Bayesian Active Learning for Bivariate Causal Discovery

Yuxuan Wang, Mingzhou Liu, Xinwei Sun, Wei Wang, Yizhou Wang
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:63734-63754, 2025.

Abstract

Determining the direction of relationships between variables is fundamental for understanding complex systems across scientific domains. While observational data can uncover relationships between variables, it cannot distinguish between cause and effect without experimental interventions. To effectively uncover causality, previous works have proposed intervention strategies that sequentially optimize the intervention values. However, most of these approaches primarily maximized information-theoretic gains that may not effectively measure the reliability of direction determination. In this paper, we formulate the causal direction identification as a hypothesis-testing problem, and propose a Bayes factor-based intervention strategy, which can quantify the evidence strength of one hypothesis (e.g., causal) over the other (e.g., non-causal). To balance the immediate and future gains of testing strength, we propose a sequential intervention objective over intervention values in multiple steps. By analyzing the objective function, we develop a dynamic programming algorithm that reduces the complexity from non-polynomial to polynomial. Experimental results on bivariate systems, tree-structured graphs, and an embodied AI environment demonstrate the effectiveness of our framework in direction determination and its extensibility to both multivariate settings and real-world applications.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-wang25bp, title = {{B}ayesian Active Learning for Bivariate Causal Discovery}, author = {Wang, Yuxuan and Liu, Mingzhou and Sun, Xinwei and Wang, Wei and Wang, Yizhou}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {63734--63754}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/wang25bp/wang25bp.pdf}, url = {https://proceedings.mlr.press/v267/wang25bp.html}, abstract = {Determining the direction of relationships between variables is fundamental for understanding complex systems across scientific domains. While observational data can uncover relationships between variables, it cannot distinguish between cause and effect without experimental interventions. To effectively uncover causality, previous works have proposed intervention strategies that sequentially optimize the intervention values. However, most of these approaches primarily maximized information-theoretic gains that may not effectively measure the reliability of direction determination. In this paper, we formulate the causal direction identification as a hypothesis-testing problem, and propose a Bayes factor-based intervention strategy, which can quantify the evidence strength of one hypothesis (e.g., causal) over the other (e.g., non-causal). To balance the immediate and future gains of testing strength, we propose a sequential intervention objective over intervention values in multiple steps. By analyzing the objective function, we develop a dynamic programming algorithm that reduces the complexity from non-polynomial to polynomial. Experimental results on bivariate systems, tree-structured graphs, and an embodied AI environment demonstrate the effectiveness of our framework in direction determination and its extensibility to both multivariate settings and real-world applications.} }
Endnote
%0 Conference Paper %T Bayesian Active Learning for Bivariate Causal Discovery %A Yuxuan Wang %A Mingzhou Liu %A Xinwei Sun %A Wei Wang %A Yizhou Wang %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-wang25bp %I PMLR %P 63734--63754 %U https://proceedings.mlr.press/v267/wang25bp.html %V 267 %X Determining the direction of relationships between variables is fundamental for understanding complex systems across scientific domains. While observational data can uncover relationships between variables, it cannot distinguish between cause and effect without experimental interventions. To effectively uncover causality, previous works have proposed intervention strategies that sequentially optimize the intervention values. However, most of these approaches primarily maximized information-theoretic gains that may not effectively measure the reliability of direction determination. In this paper, we formulate the causal direction identification as a hypothesis-testing problem, and propose a Bayes factor-based intervention strategy, which can quantify the evidence strength of one hypothesis (e.g., causal) over the other (e.g., non-causal). To balance the immediate and future gains of testing strength, we propose a sequential intervention objective over intervention values in multiple steps. By analyzing the objective function, we develop a dynamic programming algorithm that reduces the complexity from non-polynomial to polynomial. Experimental results on bivariate systems, tree-structured graphs, and an embodied AI environment demonstrate the effectiveness of our framework in direction determination and its extensibility to both multivariate settings and real-world applications.
APA
Wang, Y., Liu, M., Sun, X., Wang, W. & Wang, Y.. (2025). Bayesian Active Learning for Bivariate Causal Discovery. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:63734-63754 Available from https://proceedings.mlr.press/v267/wang25bp.html.

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