Estimating the structure of a Bayesian network, in the form of a directed acyclic graph (DAG), from observational data is a statistically and computationally hard problem with essential applications in areas such as causal discovery. Bayesian approaches are a promising direction for solving this task, as they allow for uncertainty quantification and deal with well-known identifiability issues. From a probabilistic inference perspective, the main challenges are (i) representing distributions over graphs that satisfy the DAG constraint and (ii) estimating a posterior over the underlying combinatorial space. We propose an approach that addresses these challenges by formulating a joint distribution on an augmented space of DAGs and permutations. We carry out posterior estimation via variational inference, where we exploit continuous relaxations of discrete distributions. We show that our approach can outperform competitive Bayesian and non-Bayesian benchmarks on a range of synthetic and real datasets.

从概率推断的角度来看，文章提出了一个解决贝叶斯网络的结构估计问题的方法，通过在一个扩展的有向无环图和排列空间上的联合分布进行后验估计，利用离散分布的连续松弛来利用变分推断，从而在一系列合成和实际数据集上胜过竞争性的贝叶斯和非贝叶斯基准模型。

通过状态增强与随机排列进行变分DAG估计