# Robust and Agnostic Learning of Conditional Distributional Treatment Effects

arXiv: https://arxiv.org/abs/2205.11486 · HTML: https://mlsanity.com/paper/2205.11486/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 72 references that are in the map.
- First posted on arXiv 23 May 2022.

## Builds on (most cited first, 29 of 29)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [Deep Generalized Method of Moments for Instrumental Variable Analysis](https://mlsanity.com/paper/1905.12495/) (2019)
- [Problem Formulation and Fairness](https://mlsanity.com/paper/1901.02547/) (2019)
- [Minimax Estimation of Conditional Moment Models](https://mlsanity.com/paper/2006.07201/) (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)
- [Orthogonal Random Forest for Causal Inference](https://mlsanity.com/paper/1806.03467/) (2018)
- [Bayesian regression tree models for causal inference: regularization, confounding, and heterogeneous effects](https://mlsanity.com/paper/1706.09523/) (2017)
- [Conditional Distributional Treatment Effect with Kernel Conditional Mean Embeddings and U-Statistic Regression](https://mlsanity.com/paper/2102.08208/) (2021)
- [The Influence Function of Semiparametric Estimators](https://mlsanity.com/paper/1508.01378/) (2015)
- [Program Evaluation and Causal Inference with High-Dimensional Data](https://mlsanity.com/paper/1311.2645/) (2013)
- [Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding](https://mlsanity.com/paper/2112.11449/) (2021)
- [Localized Debiased Machine Learning: Efficient Inference on Quantile Treatment Effects and Beyond](https://mlsanity.com/paper/1912.12945/) (2019)
- [The Variational Method of Moments](https://mlsanity.com/paper/2012.09422/) (2020)
- [Structural Nested Models and G-estimation: The Partially Realized Promise](https://mlsanity.com/paper/1503.01589/) (2015)
- [Treatment Effect Risk: Bounds and Inference](https://mlsanity.com/paper/2201.05893/) (2022)
- [Estimating Potential Outcome Distributions with Collaborating Causal Networks](https://mlsanity.com/paper/2110.01664/) (2021)
- [Median Optimal Treatment Regimes](https://mlsanity.com/paper/2103.01802/) (2021)
- [Non-Parametric Inference Adaptive to Intrinsic Dimension](https://mlsanity.com/paper/1901.03719/) (2019)
- [Controlling for Unmeasured Confounding in Panel Data Using Minimal Bridge Functions: From Two-Way Fixed Effects to Factor Models](https://mlsanity.com/paper/2108.03849/) (2021)
- [Network and Panel Quantile Effects Via Distribution Regression](https://mlsanity.com/paper/1803.08154/) (2018)

## Built on by (most cited first, 18 of 18)

- [B-Learner: Quasi-Oracle Bounds on Heterogeneous Causal Effects Under Hidden Confounding](https://mlsanity.com/paper/2304.10577/) (2023)
- [Reliable Off-Policy Learning for Dosage Combinations](https://mlsanity.com/paper/2305.19742/) (2023)
- [Quantifying Aleatoric Uncertainty of the Treatment Effect: A Novel Orthogonal Learner](https://mlsanity.com/paper/2411.03387/) (2024)
- [Ensembled Prediction Intervals for Causal Outcomes Under Hidden Confounding](https://mlsanity.com/paper/2306.09520/) (2023)
- [Positivity-free Policy Learning with Observational Data](https://mlsanity.com/paper/2310.06969/) (2023)
- [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 Distributional Treatment Effects: Doubly Robust Estimation and Testing](https://mlsanity.com/paper/2603.16829/) (2026)
- [Asymptotically Unbiased Synthetic Control Methods by Moment Matching](https://mlsanity.com/paper/2307.11127/) (2023)
- [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)
- [Robust Direct Learning for Causal Data Fusion](https://mlsanity.com/paper/2211.00249/) (2022)
- [GDR-learners: Orthogonal Learning of Generative Models for Potential Outcomes](https://mlsanity.com/paper/2509.22953/) (2025)
- [Preference-based Conditional Treatment Effects and Policy Learning](https://mlsanity.com/paper/2602.03823/) (2026)
- [A fine-grained look at causal effects in causal spaces](https://mlsanity.com/paper/2512.11919/) (2025)
- [Direct Doubly Robust Estimation of Conditional Quantile Contrasts](https://mlsanity.com/paper/2601.19666/) (2026)
- [Distributional Causal Mediation via Conditional Generative Modeling](https://mlsanity.com/paper/2605.01765/) (2026)
- [Wasserstein Causal Forests for Distribution-Valued Outcomes](https://mlsanity.com/paper/2609.35898/) (2026)

## Abstract (arXiv)

The conditional average treatment effect (CATE) is the best measure of individual causal effects given baseline covariates. However, the CATE only captures the (conditional) average, and can overlook risks and tail events, which are important to treatment choice. In aggregate analyses, this is usually addressed by measuring the distributional treatment effect (DTE), such as differences in quantiles or tail expectations between treatment groups. Hypothetically, one can similarly fit conditional quantile regressions in each treatment group and take their difference, but this would not be robust to misspecification or provide agnostic best-in-class predictions. We provide a new robust and model-agnostic methodology for learning the conditional DTE (CDTE) for a class of problems that includes conditional quantile treatment effects, conditional super-quantile treatment effects, and conditional treatment effects on coherent risk measures given by f-divergences. Our method is based on constructing a special pseudo-outcome and regressing it on covariates using any regression learner. Our method is model-agnostic in that it can provide the best projection of CDTE onto the regression model class. Our method is robust in that even if we learn these nuisances nonparametrically at very slow rates, we can still learn CDTEs at rates that depend on the class complexity and even conduct inferences on linear projections of CDTEs. We investigate the behavior of our proposal in simulations, as well as in a case study of 401(k) eligibility effects on wealth.