Directed acyclic graph (DAG) learning is a rapidly expanding field of
research. Though 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. Our article addresses the difficult task of quantifying graph
uncertainty by developing a variational Bayes inference framework based on
novel distributions that have support directly on the space of DAGs. The
distributions, which we use to form our prior and variational posterior, are
induced by a projection operation, whereby an arbitrary continuous distribution
is projected onto the space of sparse weighted acyclic adjacency matrices
(matrix representations of DAGs) with probability mass on exact zeros. Though
the projection constitutes a combinatorial optimization problem, it is solvable
at scale via recently developed techniques that reformulate acyclicity as a
continuous constraint. We empirically demonstrate that our method, ProDAG, can
deliver accurate inference, and often outperforms existing state-of-the-art
alternatives.

基于变分贝叶斯推理框架，我们开发了一种在有向无环图中量化不确定性的方法，通过引入新的分布，该分布直接在 DAG 空间上支持，我们的方法 ProDAG 可以提供准确的推理，通常优于现有的先进方法。