# Personalized Public Policy Analysis in Social Sciences using Causal-Graphical Normalizing Flows

arXiv: https://arxiv.org/abs/2202.03281 · HTML: https://mlsanity.com/paper/2202.03281/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 48 references that are in the map.
- First posted on arXiv 7 Feb 2022.

## Builds on (most cited first, 17 of 17)

- [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)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design](https://mlsanity.com/paper/1902.00275/) (2019)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Causal Autoregressive Flows](https://mlsanity.com/paper/2011.02268/) (2020)
- [Unconstrained Monotonic Neural Networks](https://mlsanity.com/paper/1908.05164/) (2019)
- [Integer Discrete Flows and Lossless Compression](https://mlsanity.com/paper/1905.07376/) (2019)
- [Discrete Flows: Invertible Generative Models of Discrete Data](https://mlsanity.com/paper/1905.10347/) (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)
- [Graphical Normalizing Flows](https://mlsanity.com/paper/2006.02548/) (2020)
- [MaCow: Masked Convolutional Generative Flow](https://mlsanity.com/paper/1902.04208/) (2019)
- [Closing the Dequantization Gap: PixelCNN as a Single-Layer Flow](https://mlsanity.com/paper/2002.02547/) (2020)

## Built on by (most cited first, 16 of 16)

- [Causal normalizing flows: from theory to practice](https://mlsanity.com/paper/2306.05415/) (2023)
- [Modeling Causal Mechanisms with Diffusion Models for Interventional and Counterfactual Queries](https://mlsanity.com/paper/2302.00860/) (2023)
- [Normalizing Flows for Interventional Density Estimation](https://mlsanity.com/paper/2209.06203/) (2022)
- [Image-based Treatment Effect Heterogeneity](https://mlsanity.com/paper/2206.06417/) (2022)
- [Conceptualizing Treatment Leakage in Text-based Causal Inference](https://mlsanity.com/paper/2205.00465/) (2022)
- [Structured Neural Networks for Density Estimation and Causal Inference](https://mlsanity.com/paper/2311.02221/) (2023)
- [Deep Learning With DAGs](https://mlsanity.com/paper/2401.06864/) (2024)
- [Counterfactual Analysis of the Impact of the IMF Program on Child Poverty in the Global-South Region using Causal-Graphical Normalizing Flows](https://mlsanity.com/paper/2202.09391/) (2022)
- [In-context Contrastive Learning for Event Causality Identification](https://mlsanity.com/paper/2405.10512/) (2024)
- [ρ-GNF: A Copula-based Sensitivity Analysis to Unobserved Confounding Using Normalizing Flows](https://mlsanity.com/paper/2209.07111/) (2022)
- [CausalImages: An R Package for Causal Inference with Earth Observation, Bio-medical, and Social Science Images](https://mlsanity.com/paper/2310.00233/) (2023)
- [Analyzing Poverty through Intra-Annual Time-Series: A Wavelet Transform Approach](https://mlsanity.com/paper/2411.02855/) (2024)
- [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)
- [Reducing normalizing flow complexity for MCMC preconditioning](https://mlsanity.com/paper/2511.02345/) (2025)
- [Beyond Interaction Effects: Two Logics for Studying Population Inequalities](https://mlsanity.com/paper/2601.04223/) (2025)

## Abstract (arXiv)

Structural Equation/Causal Models (SEMs/SCMs) are widely used in epidemiology and social sciences to identify and analyze the average causal effect (ACE) and conditional ACE (CACE). Traditional causal effect estimation methods such as Inverse Probability Weighting (IPW) and more recently Regression-With-Residuals (RWR) are widely used - as they avoid the challenging task of identifying the SCM parameters - to estimate ACE and CACE. However, much work remains before traditional estimation methods can be used for counterfactual inference, and for the benefit of Personalized Public Policy Analysis (P3A) in the social sciences. While doctors rely on personalized medicine to tailor treatments to patients in laboratory settings (relatively closed systems), P3A draws inspiration from such tailoring but adapts it for open social systems. In this article, we develop a method for counterfactual inference that we name causal-Graphical Normalizing Flow (c-GNF), facilitating P3A. First, we show how c-GNF captures the underlying SCM without making any assumption about functional forms. Second, we propose a novel dequantization trick to deal with discrete variables, which is a limitation of normalizing flows in general. Third, we demonstrate in experiments that c-GNF performs on-par with IPW and RWR in terms of bias and variance for estimating the ATE, when the true functional forms are known, and better when they are unknown. Fourth and most importantly, we conduct counterfactual inference with c-GNFs, demonstrating promising empirical performance. Because IPW and RWR, like other traditional methods, lack the capability of counterfactual inference, c-GNFs will likely play a major role in tailoring personalized treatment, facilitating P3A, optimizing social interventions - in contrast to the current `one-size-fits-all' approach of existing methods.