Deep Learning With DAGs (2401.06864v1)

Abstract: 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.

• The paper introduces cGNFs, a novel approach that fuses deep learning with DAGs to estimate a wide range of causal effects without strict parametric assumptions.
• It leverages unconstrained monotonic neural networks to estimate complete joint distributions, enabling efficient Monte Carlo sampling for various causal estimands.
• Empirical examples in social mobility studies highlight how cGNFs uncover non-linear, nuanced relationships that traditional parametric models may oversimplify.

A Novel Approach to Causal Inference: Causal-Graphical Normalizing Flows

This paper introduces causal-graphical normalizing flows (cGNFs), an innovative methodology that merges deep learning with directed acyclic graphs (DAGs) for causal inference. The aim is to facilitate the estimation of a wide spectrum of causal effects within complex systems, without reliance on conventional parametric assumptions. The approach leverages the flexibility of deep neural networks, specifically unconstrained monotonic neural networks (UMNNs), to estimate joint probability distributions from observed data, thus advancing the capabilities of DAGs in empirical applications.

Key Contributions and Methodology

The core contribution of cGNFs lies in their ability to model entire causal systems while relaxing the functional form constraints that commonly restrict traditional methods like linear path analysis or standard structural equation modeling (SEM). Unlike other semi-parametric approaches, cGNFs account for the entire joint distribution of the data, leveraging the Markov factorization provided by a DAG specified by the analyst.

A cGNF models the relationships between variables as a series of transformations using UMNNs, which are adept at approximating monotonic functions. These transformations map variables onto a standard normal distribution, thus accommodating both continuous and discrete data through dequantization techniques. The invertibility of UMNNs permits straightforward Monte Carlo sampling from both observational and interventional distributions, making it feasible to estimate a wide range of causal estimands, including total, conditional, direct, indirect, and path-specific effects.

The paper describes a detailed workflow for implementing cGNFs, from the specification of a DAG, through training the model on data via stochastic gradient descent, to Monte Carlo estimation of causal effects. Notably, it provides a method to conduct sensitivity analyses that address unobserved confounding, by recalibrating the relationship between disturbances in the model to account for potential biases due to unmeasured variables.

Empirical Illustrations

To demonstrate the efficacy of cGNFs, the authors revisit two seminal studies of social mobility using this methodology:

1. Blau and Duncan's Status Attainment Model (1967): The reanalysis using cGNFs reveals non-linear relationships between variables, such as the impact of father's occupational status and son's education on son's occupational status. This finding suggests that traditional parametric models may oversimplify the complexities inherent in social stratification processes.
2. Zhou's Conditional vs Controlled Mobility (2019): In this replication, cGNFs reveal nuanced insights into parental income's influence on respondent income, mediated by educational expectations and test scores, which are critical factors confounding the evaluation of education's role in mobility.

The empirical examples underscore the potential of cGNFs to capture the intricacies in data that traditional models might fail to detect.

Implications and Future Directions

The development of cGNFs signifies a significant leap in the methodological toolkit available for causal analysis, particularly in the social sciences where complex causal systems abound. By dispensing with rigid assumptions of linearity and additivity, they allow for a more authentic and comprehensive evaluation of theoretical models.

However, the implementation of cGNFs depends heavily on the accurate specification of the DAG, and their efficacy is contingent on the richness of available data. The paper identifies current limitations, such as the need for large sample sizes and computational resources, and highlights areas for further research, including ensuring valid inference and improving computational efficiency.

In conclusion, cGNFs offer a versatile and powerful approach to causal inference, paving the way for future advancements that will further reconcile the fields of deep learning and traditional causal analysis. Their application promises to yield deeper insights across various domains by unveiling complexities obscured by standard methods.