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Privacy Amplification by Missing Data

Simon Roburin, Rafaël Pinot, Erwan Scornet

TL;DR

Privacy Amplification by Missing Data shows that missingness can strengthen differential privacy guarantees when data are MAR or MCAR, by modeling the data-release process as a composition of a missing-data mechanism and a DP procedure. It introduces a formal framework for incomplete-data DP, derives a general amplification bound $\epsilon' = \ln(1 + p_{\ast}(e^{\epsilon}-1))$ with $\delta' \le p_{\ast}\delta$, and provides practical results for feature-wise Lipschitz queries under Laplace and Gaussian mechanisms that also depend on the observed-feature fraction $\rho$. The work identifies scenarios where amplification occurs even when all records are partially observed (e.g., certain MAR mechanisms) and clarifies limitations under MNAR and per-sample independence assumptions, suggesting new directions for privacy-preserving algorithm design that leverage missing data as a principled amplification resource. Overall, it reframes missing data from a nuisance to a tunable privacy resource, with potential implications for DP pipelines in sensitive domains. The findings bridge missing-data theory and differential privacy, offering concrete tools for quantifying privacy gains and guiding the design of privacy-aware data collection and analysis strategies.

Abstract

Privacy preservation is a fundamental requirement in many high-stakes domains such as medicine and finance, where sensitive personal data must be analyzed without compromising individual confidentiality. At the same time, these applications often involve datasets with missing values due to non-response, data corruption, or deliberate anonymization. Missing data is traditionally viewed as a limitation because it reduces the information available to analysts and can degrade model performance. In this work, we take an alternative perspective and study missing data from a privacy preservation standpoint. Intuitively, when features are missing, less information is revealed about individuals, suggesting that missingness could inherently enhance privacy. We formalize this intuition by analyzing missing data as a privacy amplification mechanism within the framework of differential privacy. We show, for the first time, that incomplete data can yield privacy amplification for differentially private algorithms.

Privacy Amplification by Missing Data

TL;DR

Privacy Amplification by Missing Data shows that missingness can strengthen differential privacy guarantees when data are MAR or MCAR, by modeling the data-release process as a composition of a missing-data mechanism and a DP procedure. It introduces a formal framework for incomplete-data DP, derives a general amplification bound with , and provides practical results for feature-wise Lipschitz queries under Laplace and Gaussian mechanisms that also depend on the observed-feature fraction . The work identifies scenarios where amplification occurs even when all records are partially observed (e.g., certain MAR mechanisms) and clarifies limitations under MNAR and per-sample independence assumptions, suggesting new directions for privacy-preserving algorithm design that leverage missing data as a principled amplification resource. Overall, it reframes missing data from a nuisance to a tunable privacy resource, with potential implications for DP pipelines in sensitive domains. The findings bridge missing-data theory and differential privacy, offering concrete tools for quantifying privacy gains and guiding the design of privacy-aware data collection and analysis strategies.

Abstract

Privacy preservation is a fundamental requirement in many high-stakes domains such as medicine and finance, where sensitive personal data must be analyzed without compromising individual confidentiality. At the same time, these applications often involve datasets with missing values due to non-response, data corruption, or deliberate anonymization. Missing data is traditionally viewed as a limitation because it reduces the information available to analysts and can degrade model performance. In this work, we take an alternative perspective and study missing data from a privacy preservation standpoint. Intuitively, when features are missing, less information is revealed about individuals, suggesting that missingness could inherently enhance privacy. We formalize this intuition by analyzing missing data as a privacy amplification mechanism within the framework of differential privacy. We show, for the first time, that incomplete data can yield privacy amplification for differentially private algorithms.
Paper Structure (40 sections, 24 theorems, 145 equations, 1 table)

This paper contains 40 sections, 24 theorems, 145 equations, 1 table.

Table of Contents

  1. Introduction
  2. Contributions
  3. Organization
  4. Setting and notations
  5. Differential privacy with missing data
  6. Incomplete datasets
  7. Missing data mechanism
  8. Adapting the definition of differential privacy
  9. Privacy amplification of missing data on generic DP algorithms
  10. Privacy amplification of missing data for feature-wise Lipschitz queries
  11. Feature-Wise Lipschitz queries and missing values
  12. Missingness amplifies Laplace mechanism privacy
  13. Missingness amplifies Gaussian mechanism privacy
  14. Related Work
  15. Discussion
  16. ...and 25 more sections

Key Result

Theorem 2.2

Let $\epsilon >0$ and $\delta \in [0,1]$. For any randomized algorithm $\mathcal{A}$ defined over $\mathcal{Z}_{\text{miss}}^n$, and any $\tilde{\underline{\mathbf{z}}}, \tilde{\underline{\mathbf{z}}}' \in \mathcal{Z}_{\text{miss}}^n$, we denote Using this notation, a randomized mechanism $\mathcal{A}$ is $(\epsilon, \delta)$-DP if and only if $\delta_{\mathcal{A}}(\epsilon) \leq \delta$, where

Theorems & Definitions (46)

  • Definition 2.1
  • Theorem 2.2: barthe2013beyond
  • Remark 2.3
  • Lemma 3.0
  • Theorem 3.1
  • proof : Sketch of proof
  • Definition 4.1
  • Lemma 4.3
  • Theorem 4.4
  • proof : Sketch of proof
  • ...and 36 more