. Due to this fact, MAG listing, listing all the MAGs in the MEC, is usually demanded in many downstream tasks. To the best of our knowledge, there are no relevant methods for MAG listing other than brute force in the literature. In this paper, we propose the first brute-force-free MAG listing method, by determining the local structures of each vertex recursively. We provide the graphical characterization for each valid local transformation of a vertex, and present sound and complete rules to incorporate the valid local transformation in the presence of latent confounders and selection variables. Based on these components, our method can efficiently output all the MAGs in the MEC with no redundance, that is, every intermediate graph in the recursive process is necessary for the MAG listing task. The empirical analysis demonstrates the superiority of our proposed method on efficiency and effectiveness.} }
Endnote
%0 Conference Paper %T An Efficient Maximal Ancestral Graph Listing Algorithm %A Tian-Zuo Wang %A Wen-Bo Du %A Zhi-Hua Zhou %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-wang24o %I PMLR %P 50353--50378 %U https://proceedings.mlr.press/v235/wang24o.html %V 235 %X Maximal ancestral graph (MAG) is a prevalent graphical model to characterize causal relations in the presence of latent variables including latent confounders and selection variables. Given observational data, only a Markov equivalence class (MEC) of MAGs is identifiable if without some additional assumptions. Due to this fact, MAG listing, listing all the MAGs in the MEC, is usually demanded in many downstream tasks. To the best of our knowledge, there are no relevant methods for MAG listing other than brute force in the literature. In this paper, we propose the first brute-force-free MAG listing method, by determining the local structures of each vertex recursively. We provide the graphical characterization for each valid local transformation of a vertex, and present sound and complete rules to incorporate the valid local transformation in the presence of latent confounders and selection variables. Based on these components, our method can efficiently output all the MAGs in the MEC with no redundance, that is, every intermediate graph in the recursive process is necessary for the MAG listing task. The empirical analysis demonstrates the superiority of our proposed method on efficiency and effectiveness.
APA
Wang, T., Du, W. & Zhou, Z.. (2024). An Efficient Maximal Ancestral Graph Listing Algorithm. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:50353-50378 Available from https://proceedings.mlr.press/v235/wang24o.html.

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