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 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.

Figuring out "what causes what" is a big challenge in science, like whether a gene causes a disease. Just looking at data often isn't enough, and doing experiments can be very expensive. Current smart methods for choosing experiments might focus on gathering the most information, rather than directly finding the correct cause-and-effect relationship most reliably.We've developed a smarter way to design these investigative experiments. Our method uses a mathematical tool called "Bayes factors" to weigh the evidence from each small experiment, much like a detective evaluating clues to solve a case. It intelligently plans the sequence of experiments to quickly make good judgments while ensuring we can reach a confident conclusion within a limited budget.This new approach helps scientists uncover causal links in complex systems – from gene networks to how robots understand their surroundings – more efficiently and cost-effectively. Our tests in simulations and robotic tasks show its effectiveness and potential for broad real-world applications.