因果发现领域长期依赖单一最优DAG，但真实数据往往支持多种解释——这篇论文用熵推断解决了这个痛点，做因果推断或复杂系统建模的研究者值得关注，方法可直接用于评估因果结构的稳健性。
传统贝叶斯网络通过优化生成有向无环图（DAG）来建模因果关系，但真实数据常允许多种因果链，导致优化结果可能包含伪影。本文提出基于熵推断的方法，生成与数据一致的因果图谱集（causal atlases），量化因果关系的结构模糊性。在2节点和20节点的线性结构方程模型模拟噪声数据上，该方法采样最大熵图集，发现“最优”DAG中存在不一致的因果伪影。这为数据驱动的因果发现提供了更忠实于数据变异的框架。
Causal Atlases from Entropic Inference: Bayesian Networks beyond Optimal DAGs
Data-driven causal relationship identification is pertinent to advancing understanding of complex systems both within and beyond science. Bayesian networks offer a probabilistic method for modelling generic causal relationships via directed acyclic graphs (DAGs). However, typical techniques for constructing Bayesian networks rely on optimization, which can be ill-suited for learning causal relationships because the underlying data may admit multiple chains of causation. More data-faithful representations of causal relationships would provide frameworks for constructing multiple causal maps that are consistent with the variability that is inherent in underlying data. Here, we show that entropy-based inference generates atlases of plausible causal relationships that are consistent with underlying data. On simulated noisy data of 2- and 20-node linear structural equation models, we sample a maximum-entropy ensemble of graphs that allow us to quantify the inherent structural ambiguity in underlying causal relationships. Our method shows that "optimized" DAGs can contain causal artifacts are not consistent across equivalently accurate topologies.