Directed acyclic graph (DAG) learning is a central task in structure discovery and causal inference. Although the field has witnessed remarkable advances over the past few years, it remains statistically and computationally challenging to learn a single (point estimate) DAG from data, let alone provide uncertainty quantification. We address the difficult task of quantifying graph uncertainty by developing a Bayesian variational inference framework based on novel, provably valid distributions that have support directly on the space of sparse DAGs. These distributions, which we use to define our prior and variational posterior, are induced by a projection operation that maps an arbitrary continuous distribution onto the space of sparse weighted acyclic adjacency matrices. While this projection is combinatorial, it can be solved efficiently using recent continuous reformulations of acyclicity constraints. We empirically demonstrate that our method, ProDAG, can outperform state-of-the-art alternatives in both accuracy and uncertainty quantification.

翻译：有向无环图学习是结构发现与因果推断的核心任务。尽管该领域在过去几年取得了显著进展，但从数据中学习单一（点估计）有向无环图在统计与计算上仍具挑战性，更遑论提供不确定性量化。我们通过构建基于新型可证明有效分布的贝叶斯变分推断框架，解决了图不确定性量化的难题——该分布直接以稀疏有向无环图空间为支撑集。我们利用该分布定义先验与变分后验，其通过投影操作导出：该操作将任意连续分布映射至稀疏加权无环邻接矩阵空间。虽然该投影具有组合复杂性，但借助近期对无环约束的连续重构方法可高效求解。实验表明，我们的方法ProDAG在准确性与不确定性量化方面均能超越当前最优的替代方法。