# Quantifying Ignorance in Individual-Level Causal-Effect Estimates under Hidden Confounding

arXiv: https://arxiv.org/abs/2103.04850 · HTML: https://mlsanity.com/paper/2103.04850/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 46 references that are in the map.
- First posted on arXiv 8 Mar 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Ray: A Distributed Framework for Emerging AI Applications](https://mlsanity.com/paper/1712.05889/) (2017)
- [Tune: A Research Platform for Distributed Model Selection and Training](https://mlsanity.com/paper/1807.05118/) (2018)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [Identifying Causal-Effect Inference Failure with Uncertainty-Aware Models](https://mlsanity.com/paper/2007.00163/) (2020)
- [Interval Estimation of Individual-Level Causal Effects Under Unobserved Confounding](https://mlsanity.com/paper/1810.02894/) (2018)
- [Bounds on the conditional and average treatment effect with unobserved confounding factors](https://mlsanity.com/paper/1808.09521/) (2018)
- [Sense and Sensitivity Analysis: Simple Post-Hoc Analysis of Bias Due to Unobserved Confounding](https://mlsanity.com/paper/2003.01747/) (2020)
- [Flexible sensitivity analysis for observational studies without observable implications](https://mlsanity.com/paper/1809.00399/) (2018)
- [Minimax Optimal Nonparametric Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/2002.06471/) (2020)

## Built on by (most cited first, 30 of 50)

- [Causal Effect Inference for Structured Treatments](https://mlsanity.com/paper/2106.01939/) (2021)
- [Causal-BALD: Deep Bayesian Active Learning of Outcomes to Infer Treatment-Effects from Observational Data](https://mlsanity.com/paper/2111.02275/) (2021)
- [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)
- [Long Story Short: Omitted Variable Bias in Causal Machine Learning](https://mlsanity.com/paper/2112.13398/) (2021)
- [Predicting the impact of treatments over time with uncertainty aware neural differential equations](https://mlsanity.com/paper/2202.11987/) (2022)
- [Normalizing Flows for Interventional Density Estimation](https://mlsanity.com/paper/2209.06203/) (2022)
- [DoWhy: Addressing Challenges in Expressing and Validating Causal Assumptions](https://mlsanity.com/paper/2108.13518/) (2021)
- [Scalable Sensitivity and Uncertainty Analysis for Causal-Effect Estimates of Continuous-Valued Interventions](https://mlsanity.com/paper/2204.10022/) (2022)
- [Bounds on Representation-Induced Confounding Bias for Treatment Effect Estimation](https://mlsanity.com/paper/2311.11321/) (2023)
- [Estimating individual treatment effects under unobserved confounding using binary instruments](https://mlsanity.com/paper/2208.08544/) (2022)
- [Counterfactual Generative Models for Time-Varying Treatments](https://mlsanity.com/paper/2305.15742/) (2023)
- [A Neural Framework for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2311.16026/) (2023)
- [Causal Multi-Agent Reinforcement Learning: Review and Open Problems](https://mlsanity.com/paper/2111.06721/) (2021)
- [Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Model](https://mlsanity.com/paper/2306.01424/) (2023)
- [Towards assessing agricultural land suitability with causal machine learning](https://mlsanity.com/paper/2204.12956/) (2022)
- [Meta-Learners for Partially-Identified Treatment Effects Across Multiple Environments](https://mlsanity.com/paper/2406.02464/) (2024)
- [Causal Fairness under Unobserved Confounding: A Neural Sensitivity Framework](https://mlsanity.com/paper/2311.18460/) (2023)
- [Quantifying Aleatoric Uncertainty of the Treatment Effect: A Novel Orthogonal Learner](https://mlsanity.com/paper/2411.03387/) (2024)
- [Hidden yet quantifiable: A lower bound for confounding strength using randomized trials](https://mlsanity.com/paper/2312.03871/) (2023)
- [Partial Identification of Dose Responses with Hidden Confounders](https://mlsanity.com/paper/2204.11206/) (2022)
- [Delphic Offline Reinforcement Learning under Nonidentifiable Hidden Confounding](https://mlsanity.com/paper/2306.01157/) (2023)
- [Ensembled Prediction Intervals for Causal Outcomes Under Hidden Confounding](https://mlsanity.com/paper/2306.09520/) (2023)
- [Advancing Deep Active Learning & Data Subset Selection: Unifying Principles with Information-Theory Intuitions](https://mlsanity.com/paper/2401.04305/) (2024)
- [Using Non-Linear Causal Models to Study Aerosol-Cloud Interactions in the Southeast Pacific](https://mlsanity.com/paper/2110.15084/) (2021)
- [Quantitative probing: Validating causal models using quantitative domain knowledge](https://mlsanity.com/paper/2209.03013/) (2022)
- [Efficient and Sharp Off-Policy Learning under Unobserved Confounding](https://mlsanity.com/paper/2502.13022/) (2025)
- [Orthogonal Representation Learning for Estimating Causal Quantities](https://mlsanity.com/paper/2502.04274/) (2025)
- [Generalizing Off-Policy Evaluation From a Causal Perspective For Sequential Decision-Making](https://mlsanity.com/paper/2201.08262/) (2022)

## Abstract (arXiv)

We study the problem of learning conditional average treatment effects (CATE) from high-dimensional, observational data with unobserved confounders. Unobserved confounders introduce ignorance -- a level of unidentifiability -- about an individual's response to treatment by inducing bias in CATE estimates. We present a new parametric interval estimator suited for high-dimensional data, that estimates a range of possible CATE values when given a predefined bound on the level of hidden confounding. Further, previous interval estimators do not account for ignorance about the CATE associated with samples that may be underrepresented in the original study, or samples that violate the overlap assumption. Our interval estimator also incorporates model uncertainty so that practitioners can be made aware of out-of-distribution data. We prove that our estimator converges to tight bounds on CATE when there may be unobserved confounding, and assess it using semi-synthetic, high-dimensional datasets.