Bayesian causal discovery benefits from prior information elicited from domain experts, and in heterogeneous domains any prior knowledge would be badly needed. However, so far prior elicitation approaches have assumed a single causal graph and hence are not suited to heterogeneous domains. We propose a causal elicitation strategy for heterogeneous settings, based on Bayesian experimental design (BED) principles, and a variational mixture structure learning (VaMSL) method -- extending the earlier differentiable Bayesian structure learning (DiBS) method -- to iteratively infer mixtures of causal Bayesian networks (CBNs). We construct an informative graph prior incorporating elicited expert feedback in the inference of mixtures of CBNs. Our proposed method successfully produces a set of alternative causal models (mixture components or clusters), and achieves an improved structure learning performance on heterogeneous synthetic data when informed by a simulated expert. Finally, we demonstrate that our approach is capable of capturing complex distributions in a breast cancer database.

翻译：贝叶斯因果发现受益于从领域专家处获取的先验信息，而在异构领域中，此类先验知识尤为亟需。然而，现有先验启发方法均假设存在单一因果图，因此不适用于异构领域。我们提出一种基于贝叶斯实验设计（BED）原理的异构场景因果启发策略，以及一种变分混合结构学习（VaMSL）方法——该方法扩展了早期的可微贝叶斯结构学习（DiBS）方法——以迭代推断因果贝叶斯网络（CBNs）的混合体。我们构建了一个信息性图先验，将获得的专家反馈纳入CBNs混合体的推断中。所提出的方法成功生成了一组替代性因果模型（混合成分或聚类），并在模拟专家指导下，于异构合成数据上实现了更优的结构学习性能。最后，我们证明了该方法能够捕获乳腺癌数据库中复杂的分布模式。