# Generative Learner for Distributional Causal Effects

arXiv: https://arxiv.org/abs/2503.17894 · HTML: https://mlsanity.com/paper/2503.17894/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 48 references that are in the map.
- First posted on arXiv 23 Mar 2025.

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

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Implicit Quantile Networks for Distributional Reinforcement Learning](https://mlsanity.com/paper/1806.06923/) (2018)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [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)
- [Deep Neural Networks for Estimation and Inference](https://mlsanity.com/paper/1809.09953/) (2018)
- [Estimating Treatment Effects with Causal Forests: An Application](https://mlsanity.com/paper/1902.07409/) (2019)
- [Posterior Concentration for Sparse Deep Learning](https://mlsanity.com/paper/1803.09138/) (2018)
- [Double/Debiased Machine Learning for Treatment and Causal Parameters](https://mlsanity.com/paper/1608.00060/) (2016)
- [Learning Summary Statistic for Approximate Bayesian Computation via Deep Neural Network](https://mlsanity.com/paper/1510.02175/) (2015)
- [Quantile regression with deep ReLU Networks: Estimators and minimax rates](https://mlsanity.com/paper/2010.08236/) (2020)
- [Causal Deep Learning](https://mlsanity.com/paper/2303.02186/) (2023)
- [Regularization and confounding in linear regression for treatment effect estimation](https://mlsanity.com/paper/1602.02176/) (2016)
- [Modified Causal Forests for Estimating Heterogeneous Causal Effects](https://mlsanity.com/paper/1812.09487/) (2018)
- [Generative Bayesian Computation for Maximum Expected Utility](https://mlsanity.com/paper/2408.16101/) (2024)
- [Causal Inference with the Instrumental Variable Approach and Bayesian Nonparametric Machine Learning](https://mlsanity.com/paper/2102.01199/) (2021)
- [Deep Partial Least Squares for Instrumental Variable Regression](https://mlsanity.com/paper/2207.02612/) (2022)
- [Joint structure learning and causal effect estimation for categorical graphical models](https://mlsanity.com/paper/2306.16068/) (2023)
- [Generative Modeling: A Review](https://mlsanity.com/paper/2501.05458/) (2024)
- [Deep Learning for Causal Inference: A Comparison of Architectures for Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2405.03130/) (2024)

## Abstract (arXiv)

We propose a generative learner for estimating conditional average treatment effects and characterizing the full distribution of these effects. The learner takes the form of a multi-head feed-forward neural network with three jointly estimated subnetworks: propensity score, baseline outcome, and the conditional average treatment effect. Here, the treatment effect subnetwork parameterizes the conditional quantile function via a compositional architecture in which covariate representation and cosine quantile embeddings are combined through element-wise multiplication. We then recover the conditional average treatment effect as an integral over conditional quantile treatment effects. Under the classical causal assumptions within the Neyman--Rubin potential outcomes framework, we find that the proposed generative learner reduces out-of-sample mean squared error relative to the generalized random forest, double machine learning, and generative adversarial networks, with gains ranging from 5.4% to 93.5% on average across experimental designs. In an empirical application, we formalize the Stefan--Boltzmann law within a unidirectional causal model and apply the method to publicly available stellar data. The estimated effects satisfy the restrictions the law implies.