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.
翻译:结构性等式模型(SEM)是解释通过定向环形图(DAG)代表的因果关系的有效框架。最近的进展使得能够从观测数据中对DAG进行有效的最大似点估计,然而,点估计可能无法准确地捕捉在实际假设中推算基本图的不确定性,即真实的DAG无法识别和(或)观察到的数据集有限。我们提议Bayesian Causal Discovery Nets (BCD Nets), 用于估计线性-Gausian SEM的DAGs分布的变异推论框架。由于图形的离散性和组合性质,开发一个完整的Bayesian 后端点对DAGs的全端点估计是具有挑战性的。我们分析了可缩放六的关键设计选择,例如1) 通过直观的变异式组合使DAGs相匹配,2 持续放松使低差异性优化,3) 与潜在变异性相匹配。我们提供一系列真实和合成数据实验,显示BCD CD 结构模型模型模型模型中低质量 标准 模型 标准 标准 模型 标准 模型 模型 模型 标准 模型 模型 模型 。