# Bias and Variance of Post-processing in Differential Privacy

arXiv: https://arxiv.org/abs/2010.04327 · HTML: https://mlsanity.com/paper/2010.04327/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2020.

## Built on by (most cited first, 14 of 14)

- [Differential Privacy and Fairness in Decisions and Learning Tasks: A Survey](https://mlsanity.com/paper/2202.08187/) (2022)
- [Pruning has a disparate impact on model accuracy](https://mlsanity.com/paper/2205.13574/) (2022)
- [Decision Making with Differential Privacy under a Fairness Lens](https://mlsanity.com/paper/2105.07513/) (2021)
- [Differentially Private Counterfactuals via Functional Mechanism](https://mlsanity.com/paper/2208.02878/) (2022)
- [A Bias-Accuracy-Privacy Trilemma for Statistical Estimation](https://mlsanity.com/paper/2301.13334/) (2023)
- [Post-processing of Differentially Private Data: A Fairness Perspective](https://mlsanity.com/paper/2201.09425/) (2022)
- [Tabular Data Synthesis with Differential Privacy: A Survey](https://mlsanity.com/paper/2411.03351/) (2024)
- [General Gaussian Noise Mechanisms and Their Optimality for Unbiased Mean Estimation](https://mlsanity.com/paper/2301.13850/) (2023)
- [Two Views of Constrained Differential Privacy: Belief Revision and Update](https://mlsanity.com/paper/2303.00228/) (2023)
- [Differentially Private Federated Quantum Learning via Quantum Noise](https://mlsanity.com/paper/2508.20310/) (2025)
- [DP-DCAN: Differentially Private Deep Contrastive Autoencoder Network for Single-cell Clustering](https://mlsanity.com/paper/2311.03410/) (2023)
- [Differentially Private Data Release on Graphs: Inefficiencies and Unfairness](https://mlsanity.com/paper/2408.05246/) (2024)
- [Optimal Allocation of Privacy Budget on Hierarchical Data Release](https://mlsanity.com/paper/2505.10871/) (2025)
- [Differentially Private Natural Gradient Descent](https://mlsanity.com/paper/2607.05866/) (2026)

## Abstract (arXiv)

Post-processing immunity is a fundamental property of differential privacy: it enables the application of arbitrary data-independent transformations to the results of differentially private outputs without affecting their privacy guarantees. When query outputs must satisfy domain constraints, post-processing can be used to project the privacy-preserving outputs onto the feasible region. Moreover, when the feasible region is convex, a widely adopted class of post-processing steps is also guaranteed to improve accuracy. Post-processing has been applied successfully in many applications including census data-release, energy systems, and mobility. However, its effects on the noise distribution is poorly understood: It is often argued that post-processing may introduce bias and increase variance. This paper takes a first step towards understanding the properties of post-processing. It considers the release of census data and examines, both theoretically and empirically, the behavior of a widely adopted class of post-processing functions.