SVI-DAG：一种用于贝叶斯因果发现的结构化变分推断方法
SVI-DAG: A Structured Variational Inference Approach to Bayesian Causal Discovery
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中文总结 AI 辅助
SVI-DAG是一种贝叶斯因果发现的结构化变分推断方法，用归一化流建模边依赖、斯坦变分梯度下降优化，在不确定性量化上优于5种现有方法，结构准确性具竞争力。
中文摘要 AI 辅助
贝叶斯因果发现旨在确定因果理论的后验分布，因果理论被解释为可解释观测数据的有向无环图（DAG）。所得后验允许对这些理论内的认知不确定性进行系统性推理。然而，由于可识别性问题和观测数据有限，寻找此类图十分困难。此外，鉴于潜在DAG的范围极广，精确近似图的后验颇具挑战性。近期的贝叶斯方法已应对了部分此类挑战，但仍存在局限：它们无法编码边之间的依赖关系，且在搜索过程中缺乏将领域知识作为归纳偏置纳入的原则性方法。为克服这些局限，我们提出SVI-DAG，一种利用观测数据和先验信念的贝叶斯因果发现结构化变分推断方法，该方法使用归一化流来建模边之间的依赖关系，支持对DAG进行表达性的多模态后验学习。为缓解证据下界优化中的模式寻求行为并促进模式覆盖，我们使用斯坦变分梯度下降，利用无环性空间中的核函数更新节点势。我们将SVI-DAG与5种最先进的贝叶斯DAG学习方法进行了对比评估，结果显示其在不确定性量化方面表现更优，同时在结构准确性方面仍具有竞争力。
英文摘要
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 competitive performance in terms of both accuracy and uncertainty quantification.
