# Conditional Outcome Equivalence: A Quantile Alternative to CATE

arXiv: https://arxiv.org/abs/2410.12454 · HTML: https://mlsanity.com/paper/2410.12454/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 35 references that are in the map.
- First posted on arXiv 16 Oct 2024.

## Builds on (most cited first, 9 of 9)

- [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)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Kernel Methods for Causal Functions: Dose, Heterogeneous, and Incremental Response Curves](https://mlsanity.com/paper/2010.04855/) (2020)
- [Mondrian Forests: Efficient Online Random Forests](https://mlsanity.com/paper/1406.2673/) (2014)
- [Robust and Agnostic Learning of Conditional Distributional Treatment Effects](https://mlsanity.com/paper/2205.11486/) (2022)
- [Nearest Neighbor and Kernel Survival Analysis: Nonasymptotic Error Bounds and Strong Consistency Rates](https://mlsanity.com/paper/1905.05285/) (2019)
- [Estimating Potential Outcome Distributions with Collaborating Causal Networks](https://mlsanity.com/paper/2110.01664/) (2021)

## Built on by (most cited first, 2 of 2)

- [Doubly-Robust Estimation of Counterfactual Policy Mean Embeddings](https://mlsanity.com/paper/2506.02793/) (2025)
- [Direct Doubly Robust Estimation of Conditional Quantile Contrasts](https://mlsanity.com/paper/2601.19666/) (2026)

## Abstract (arXiv)

Conditional quantile treatment effect (CQTE) can provide insight into the effect of a treatment beyond the conditional average treatment effect (CATE). This ability to provide information over multiple quantiles of the response makes CQTE especially valuable in cases where the effect of a treatment is not well-modelled by a location shift, even conditionally on the covariates. Nevertheless, the estimation of CQTE is challenging and often depends upon the smoothness of the individual quantiles as a function of the covariates rather than smoothness of the CQTE itself. This is in stark contrast to CATE where it is possible to obtain high-quality estimates which have less dependency upon the smoothness of the nuisance parameters when the CATE itself is smooth. Moreover, relative smoothness of the CQTE lacks the interpretability of smoothness of the CATE making it less clear whether it is a reasonable assumption to make. We combine the desirable properties of CATE and CQTE by considering a new estimand, the conditional quantile comparator (CQC). The CQC not only retains information about the whole treatment distribution, similar to CQTE, but also having more natural examples of smoothness and is able to leverage simplicity in an auxiliary estimand. We provide finite sample bounds on the error of our estimator, demonstrating its ability to exploit simplicity. We validate our theory in numerical simulations which show that our method produces more accurate estimates than baselines. Finally, we apply our methodology to a study on the effect of employment incentives on earnings across different age groups. We see that our method is able to reveal heterogeneity of the effect across different quantiles.