# Partial Identifiability in Discrete Data With Measurement Error

arXiv: https://arxiv.org/abs/2012.12449 · HTML: https://mlsanity.com/paper/2012.12449/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2020.

## Built on by (most cited first, 10 of 10)

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- [An Automated Approach to Causal Inference in Discrete Settings](https://mlsanity.com/paper/2109.13471/) (2021)
- [Partial Identification of Treatment Effects with Implicit Generative Models](https://mlsanity.com/paper/2210.08139/) (2022)
- [Partial Identification with Noisy Covariates: A Robust Optimization Approach](https://mlsanity.com/paper/2202.10665/) (2022)
- [Counterfactual Prediction Under Outcome Measurement Error](https://mlsanity.com/paper/2302.11121/) (2023)
- [Causal Inference with Treatment Measurement Error: A Nonparametric Instrumental Variable Approach](https://mlsanity.com/paper/2206.09186/) (2022)
- [Scalable Computation of Causal Bounds](https://mlsanity.com/paper/2308.02709/) (2023)
- [Algorithmic Recourse in Partially and Fully Confounded Settings Through Bounding Counterfactual Effects](https://mlsanity.com/paper/2106.11849/) (2021)
- [Robust Bayesian Inference for Measurement Error Misspecification: The Berkson and Classical Cases](https://mlsanity.com/paper/2306.01468/) (2023)
- [The Delegation Blind Spot: Auditing Product Decisions from Agent Choices](https://mlsanity.com/paper/2609.26642/) (2026)

## Abstract (arXiv)

When data contains measurement errors, it is necessary to make assumptions relating the observed, erroneous data to the unobserved true phenomena of interest. These assumptions should be justifiable on substantive grounds, but are often motivated by mathematical convenience, for the sake of exactly identifying the target of inference. We adopt the view that it is preferable to present bounds under justifiable assumptions than to pursue exact identification under dubious ones. To that end, we demonstrate how a broad class of modeling assumptions involving discrete variables, including common measurement error and conditional independence assumptions, can be expressed as linear constraints on the parameters of the model. We then use linear programming techniques to produce sharp bounds for factual and counterfactual distributions under measurement error in such models. We additionally propose a procedure for obtaining outer bounds on non-linear models. Our method yields sharp bounds in a number of important settings -- such as the instrumental variable scenario with measurement error -- for which no bounds were previously known.