# Partial Identification with Noisy Covariates: A Robust Optimization Approach arXiv: https://arxiv.org/abs/2202.10665 ยท HTML: https://mlsanity.com/paper/2202.10665/ ## Key facts - Cited by 11 papers in the map (data through 14 Oct 2026). - Builds on 28 of its 80 references that are in the map. - First posted on arXiv 22 Feb 2022. ## Builds on (most cited first, 28 of 28) - [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018) - [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017) - [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018) - [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015) - [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019) - [Recommendations as Treatments: Debiasing Learning and Evaluation](https://mlsanity.com/paper/1602.05352/) (2016) - [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016) - [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020) - [Counterfactual Probabilities: Computational Methods, Bounds and Applications](https://mlsanity.com/paper/1302.6784/) (2013) - [Semiparametric proximal causal inference](https://mlsanity.com/paper/2011.08411/) (2020) - [An Automated Approach to Causal Inference in Discrete Settings](https://mlsanity.com/paper/2109.13471/) (2021) - [Conformal Sensitivity Analysis for Individual Treatment Effects](https://mlsanity.com/paper/2112.03493/) (2021) - [Bounds on the conditional and average treatment effect with unobserved confounding factors](https://mlsanity.com/paper/1808.09521/) (2018) - [Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap](https://mlsanity.com/paper/1711.11286/) (2017) - [Causal Inference with Noisy and Missing Covariates via Matrix Factorization](https://mlsanity.com/paper/1806.00811/) (2018) - [Orthogonal Machine Learning: Power and Limitations](https://mlsanity.com/paper/1711.00342/) (2017) - [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) - [Proximal Causal Inference for Complex Longitudinal Studies](https://mlsanity.com/paper/2109.07030/) (2021) - [Sensitivity analysis via the proportion of unmeasured confounding](https://mlsanity.com/paper/1912.02793/) (2019) - [Nonparametric Bounds and Sensitivity Analysis of Treatment Effects](https://mlsanity.com/paper/1503.01598/) (2015) - [The Proximal ID Algorithm](https://mlsanity.com/paper/2108.06818/) (2021) - [Partial Identifiability in Discrete Data With Measurement Error](https://mlsanity.com/paper/2012.12449/) (2020) - [Proximal mediation analysis](https://mlsanity.com/paper/2109.11904/) (2021) - [Instrumentality Tests Revisited](https://mlsanity.com/paper/1301.2258/) (2013) - [Quantifier Elimination for Statistical Problems](https://mlsanity.com/paper/1301.6698/) (2013) - [Estimating Treatment Effects with Observed Confounders and Mediators](https://mlsanity.com/paper/2003.11991/) (2020) - [A First-Order Algorithmic Framework for Wasserstein Distributionally Robust Logistic Regression](https://mlsanity.com/paper/1910.12778/) (2019) ## Built on by (most cited first, 11 of 11) - [Sharp Bounds for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2305.16988/) (2023) - [Partial Identification of Treatment Effects with Implicit Generative Models](https://mlsanity.com/paper/2210.08139/) (2022) - [Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Model](https://mlsanity.com/paper/2306.01424/) (2023) - [Quantifying Aleatoric Uncertainty of the Treatment Effect: A Novel Orthogonal Learner](https://mlsanity.com/paper/2411.03387/) (2024) - [Partial Identification of Dose Responses with Hidden Confounders](https://mlsanity.com/paper/2204.11206/) (2022) - [Confounding-Robust Policy Improvement with Human-AI Teams](https://mlsanity.com/paper/2310.08824/) (2023) - [Weak Supervision Performance Evaluation via Partial Identification](https://mlsanity.com/paper/2312.04601/) (2023) - [Learning Representations of Instruments for Partial Identification of Treatment Effects](https://mlsanity.com/paper/2410.08976/) (2024) - [The Blessings of Multiple Treatments and Outcomes in Treatment Effect Estimation](https://mlsanity.com/paper/2309.17283/) (2023) - [Data-Poisoning Audits for Causal Effect Estimation](https://mlsanity.com/paper/2607.19692/) (2026) - [What a Data Release Must Preserve for Off-Policy Evaluation](https://mlsanity.com/paper/2610.15283/) (2026) ## Abstract (arXiv) Causal inference from observational datasets often relies on measuring and adjusting for covariates. In practice, measurements of the covariates can often be noisy and/or biased, or only measurements of their proxies may be available. Directly adjusting for these imperfect measurements of the covariates can lead to biased causal estimates. Moreover, without additional assumptions, the causal effects are not point-identifiable due to the noise in these measurements. To this end, we study the partial identification of causal effects given noisy covariates, under a user-specified assumption on the noise level. The key observation is that we can formulate the identification of the average treatment effects (ATE) as a robust optimization problem. This formulation leads to an efficient robust optimization algorithm that bounds the ATE with noisy covariates. We show that this robust optimization approach can extend a wide range of causal adjustment methods to perform partial identification, including backdoor adjustment, inverse propensity score weighting, double machine learning, and front door adjustment. Across synthetic and real datasets, we find that this approach provides ATE bounds with a higher coverage probability than existing methods.