# Deconfounding Scores: Feature Representations for Causal Effect Estimation with Weak Overlap

arXiv: https://arxiv.org/abs/2104.05762 · HTML: https://mlsanity.com/paper/2104.05762/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 25 references that are in the map.
- First posted on arXiv 12 Apr 2021.

## Builds on (most cited first, 7 of 7)

- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Machine Learning Methods Economists Should Know About](https://mlsanity.com/paper/1903.10075/) (2019)
- [Balanced Policy Evaluation and Learning](https://mlsanity.com/paper/1705.07384/) (2017)
- [Approximate Residual Balancing: De-Biased Inference of Average Treatment Effects in High Dimensions](https://mlsanity.com/paper/1604.07125/) (2016)
- [Minimal Dispersion Approximately Balancing Weights: Asymptotic Properties and Practical Considerations](https://mlsanity.com/paper/1705.00998/) (2017)
- [Entropy balancing is doubly robust](https://mlsanity.com/paper/1501.03571/) (2015)
- [Efficient adjustment sets for population average treatment effect estimation in non-parametric causal graphical models](https://mlsanity.com/paper/1912.00306/) (2019)

## Built on by (most cited first, 9 of 9)

- [Causal-BALD: Deep Bayesian Active Learning of Outcomes to Infer Treatment-Effects from Observational Data](https://mlsanity.com/paper/2111.02275/) (2021)
- [Causal Estimation for Text Data with (Apparent) Overlap Violations](https://mlsanity.com/paper/2210.00079/) (2022)
- [β-Intact-VAE: Identifying and Estimating Causal Effects under Limited Overlap](https://mlsanity.com/paper/2110.05225/) (2021)
- [RCT Rejection Sampling for Causal Estimation Evaluation](https://mlsanity.com/paper/2307.15176/) (2023)
- [Orthogonal Representation Learning for Estimating Causal Quantities](https://mlsanity.com/paper/2502.04274/) (2025)
- [Learning Invariant Representations with Missing Data](https://mlsanity.com/paper/2112.00881/) (2021)
- [Towards Representation Learning for Weighting Problems in Design-Based Causal Inference](https://mlsanity.com/paper/2409.16407/) (2024)
- [When AI Generates Covariates: Causal Typing and Estimand Drift in Sequential Experiments](https://mlsanity.com/paper/2609.17772/) (2026)
- [Information Set Emulation: Causal Certificates for AI Derived EHR Features](https://mlsanity.com/paper/2609.17777/) (2026)

## Abstract (arXiv)

A key condition for obtaining reliable estimates of the causal effect of a treatment is overlap (a.k.a. positivity): the distributions of the features used to perform causal adjustment cannot be too different in the treated and control groups. In cases where overlap is poor, causal effect estimators can become brittle, especially when they incorporate weighting. To address this problem, a number of proposals (including confounder selection or dimension reduction methods) incorporate feature representations to induce better overlap between the treated and control groups. A key concern in these proposals is that the representation may introduce confounding bias into the effect estimator. In this paper, we introduce deconfounding scores, which are feature representations that induce better overlap without biasing the target of estimation. We show that deconfounding scores satisfy a zero-covariance condition that is identifiable in observed data. As a proof of concept, we characterize a family of deconfounding scores in a simplified setting with Gaussian covariates, and show that in some simple simulations, these scores can be used to construct estimators with good finite-sample properties. In particular, we show that this technique could be an attractive alternative to standard regularizations that are often applied to IPW and balancing weights.