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 performs competitively when compared with a wide range of Bayesian and non-Bayesian benchmarks on a range of synthetic and real datasets.

翻译：从观测数据中估计贝叶斯网络的结构（以有向无环图（DAG）形式表示）是一个统计与计算上极具挑战性的问题，在因果发现等领域具有重要应用。贝叶斯方法是解决该任务的一个有前景的方向，因为它允许进行不确定性量化并处理众所周知的识别性问题。从概率推断的角度来看，主要挑战在于：（i）表示满足DAG约束的图分布；（ii）在底层的组合空间上估计后验分布。我们提出了一种方法，通过在DAG与排列的增广空间上构建联合分布来解决这些挑战。我们通过变分推断进行后验估计，并利用了离散分布的连续松弛技术。实验表明，在一系列合成与真实数据集上，与广泛的贝叶斯及非贝叶斯基准方法相比，我们的方法表现具有竞争力。