# Deep Learning With DAGs

arXiv: https://arxiv.org/abs/2401.06864 · HTML: https://mlsanity.com/paper/2401.06864/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 87 references that are in the map.
- First posted on arXiv 12 Jan 2024.

## Builds on (most cited first, 22 of 22)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Learning and Generalization in Overparameterized Neural Networks, Going Beyond Two Layers](https://mlsanity.com/paper/1811.04918/) (2018)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Rethinking Bias-Variance Trade-off for Generalization of Neural Networks](https://mlsanity.com/paper/2002.11328/) (2020)
- [Unconstrained Monotonic Neural Networks](https://mlsanity.com/paper/1908.05164/) (2019)
- [Latent Normalizing Flows for Discrete Sequences](https://mlsanity.com/paper/1901.10548/) (2019)
- [RNADE: The real-valued neural autoregressive density-estimator](https://mlsanity.com/paper/1306.0186/) (2013)
- [Theoretical Impediments to Machine Learning With Seven Sparks from the Causal Revolution](https://mlsanity.com/paper/1801.04016/) (2018)
- [Causal normalizing flows: from theory to practice](https://mlsanity.com/paper/2306.05415/) (2023)
- [Counterfactual Identifiability of Bijective Causal Models](https://mlsanity.com/paper/2302.02228/) (2023)
- [Graphical Normalizing Flows](https://mlsanity.com/paper/2006.02548/) (2020)
- [Validating Causal Inference Methods](https://mlsanity.com/paper/2202.04208/) (2022)
- [Statistical modeling: the three cultures](https://mlsanity.com/paper/2012.04570/) (2020)
- [Personalized Public Policy Analysis in Social Sciences using Causal-Graphical Normalizing Flows](https://mlsanity.com/paper/2202.03281/) (2022)
- [Semiparametric Estimation for Causal Mediation Analysis with Multiple Causally Ordered Mediators](https://mlsanity.com/paper/2011.12751/) (2020)
- [Measurement error models: from nonparametric methods to deep neural networks](https://mlsanity.com/paper/2007.07498/) (2020)

## Built on by (most cited first, 7 of 7)

- [Interpretable Neural Causal Models with TRAM-DAGs](https://mlsanity.com/paper/2503.16206/) (2025)
- [Causal Mediation Analysis with Multiple Mediators: A Simulation Approach](https://mlsanity.com/paper/2506.14019/) (2025)
- [Flow IV: Counterfactual Inference In Nonseparable Outcome Models Using Instrumental Variables](https://mlsanity.com/paper/2508.01321/) (2025)
- [Sensitivity Analysis to Unobserved Confounding with Copula-based Normalizing Flows](https://mlsanity.com/paper/2508.08752/) (2025)
- [Detecting and Mitigating Treatment Leakage in Text-Based Causal Inference: Distillation and Sensitivity Analysis](https://mlsanity.com/paper/2601.02400/) (2025)
- [Beyond Interaction Effects: Two Logics for Studying Population Inequalities](https://mlsanity.com/paper/2601.04223/) (2025)
- [Kolmogorov-Arnold causal generative models](https://mlsanity.com/paper/2603.20184/) (2026)

## Abstract (arXiv)

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.