# Causal Inference with Corrupted Data: Measurement Error, Missing Values, Discretization, and Differential Privacy

arXiv: https://arxiv.org/abs/2107.02780 · HTML: https://mlsanity.com/paper/2107.02780/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jul 2021.

## Built on by (most cited first, 18 of 18)

- [Causal Matrix Completion](https://mlsanity.com/paper/2109.15154/) (2021)
- [Augmented balancing weights as linear regression](https://mlsanity.com/paper/2304.14545/) (2023)
- [Differentially Private Estimation of Heterogeneous Causal Effects](https://mlsanity.com/paper/2202.11043/) (2022)
- [Synthetic Combinations: A Causal Inference Framework for Combinatorial Interventions](https://mlsanity.com/paper/2303.14226/) (2023)
- [Causal Inference with Treatment Measurement Error: A Nonparametric Instrumental Variable Approach](https://mlsanity.com/paper/2206.09186/) (2022)
- [Adaptive Principal Component Regression with Applications to Panel Data](https://mlsanity.com/paper/2307.01357/) (2023)
- [Differentially Private Covariate Balancing Causal Inference](https://mlsanity.com/paper/2410.14789/) (2024)
- [Differentially Private Learners for Heterogeneous Treatment Effects](https://mlsanity.com/paper/2503.03486/) (2025)
- [Causal Discovery Under Local Privacy](https://mlsanity.com/paper/2311.04037/) (2023)
- [A Causal Inference Framework for Data Rich Environments](https://mlsanity.com/paper/2504.01702/) (2025)
- [Model Agnostic Differentially Private Causal Inference](https://mlsanity.com/paper/2505.19589/) (2025)
- [PrivATE: Differentially Private Confidence Intervals for Average Treatment Effects](https://mlsanity.com/paper/2505.21641/) (2025)
- [Privacy Preserving Adaptive Experiment Design](https://mlsanity.com/paper/2401.08224/) (2024)
- [Online Linear Regression with Paid Stochastic Features](https://mlsanity.com/paper/2511.08073/) (2025)
- [Privacy-Robust Incrementality Measurement for Advertising Systems under Signal Loss](https://mlsanity.com/paper/2606.03878/) (2026)
- [Beyond ATE: Multi-Criteria Design for A/B Testing](https://mlsanity.com/paper/2509.05864/) (2025)
- [Stress-Testing Causal Claims via Cardinality Repairs](https://mlsanity.com/paper/2512.02491/) (2025)
- [Canonical correlation regression with noisy data](https://mlsanity.com/paper/2512.22697/) (2025)

## Abstract (arXiv)

The US Census Bureau will deliberately corrupt data sets derived from the 2020 US Census, enhancing the privacy of respondents while potentially reducing the precision of economic analysis. To investigate whether this trade-off is inevitable, we formulate a semiparametric model of causal inference with high dimensional corrupted data. We propose a procedure for data cleaning, estimation, and inference with data cleaning-adjusted confidence intervals. We prove consistency and Gaussian approximation by finite sample arguments, with a rate of n 1/2 for semiparametric estimands that degrades gracefully for nonparametric estimands. Our key assumption is that the true covariates are approximately low rank, which we interpret as approximate repeated measurements and empirically validate. Our analysis provides nonasymptotic theoretical contributions to matrix completion, statistical learning, and semiparametric statistics. Calibrated simulations verify the coverage of our data cleaning adjusted confidence intervals and demonstrate the relevance of our results for Census-derived data.