# Comparison of meta-learners for estimating multi-valued treatment heterogeneous effects

arXiv: https://arxiv.org/abs/2205.14714 · HTML: https://mlsanity.com/paper/2205.14714/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 66 references that are in the map.
- First posted on arXiv 29 May 2022.

## Builds on (most cited first, 25 of 25)

- [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)
- [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)
- [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)
- [Bias and Debias in Recommender System: A Survey and Future Directions](https://mlsanity.com/paper/2010.03240/) (2020)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms](https://mlsanity.com/paper/2101.10943/) (2021)
- [Automated versus do-it-yourself methods for causal inference: Lessons learned from a data analysis competition](https://mlsanity.com/paper/1707.02641/) (2017)
- [Learning Counterfactual Representations for Estimating Individual Dose-Response Curves](https://mlsanity.com/paper/1902.00981/) (2019)
- [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)
- [On Inductive Biases for Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2106.03765/) (2021)
- [Nonparametric methods for doubly robust estimation of continuous treatment effects](https://mlsanity.com/paper/1507.00747/) (2015)
- [VCNet and Functional Targeted Regularization For Learning Causal Effects of Continuous Treatments](https://mlsanity.com/paper/2103.07861/) (2021)
- [Some methods for heterogeneous treatment effect estimation in high-dimensions](https://mlsanity.com/paper/1707.00102/) (2017)
- [Causal Effect Inference for Structured Treatments](https://mlsanity.com/paper/2106.01939/) (2021)
- [Recursive Partitioning for Personalization using Observational Data](https://mlsanity.com/paper/1608.08925/) (2016)
- [On the Opportunity of Causal Learning in Recommendation Systems: Foundation, Estimation, Prediction and Challenges](https://mlsanity.com/paper/2201.06716/) (2022)
- [Uplift Modeling for Multiple Treatments with Cost Optimization](https://mlsanity.com/paper/1908.05372/) (2019)
- [Estimating Individual Treatment Effects using Non-Parametric Regression Models: a Review](https://mlsanity.com/paper/2009.06472/) (2020)
- [GraphITE: Estimating Individual Effects of Graph-structured Treatments](https://mlsanity.com/paper/2009.14061/) (2020)
- [Estimation of Causal Effects of Multiple Treatments in Observational Studies with a Binary Outcome](https://mlsanity.com/paper/2001.06483/) (2020)
- [Shrinkage Bayesian Causal Forests for Heterogeneous Treatment Effects Estimation](https://mlsanity.com/paper/2102.06573/) (2021)
- [Meta-Learners for Estimation of Causal Effects: Finite Sample Cross-Fit Performance](https://mlsanity.com/paper/2201.12692/) (2022)

## Built on by (most cited first, 10 of 10)

- [Model-agnostic meta-learners for estimating heterogeneous treatment effects over time](https://mlsanity.com/paper/2407.05287/) (2024)
- [Meta-Learners for Partially-Identified Treatment Effects Across Multiple Environments](https://mlsanity.com/paper/2406.02464/) (2024)
- [Position: Causal Machine Learning Requires Rigorous Synthetic Experiments for Broader Adoption](https://mlsanity.com/paper/2508.08883/) (2025)
- [Multi-Study R-Learner for Estimating Heterogeneous Treatment Effects Across Studies Using Statistical Machine Learning](https://mlsanity.com/paper/2306.01086/) (2023)
- [Hybrid Meta-learners for Estimating Heterogeneous Treatment Effects](https://mlsanity.com/paper/2506.13680/) (2025)
- [Flow-based Generative Modeling of Potential Outcomes and Counterfactuals](https://mlsanity.com/paper/2505.16051/) (2025)
- [GUSH3R: Everyone Everywhere All at Once as Gaussians](https://mlsanity.com/paper/2607.05243/) (2026)
- [Robust CATE Estimation Using Novel Ensemble Methods](https://mlsanity.com/paper/2407.03690/) (2024)
- [Educational Effects in Mathematics: Conditional Average Treatment Effect depending on the Number of Treatments](https://mlsanity.com/paper/2411.01498/) (2024)
- [SCOPE: Sequential Causal Optimization of Process Interventions](https://mlsanity.com/paper/2512.17629/) (2025)

## Abstract (arXiv)

Conditional Average Treatment Effects (CATE) estimation is one of the main challenges in causal inference with observational data. In addition to Machine Learning based-models, nonparametric estimators called meta-learners have been developed to estimate the CATE with the main advantage of not restraining the estimation to a specific supervised learning method. This task becomes, however, more complicated when the treatment is not binary as some limitations of the naive extensions emerge. This paper looks into meta-learners for estimating the heterogeneous effects of multi-valued treatments. We consider different meta-learners, and we carry out a theoretical analysis of their error upper bounds as functions of important parameters such as the number of treatment levels, showing that the naive extensions do not always provide satisfactory results. We introduce and discuss meta-learners that perform well as the number of treatments increases. We empirically confirm the strengths and weaknesses of those methods with synthetic and semi-synthetic datasets.