# Frugal, Flexible, Faithful: Causal Data Simulation via Frengression

arXiv: https://arxiv.org/abs/2508.01018 · HTML: https://mlsanity.com/paper/2508.01018/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 54 references that are in the map.
- First posted on arXiv 1 Aug 2025.

## Builds on (most cited first, 24 of 24)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Discussion on "Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects" by Hahn, Murray and Carvalho](https://mlsanity.com/paper/2108.02836/) (2021)
- [Engression: Extrapolation through the Lens of Distributional Regression](https://mlsanity.com/paper/2307.00835/) (2023)
- [RealCause: Realistic Causal Inference Benchmarking](https://mlsanity.com/paper/2011.15007/) (2020)
- [Statistical Inference for Generative Models with Maximum Mean Discrepancy](https://mlsanity.com/paper/1906.05944/) (2019)
- [Semiparametric counterfactual density estimation](https://mlsanity.com/paper/2102.12034/) (2021)
- [Conditional Distributional Treatment Effect with Kernel Conditional Mean Embeddings and U-Statistic Regression](https://mlsanity.com/paper/2102.08208/) (2021)
- [Copula Flows for Synthetic Data Generation](https://mlsanity.com/paper/2101.00598/) (2021)
- [Using Wasserstein Generative Adversarial Networks for the Design of Monte Carlo Simulations](https://mlsanity.com/paper/1909.02210/) (2019)
- [Estimating average causal effects from patient trajectories](https://mlsanity.com/paper/2203.01228/) (2022)
- [The Impact of the U.S. Census Disclosure Avoidance System on Redistricting and Voting Rights Analysis](https://mlsanity.com/paper/2105.14197/) (2021)
- [Longitudinal Targeted Minimum Loss-based Estimation with Temporal-Difference Heterogeneous Transformer](https://mlsanity.com/paper/2404.04399/) (2024)
- [Parameterizing and Simulating from Causal Models](https://mlsanity.com/paper/2109.03694/) (2021)
- [Marginal Causal Flows for Validation and Inference](https://mlsanity.com/paper/2411.01295/) (2024)
- [On the role of benchmarking data sets and simulations in method comparison studies](https://mlsanity.com/paper/2208.01457/) (2022)
- [An AI-powered Bayesian generative modeling approach for causal inference in observational studies](https://mlsanity.com/paper/2501.00755/) (2025)
- [Efficient Estimation of Quantiles in Missing Data Models](https://mlsanity.com/paper/1512.08110/) (2015)
- [Simulating longitudinal data from marginal structural models using the additive hazard model](https://mlsanity.com/paper/2002.03678/) (2020)
- [Distributional Instrumental Variable Method](https://mlsanity.com/paper/2502.07641/) (2025)
- [Making Differential Privacy Work for Census Data Users](https://mlsanity.com/paper/2305.07208/) (2023)

## Built on by (most cited first, 2 of 2)

- [Theoretical Analysis of Engression and Reverse Markov Engression](https://mlsanity.com/paper/2606.01002/) (2026)
- [Controllable Generative Sandbox for Causal Inference](https://mlsanity.com/paper/2603.03587/) (2026)

## Abstract (arXiv)

Machine learning has revitalized causal inference by combining flexible models and principled estimators, yet robust benchmarking and evaluation remain challenging with real-world data. In this work, we introduce frengression, a deep generative realization of the frugal parameterization that models the joint distribution of covariates, treatments and outcomes around the causal margin of interest. Frengression provides accurate estimation and flexible, faithful simulation of multivariate, time-varying data; it also enables direct sampling from user-specified interventional distributions. Model consistency and extrapolation guarantees are established, with validation on real-world clinical trial data demonstrating frengression's practical utility. We envision this framework sparking new research into generative approaches for causal margin modelling.