# Orthogonal prediction of counterfactual outcomes

arXiv: https://arxiv.org/abs/2311.09423 · HTML: https://mlsanity.com/paper/2311.09423/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2023.

## Built on by (most cited first, 7 of 7)

- [DiffPO: A causal diffusion model for learning distributions of potential outcomes](https://mlsanity.com/paper/2410.08924/) (2024)
- [Quantifying Aleatoric Uncertainty of the Treatment Effect: A Novel Orthogonal Learner](https://mlsanity.com/paper/2411.03387/) (2024)
- [Orthogonal Representation Learning for Estimating Causal Quantities](https://mlsanity.com/paper/2502.04274/) (2025)
- [Causal machine learning for heterogeneous treatment effects in the presence of missing outcome data](https://mlsanity.com/paper/2412.19711/) (2024)
- [GDR-learners: Orthogonal Learning of Generative Models for Potential Outcomes](https://mlsanity.com/paper/2509.22953/) (2025)
- [Targeted Regularization for Causal Effect Estimation with Exponential Dispersion Family Outcomes](https://mlsanity.com/paper/2502.07295/) (2025)
- [Targeted Highly Adaptive Lasso Minimum Loss Estimation of Target Functions](https://mlsanity.com/paper/2607.03824/) (2026)

## Abstract (arXiv)

Orthogonal meta-learners, such as DR-learner, R-learner and IF-learner, are increasingly used to estimate conditional average treatment effects. They improve convergence rates relative to na"ive meta-learners (e.g., T-, S- and X-learner) through de-biasing procedures that involve applying standard learners to specifically transformed outcome data. This leads them to disregard the possibly constrained outcome space, which can be particularly problematic for dichotomous outcomes: these typically get transformed to values that are no longer constrained to the unit interval, making it difficult for standard learners to guarantee predictions within the unit interval. To address this, we construct orthogonal meta-learners for the prediction of counterfactual outcomes which respect the outcome space. As such, the obtained i-learner or imputation-learner is more generally expected to outperform existing learners, even when the outcome is unconstrained, as we confirm empirically in simulation studies and an analysis of critical care data. Our development also sheds broader light onto the construction of orthogonal learners for other estimands.