A structural equation model (SEM) is an effective framework to reason over causal relationships represented via a directed acyclic graph (DAG). Recent advances have enabled effective maximum-likelihood point estimation of DAGs from observational data. However, a point estimate may not accurately capture the uncertainty in inferring the underlying graph in practical scenarios, wherein the true DAG is non-identifiable and/or the observed dataset is limited. We propose Bayesian Causal Discovery Nets (BCD Nets), a variational inference framework for estimating a distribution over DAGs characterizing a linear-Gaussian SEM. Developing a full Bayesian posterior over DAGs is challenging due to the the discrete and combinatorial nature of graphs. We analyse key design choices for scalable VI over DAGs, such as 1) the parametrization of DAGs via an expressive variational family, 2) a continuous relaxation that enables low-variance stochastic optimization, and 3) suitable priors over the latent variables. We provide a series of experiments on real and synthetic data showing that BCD Nets outperform maximum-likelihood methods on standard causal discovery metrics such as structural Hamming distance in low data regimes.

本文提出了Bayesian Causal Discovery Nets(BCD Nets)，它是一个用于估计线性-Gaussian SEM中描述一个DAG的概率分布的变分推理框架。本框架采用了连续松弛，适当的先验分布以及表达力强的变分族等重要设计，旨在解决实际情况下对潜在图进行的不确定性估计问题。最终实验表明，与基于最大似然的方法相比，BCD Nets在低数据环境下的结构Hamming距离等标准因果分析评估指标上表现更好。

BCD 网络：用于贝叶斯因果发现的可扩展变分方法