Social science theories often postulate causal relationships among a set of
variables or events. Although directed acyclic graphs (DAGs) are increasingly
used to represent these theories, their full potential has not yet been
realized in practice. As non-parametric causal models, DAGs require no
assumptions about the functional form of the hypothesized relationships.
Nevertheless, to simplify the task of empirical evaluation, researchers tend to
invoke such assumptions anyway, even though they are typically arbitrary and do
not reflect any theoretical content or prior knowledge. Moreover, functional
form assumptions can engender bias, whenever they fail to accurately capture
the complexity of the causal system under investigation. In this article, we
introduce causal-graphical normalizing flows (cGNFs), a novel approach to
causal inference that leverages deep neural networks to empirically evaluate
theories represented as DAGs. Unlike conventional approaches, cGNFs model the
full joint distribution of the data according to a DAG supplied by the analyst,
without relying on stringent assumptions about functional form. In this way,
the method allows for flexible, semi-parametric estimation of any causal
estimand that can be identified from the DAG, including total effects,
conditional effects, direct and indirect effects, and path-specific effects. We
illustrate the method with a reanalysis of Blau and Duncan's (1967) model of
status attainment and Zhou's (2019) model of conditional versus controlled
mobility. To facilitate adoption, we provide open-source software together with
a series of online tutorials for implementing cGNFs. The article concludes with
a discussion of current limitations and directions for future development.

引入因果图归一化流（causal-graphical normalizing flows, cGNFs）这一新方法，该方法利用深度神经网络对以有向无环图（directed acyclic graphs, DAGs）表示的理论进行经验评估，模型所显示的数据的完整联合分布，而无需对函数形式进行严格的假设，从而可以对由 DAGs 确定的任何因果估计量进行灵活的半参数估计，包括总效应、条件效应、直接和间接效应以及路径特定效应。