On the Inherent Privacy Amplification of Missing Data

Privacy preservation is critical in many high-stakes domains such as medicine and finance, where sensitive data must be analyzed without compromising individual confidentiality. At the same time, these applications often involve datasets with inherent missing values due to non-response or data corruption for example. Missing data is traditionally analyzed through its impact on statistical efficiency and model performance. In fact, it reduces the information available to analysts and can degrade the final utility of the model. In this work, we take an alternative approach and study missing data through the lens of privacy preservation. Intuitively, when features are missing, less information is revealed about individuals, suggesting that data missingness could inherently enhance privacy. We formalize this intuition within a novel framework that integrates missing data into differential privacy. In essence, our approach accounts for the de facto missingness in the data to refine existing privacy guarantees without modifying the underlying mechanism. Using this framework, we show for the first time that missing data can induce inherent privacy amplification for differentially private algorithms, highlighting a previously overlooked interaction between missing data and formal privacy guarantees..