# Bounds on Representation-Induced Confounding Bias for Treatment Effect Estimation

arXiv: https://arxiv.org/abs/2311.11321 · HTML: https://mlsanity.com/paper/2311.11321/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 67 references that are in the map.
- First posted on arXiv 19 Nov 2023.

## Builds on (most cited first, 30 of 34)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [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)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [Estimating Counterfactual Treatment Outcomes over Time Through Adversarially Balanced Representations](https://mlsanity.com/paper/2002.04083/) (2020)
- [Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms](https://mlsanity.com/paper/2101.10943/) (2021)
- [Causal Transformer for Estimating Counterfactual Outcomes](https://mlsanity.com/paper/2204.07258/) (2022)
- [Causal Consistency of Structural Equation Models](https://mlsanity.com/paper/1707.00819/) (2017)
- [Double/Debiased/Neyman Machine Learning of Treatment Effects](https://mlsanity.com/paper/1701.08687/) (2017)
- [On Inductive Biases for Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2106.03765/) (2021)
- [Generalization Bounds and Representation Learning for Estimation of Potential Outcomes and Causal Effects](https://mlsanity.com/paper/2001.07426/) (2020)
- [Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equations](https://mlsanity.com/paper/2206.08311/) (2022)
- [Identifying Causal-Effect Inference Failure with Uncertainty-Aware Models](https://mlsanity.com/paper/2007.00163/) (2020)
- [Perfect Match: A Simple Method for Learning Representations For Counterfactual Inference With Neural Networks](https://mlsanity.com/paper/1810.00656/) (2018)
- [Conditional Density Estimation with Bayesian Normalising Flows](https://mlsanity.com/paper/1802.04908/) (2018)
- [Interval Estimation of Individual-Level Causal Effects Under Unobserved Confounding](https://mlsanity.com/paper/1810.02894/) (2018)
- [Quantifying Ignorance in Individual-Level Causal-Effect Estimates under Hidden Confounding](https://mlsanity.com/paper/2103.04850/) (2021)
- [Counterfactual Representation Learning with Balancing Weights](https://mlsanity.com/paper/2010.12618/) (2020)
- [Learning Weighted Representations for Generalization Across Designs](https://mlsanity.com/paper/1802.08598/) (2018)
- [Causal Effect Identification in Cluster DAGs](https://mlsanity.com/paper/2202.12263/) (2022)
- [Sharp Sensitivity Analysis for Inverse Propensity Weighting via Quantile Balancing](https://mlsanity.com/paper/2102.04543/) (2021)
- [Optimal Transport for Treatment Effect Estimation](https://mlsanity.com/paper/2310.18286/) (2023)
- [Adversarial Balancing-based Representation Learning for Causal Effect Inference with Observational Data](https://mlsanity.com/paper/1904.13335/) (2019)
- [B-Learner: Quasi-Oracle Bounds on Heterogeneous Causal Effects Under Hidden Confounding](https://mlsanity.com/paper/2304.10577/) (2023)
- [Bayesian Neural Controlled Differential Equations for Treatment Effect Estimation](https://mlsanity.com/paper/2310.17463/) (2023)
- [Sharp Bounds for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2305.16988/) (2023)
- [Noise Regularization for Conditional Density Estimation](https://mlsanity.com/paper/1907.08982/) (2019)
- [Counterfactual Predictions under Runtime Confounding](https://mlsanity.com/paper/2006.16916/) (2020)

## Built on by (most cited first, 20 of 20)

- [Model-agnostic meta-learners for estimating heterogeneous treatment effects over time](https://mlsanity.com/paper/2407.05287/) (2024)
- [DiffPO: A causal diffusion model for learning distributions of potential outcomes](https://mlsanity.com/paper/2410.08924/) (2024)
- [IGC-Net for conditional average potential outcome estimation over time](https://mlsanity.com/paper/2405.21012/) (2024)
- [Quantifying Aleatoric Uncertainty of the Treatment Effect: A Novel Orthogonal Learner](https://mlsanity.com/paper/2411.03387/) (2024)
- [MAVias: Mitigate any Visual Bias](https://mlsanity.com/paper/2412.06632/) (2024)
- [Orthogonal Representation Learning for Estimating Causal Quantities](https://mlsanity.com/paper/2502.04274/) (2025)
- [Uncertainty-Aware Optimal Treatment Selection for Clinical Time Series](https://mlsanity.com/paper/2410.08816/) (2024)
- [Towards Representation Learning for Weighting Problems in Design-Based Causal Inference](https://mlsanity.com/paper/2409.16407/) (2024)
- [DAG-aware Transformer for Causal Effect Estimation](https://mlsanity.com/paper/2410.10044/) (2024)
- [DeepBlip: Estimating Conditional Average Treatment Effects Over Time](https://mlsanity.com/paper/2511.14545/) (2025)
- [Cluster-Dags as Powerful Background Knowledge For Causal Discovery](https://mlsanity.com/paper/2512.10032/) (2025)
- [Overlap-Adaptive Regularization for Conditional Average Treatment Effect Estimation](https://mlsanity.com/paper/2509.24962/) (2025)
- [Estimating Treatment Effects in Networks under Unknown Exposure Mappings](https://mlsanity.com/paper/2510.21457/) (2025)
- [CAETC: Causal Autoencoding and Treatment Conditioning for Counterfactual Estimation over Time](https://mlsanity.com/paper/2603.11565/) (2026)
- [From Text to Treatment Effects: A Meta-Learning Approach to Handling Text-Based Confounding](https://mlsanity.com/paper/2409.15503/) (2024)
- [Conditional Average Treatment Effect Estimation Under Hidden Confounders](https://mlsanity.com/paper/2506.12304/) (2025)
- [Annotation-Assisted Learning of Treatment Policies From Multimodal Electronic Health Records](https://mlsanity.com/paper/2507.20993/) (2025)
- [Causal Representation Learning with Optimal Compression under Complex Treatments](https://mlsanity.com/paper/2603.11907/) (2026)
- [Causal State-Space Model for Causal Inference: Estimating Longitudinal Individual Treatment Effects](https://mlsanity.com/paper/2608.08288/) (2026)
- [Admissible Diffusion for Multimodal Interventional Trajectories](https://mlsanity.com/paper/2609.34433/) (2026)

## Abstract (arXiv)

State-of-the-art methods for conditional average treatment effect (CATE) estimation make widespread use of representation learning. Here, the idea is to reduce the variance of the low-sample CATE estimation by a (potentially constrained) low-dimensional representation. However, low-dimensional representations can lose information about the observed confounders and thus lead to bias, because of which the validity of representation learning for CATE estimation is typically violated. In this paper, we propose a new, representation-agnostic refutation framework for estimating bounds on the representation-induced confounding bias that comes from dimensionality reduction (or other constraints on the representations) in CATE estimation. First, we establish theoretically under which conditions CATE is non-identifiable given low-dimensional (constrained) representations. Second, as our remedy, we propose a neural refutation framework which performs partial identification of CATE or, equivalently, aims at estimating lower and upper bounds of the representation-induced confounding bias. We demonstrate the effectiveness of our bounds in a series of experiments. In sum, our refutation framework is of direct relevance in practice where the validity of CATE estimation is of importance.