# Marginal Causal Flows for Validation and Inference

arXiv: https://arxiv.org/abs/2411.01295 · HTML: https://mlsanity.com/paper/2411.01295/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 62 references that are in the map.
- First posted on arXiv 2 Nov 2024.

## Builds on (most cited first, 19 of 19)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [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)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Causal normalizing flows: from theory to practice](https://mlsanity.com/paper/2306.05415/) (2023)
- [RealCause: Realistic Causal Inference Benchmarking](https://mlsanity.com/paper/2011.15007/) (2020)
- [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)
- [Neural Likelihoods via Cumulative Distribution Functions](https://mlsanity.com/paper/1811.00974/) (2018)
- [Deep Archimedean Copulas](https://mlsanity.com/paper/2012.03137/) (2020)
- [Validating Causal Inference Methods](https://mlsanity.com/paper/2202.04208/) (2022)
- [A Selective Review of Negative Control Methods in Epidemiology](https://mlsanity.com/paper/2009.05641/) (2020)
- [Copula Density Neural Estimation](https://mlsanity.com/paper/2211.15353/) (2022)
- [Parameterizing and Simulating from Causal Models](https://mlsanity.com/paper/2109.03694/) (2021)
- [Neural Copula: A unified framework for estimating generic high-dimensional Copula functions](https://mlsanity.com/paper/2205.15031/) (2022)
- [Simulating longitudinal data from marginal structural models using the additive hazard model](https://mlsanity.com/paper/2002.03678/) (2020)

## Built on by (most cited first, 8 of 8)

- [DeCaFlow: A deconfounding causal generative model](https://mlsanity.com/paper/2503.15114/) (2025)
- [Position: Causal Machine Learning Requires Rigorous Synthetic Experiments for Broader Adoption](https://mlsanity.com/paper/2508.08883/) (2025)
- [Frugal, Flexible, Faithful: Causal Data Simulation via Frengression](https://mlsanity.com/paper/2508.01018/) (2025)
- [ProCause: Generating Counterfactual Outcomes to Evaluate Prescriptive Process Monitoring Methods](https://mlsanity.com/paper/2509.00797/) (2025)
- [Causal Foundation Models](https://mlsanity.com/paper/2609.03003/) (2026)
- [Testing Generalizability in Causal Inference](https://mlsanity.com/paper/2411.03021/) (2024)
- [Improving Generative Methods for Causal Evaluation via Simulation-Based Inference](https://mlsanity.com/paper/2509.02892/) (2025)
- [Counterfactual identifiability beyond global monotonicity: non-monotone triangular structural causal models](https://mlsanity.com/paper/2605.04413/) (2026)

## Abstract (arXiv)

Investigating the marginal causal effect of an intervention on an outcome from complex data remains challenging due to the inflexibility of employed models and the lack of complexity in causal benchmark datasets, which often fail to reproduce intricate real-world data patterns. In this paper we introduce Frugal Flows, a novel likelihood-based machine learning model that uses normalising flows to flexibly learn the data-generating process, while also directly inferring the marginal causal quantities from observational data. We propose that these models are exceptionally well suited for generating synthetic data to validate causal methods. They can create synthetic datasets that closely resemble the empirical dataset, while automatically and exactly satisfying a user-defined average treatment effect. To our knowledge, Frugal Flows are the first generative model to both learn flexible data representations and also exactly parameterise quantities such as the average treatment effect and the degree of unobserved confounding. We demonstrate the above with experiments on both simulated and real-world datasets.