Generative Flow Networks (GFlowNets), a class of generative models over discrete and structured sample spaces, have been previously applied to the problem of inferring the marginal posterior distribution over the directed acyclic graph (DAG) of a Bayesian Network, given a dataset of observations. Based on recent advances extending this framework to non-discrete sample spaces, we propose in this paper to approximate the joint posterior over not only the structure of a Bayesian Network, but also the parameters of its conditional probability distributions. We use a single GFlowNet whose sampling policy follows a two-phase process: the DAG is first generated sequentially one edge at a time, and then the corresponding parameters are picked once the full structure is known. Since the parameters are included in the posterior distribution, this leaves more flexibility for the local probability models of the Bayesian Network, making our approach applicable even to non-linear models parametrized by neural networks. We show that our method, called JSP-GFN, offers an accurate approximation of the joint posterior, while comparing favorably against existing methods on both simulated and real data.

翻译：生成流网络（GFlowNets）作为一类适用于离散结构化样本空间的生成模型，此前已被应用于给定观测数据集时推断贝叶斯网络有向无环图（DAG）的边际后验分布问题。基于将该框架扩展至非离散样本空间的最新进展，本文提出在贝叶斯网络中不仅近似结构后验分布，还对其条件概率分布参数进行联合后验近似。我们采用单一GFlowNet，其采样策略遵循两阶段过程：首先逐边顺序生成DAG，待完整结构确定后再选取相应参数。由于参数被纳入后验分布，这为贝叶斯网络的局部概率模型提供了更大灵活性，使得我们的方法甚至适用于由神经网络参数化的非线性模型。实验表明，我们提出的JSP-GFN方法能精确逼近联合后验分布，且在模拟数据与真实数据上均优于现有方法。