论文提出SVI-DAG，用归一化流建模边依赖，在贝叶斯DAG学习里不确定性量化赢过5个基线，结构精度也没落下。
SVI-DAG是一种基于结构化变分推断的贝叶斯因果发现方法，利用归一化流建模边之间的依赖关系。该方法通过斯坦变分梯度下降更新节点势，并使用无环性空间中的核函数缓解ELBO优化中的模式寻求行为。在5种先进的贝叶斯DAG学习方法对比中，SVI-DAG在不确定性量化上表现更优，同时结构精度保持竞争力。该方法还支持将领域知识作为归纳偏置纳入搜索过程。
SVI-DAG: A Structured Variational Inference Approach to Bayesian Causal Discovery
Bayesian causal discovery seeks to determine the posterior distribution of causal theories, which are interpreted as directed acyclic graphs (DAGs) that explain the observed data. The resulting posterior allows systematic reasoning regarding epistemic uncertainty within these theories. Nonetheless, finding such graphs is difficult due to identifiability problems and limited observational data. Furthermore, precisely approximating posterior over graphs is challenging given vast range of potential DAGs. Recent Bayesian approaches have addressed some of these challenges, yet they remain limited as they fail to encode dependencies between edges, and lack principled ways to incorporate domain knowledge as inductive biases during the search process. To overcome these limitations, we propose SVI-DAG, a structured variational inference approach to Bayesian causal discovery using observational data and prior beliefs that uses normalizing flows to model dependencies between edges, supporting expressive and multimodal posterior learning over DAGs. To mitigate mode seeking behaviour in evidence lower bound optimization and promote mode coverage, we use stein variational gradient descent to update the node potentials using a kernel in acyclicity space. We evaluate SVI-DAG against 5 state-of-the-art Bayesian DAG learning methods and demonstrate superior performance in uncertainty quantification while remaining competitive in terms of structural accuracy.