Learning the causal structure of observable variables is a central focus for scientific discovery. Bayesian causal discovery methods tackle this problem by learning a posterior over the set of admissible graphs given our priors and observations. Existing methods primarily consider observations from static systems and assume the underlying causal structure takes the form of a directed acyclic graph (DAG). In settings with dynamic feedback mechanisms that regulate the trajectories of individual variables, this acyclicity assumption fails unless we account for time. We focus on learning Bayesian posteriors over cyclic graphs and treat causal discovery as a problem of sparse identification of a dynamical system. This imposes a natural temporal causal order between variables and captures cyclic feedback loops through time. Under this lens, we propose a new framework for Bayesian causal discovery for dynamical systems and present a novel generative flow network architecture (DynGFN) tailored for this task. Our results indicate that DynGFN learns posteriors that better encapsulate the distributions over admissible cyclic causal structures compared to counterpart state-of-the-art approaches.

翻译：学习可观测变量间的因果结构是科学发现的核心目标。贝叶斯因果发现方法通过基于先验知识与观测数据，学习可行图集合上的后验分布来解决该问题。现有方法主要考虑静态系统的观测数据，并假设潜在因果结构采用有向无环图（DAG）形式。在存在动态反馈机制调节个体变量轨迹的场景中，除非考虑时间因素，否则这种无环性假设将失效。本文重点学习循环图上的贝叶斯后验分布，将因果发现视为动力系统稀疏辨识问题。该方法在变量间施加自然的时间因果顺序，并通过时间维度捕获循环反馈回路。基于这一视角，我们提出了面向动力系统的贝叶斯因果发现新框架，并创新性地设计了专用于该任务的生成流网络架构（DynGFN）。实验结果表明，与现有最优方法相比，DynGFN学习的后验分布能够更准确地反映可行循环因果结构的分布特性。