# Causal Q-Aggregation for CATE Model Selection

arXiv: https://arxiv.org/abs/2310.16945 · HTML: https://mlsanity.com/paper/2310.16945/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 44 references that are in the map.
- First posted on arXiv 25 Oct 2023.

## Builds on (most cited first, 16 of 16)

- [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)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Automated versus do-it-yourself methods for causal inference: Lessons learned from a data analysis competition](https://mlsanity.com/paper/1707.02641/) (2017)
- [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)
- [Machine Learning Estimation of Heterogeneous Treatment Effects with Instruments](https://mlsanity.com/paper/1905.10176/) (2019)
- [In Search of Insights, Not Magic Bullets: Towards Demystification of the Model Selection Dilemma in Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2302.02923/) (2023)
- [A comparison of methods for model selection when estimating individual treatment effects](https://mlsanity.com/paper/1804.05146/) (2018)
- [Empirical Analysis of Model Selection for Heterogeneous Causal Effect Estimation](https://mlsanity.com/paper/2211.01939/) (2022)
- [Stable discovery of interpretable subgroups via calibration in causal studies](https://mlsanity.com/paper/2008.10109/) (2020)
- [Dynamic Bayesian Predictive Synthesis in Time Series Forecasting](https://mlsanity.com/paper/1601.07463/) (2016)
- [Ensemble Method for Estimating Individualized Treatment Effects](https://mlsanity.com/paper/2202.12445/) (2022)
- [Bayesian Causal Synthesis for Meta-Inference on Heterogeneous Treatment Effects](https://mlsanity.com/paper/2304.07726/) (2023)

## Built on by (most cited first, 4 of 4)

- [Orthogonal Causal Calibration](https://mlsanity.com/paper/2406.01933/) (2024)
- [A Meta-learner for Heterogeneous Effects in Difference-in-Differences](https://mlsanity.com/paper/2502.04699/) (2025)
- [Triple/Debiased Lasso for Statistical Inference of Conditional Average Treatment Effects](https://mlsanity.com/paper/2403.03240/) (2024)
- [Robust CATE Estimation Using Novel Ensemble Methods](https://mlsanity.com/paper/2407.03690/) (2024)

## Abstract (arXiv)

Accurate estimation of conditional average treatment effects (CATE) is at the core of personalized decision making. While there is a plethora of models for CATE estimation, model selection is a nontrivial task, due to the fundamental problem of causal inference. Recent empirical work provides evidence in favor of proxy loss metrics with double robust properties and in favor of model ensembling. However, theoretical understanding is lacking. Direct application of prior theoretical work leads to suboptimal oracle model selection rates due to the non-convexity of the model selection problem. We provide regret rates for the major existing CATE ensembling approaches and propose a new CATE model ensembling approach based on Q-aggregation using the doubly robust loss. Our main result shows that causal Q-aggregation achieves statistically optimal oracle model selection regret rates of fraclog(M)n (with M models and n samples), with the addition of higher-order estimation error terms related to products of errors in the nuisance functions. Crucially, our regret rate does not require that any of the candidate CATE models be close to the truth. We validate our new method on many semi-synthetic datasets and also provide extensions of our work to CATE model selection with instrumental variables and unobserved confounding.