Bayesian Active Learning for Bivariate Causal Discovery

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 hypothesistesting 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, treestructured 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.