# Efficient adjustment for complex covariates: Gaining efficiency with DOPE

arXiv: https://arxiv.org/abs/2402.12980 · HTML: https://mlsanity.com/paper/2402.12980/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 48 references that are in the map.
- First posted on arXiv 20 Feb 2024.

## Builds on (most cited first, 13 of 13)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Kaggle forecasting competitions: An overlooked learning opportunity](https://mlsanity.com/paper/2009.07701/) (2020)
- [A unifying approach for doubly-robust ℓ1 regularized estimation of causal contrasts](https://mlsanity.com/paper/1904.03737/) (2019)
- [Machine learning for causal inference: on the use of cross-fit estimators](https://mlsanity.com/paper/2004.10337/) (2020)
- [ReLU Neural Networks with Linear Layers are Biased Towards Single- and Multi-Index Models](https://mlsanity.com/paper/2305.15598/) (2023)
- [Nonparametric Conditional Local Independence Testing](https://mlsanity.com/paper/2203.13559/) (2022)
- [High-Dimensional Feature Selection for Sample Efficient Treatment Effect Estimation](https://mlsanity.com/paper/2011.01979/) (2020)
- [Confounder Selection: Objectives and Approaches](https://mlsanity.com/paper/2208.13871/) (2022)
- [A nonparametric super-efficient estimator of the average treatment effect](https://mlsanity.com/paper/1901.05056/) (2019)
- [Scalable Collaborative Targeted Learning for High-Dimensional Data](https://mlsanity.com/paper/1703.02237/) (2017)
- [Boosted Control Functions: Distribution generalization and invariance in confounded models](https://mlsanity.com/paper/2310.05805/) (2023)
- [Perturbation-based Effect Measures for Compositional Data](https://mlsanity.com/paper/2311.18501/) (2023)

## Built on by (most cited first, 5 of 5)

- [What is causal about causal models and representations?](https://mlsanity.com/paper/2501.19335/) (2025)
- [Orthogonal Representation Learning for Estimating Causal Quantities](https://mlsanity.com/paper/2502.04274/) (2025)
- [Adjustment for Confounding using Pre-Trained Representations](https://mlsanity.com/paper/2506.14329/) (2025)
- [Unveiling the Structure of Do-Calculus Reasoning via Derivation Graphs](https://mlsanity.com/paper/2606.03719/) (2026)
- [Outcome-adapted Automatic Debiased Machine Learning](https://mlsanity.com/paper/2607.03351/) (2026)

## Abstract (arXiv)

Covariate adjustment is a ubiquitous method used to estimate the average treatment effect (ATE) from observational data. Assuming a known graphical structure of the data generating model, recent results give graphical criteria for optimal adjustment, which enables efficient estimation of the ATE. However, graphical approaches are challenging for high-dimensional and complex data, and it is not straightforward to specify a meaningful graphical model of non-Euclidean data such as texts. We propose a new framework that accommodates adjustment for any subset of information expressed by the covariates, and we show that the information that is minimally sufficient for prediction of the outcome given the treatment is also most efficient for adjustment. Based on our theoretical results, we propose the Debiased Outcome-adapted Propensity Estimator (DOPE) for efficient estimation of the ATE, and we provide asymptotic results for DOPE under general conditions. Compared to the augmented inverse propensity weighted (AIPW) estimator, DOPE can retain its efficiency even when the covariates are highly predictive of treatment. We illustrate this with a single-index model, and with an implementation of DOPE based on neural networks, we demonstrate its performance on simulated and real data. Our results show that DOPE provides an efficient and robust methodology for ATE estimation in various observational settings.