# Estimating Potential Outcome Distributions with Collaborating Causal Networks

arXiv: https://arxiv.org/abs/2110.01664 · HTML: https://mlsanity.com/paper/2110.01664/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 83 references that are in the map.
- First posted on arXiv 4 Oct 2021.

## 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)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Data-Efficient Off-Policy Policy Evaluation for Reinforcement Learning](https://mlsanity.com/paper/1604.00923/) (2016)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [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)
- [Confounding-Robust Policy Improvement](https://mlsanity.com/paper/1805.08593/) (2018)
- [Generalization Bounds and Representation Learning for Estimation of Potential Outcomes and Causal Effects](https://mlsanity.com/paper/2001.07426/) (2020)
- [Identifying Causal-Effect Inference Failure with Uncertainty-Aware Models](https://mlsanity.com/paper/2007.00163/) (2020)
- [Perfect Match: A Simple Method for Learning Representations For Counterfactual Inference With Neural Networks](https://mlsanity.com/paper/1810.00656/) (2018)
- [Counterfactual Representation Learning with Balancing Weights](https://mlsanity.com/paper/2010.12618/) (2020)
- [Universal Off-Policy Evaluation](https://mlsanity.com/paper/2104.12820/) (2021)
- [Conditional Distributional Treatment Effect with Kernel Conditional Mean Embeddings and U-Statistic Regression](https://mlsanity.com/paper/2102.08208/) (2021)
- [An Exact and Robust Conformal Inference Method for Counterfactual and Synthetic Controls](https://mlsanity.com/paper/1712.09089/) (2017)
- [Deep Counterfactual Networks with Propensity-Dropout](https://mlsanity.com/paper/1706.05966/) (2017)
- [Adversarial Balancing-based Representation Learning for Causal Effect Inference with Observational Data](https://mlsanity.com/paper/1904.13335/) (2019)
- [Causal Inference: A Missing Data Perspective](https://mlsanity.com/paper/1712.06170/) (2017)
- [Estimating Uncertainty Intervals from Collaborating Networks](https://mlsanity.com/paper/2002.05212/) (2020)
- [On the Distinction Between "Conditional Average Treatment Effects" (CATE) and "Individual Treatment Effects" (ITE) Under Ignorability Assumptions](https://mlsanity.com/paper/2108.04939/) (2021)
- [Causal Inference for Quantile Treatment Effects](https://mlsanity.com/paper/2109.03757/) (2021)

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

- [Robust and Agnostic Learning of Conditional Distributional Treatment Effects](https://mlsanity.com/paper/2205.11486/) (2022)
- [Conformal Convolution and Monte Carlo Meta-learners for Predictive Inference of Individual Treatment Effects](https://mlsanity.com/paper/2402.04906/) (2024)
- [On Efficient Estimation of Distributional Treatment Effects under Covariate-Adaptive Randomization](https://mlsanity.com/paper/2506.05945/) (2025)
- [Estimating Distributional Treatment Effects in Randomized Experiments: Machine Learning for Variance Reduction](https://mlsanity.com/paper/2407.16037/) (2024)
- [Conditional Outcome Equivalence: A Quantile Alternative to CATE](https://mlsanity.com/paper/2410.12454/) (2024)
- [Beyond the Average: Distributional Causal Inference under Imperfect Compliance](https://mlsanity.com/paper/2509.15594/) (2025)
- [Advancing Counterfactual Inference through Nonlinear Quantile Regression](https://mlsanity.com/paper/2306.05751/) (2023)
- [GDR-learners: Orthogonal Learning of Generative Models for Potential Outcomes](https://mlsanity.com/paper/2509.22953/) (2025)

## Abstract (arXiv)

Traditional causal inference approaches leverage observational study data to estimate the difference in observed and unobserved outcomes for a potential treatment, known as the Conditional Average Treatment Effect (CATE). However, CATE corresponds to the comparison on the first moment alone, and as such may be insufficient in reflecting the full picture of treatment effects. As an alternative, estimating the full potential outcome distributions could provide greater insights. However, existing methods for estimating treatment effect potential outcome distributions often impose restrictive or simplistic assumptions about these distributions. Here, we propose Collaborating Causal Networks (CCN), a novel methodology which goes beyond the estimation of CATE alone by learning the full potential outcome distributions. Estimation of outcome distributions via the CCN framework does not require restrictive assumptions of the underlying data generating process. Additionally, CCN facilitates estimation of the utility of each possible treatment and permits individual-specific variation through utility functions. CCN not only extends outcome estimation beyond traditional risk difference, but also enables a more comprehensive decision-making process through definition of flexible comparisons. Under assumptions commonly made in the causal literature, we show that CCN learns distributions that asymptotically capture the true potential outcome distributions. Furthermore, we propose an adjustment approach that is empirically effective in alleviating sample imbalance between treatment groups in observational data. Finally, we evaluate the performance of CCN in multiple synthetic and semi-synthetic experiments. We demonstrate that CCN learns improved distribution estimates compared to existing Bayesian and deep generative methods as well as improved decisions with respects to a variety of utility functions.