Differential privacy allows adjustable protection of data relationships
Differential privacy with adjustable preservation of multivariate relationships
Cryptography and Security
Summary
Privacy methods often change data to protect individuals but can hide important connections between data points. This paper shows how to control exactly how much these connections are hidden by adjusting privacy settings for each data attribute. The authors provide a clear mathematical way to understand and control how relationships between different parts of private data are preserved or weakened. This helps users keep useful data patterns while still protecting privacy.
What this means in practice
- •For data privacy engineers: Configure privacy tools to selectively preserve correlations between dataset attributes based on specific privacy budgets.
- •For financial analysts: Maintain key relationships in anonymized financial datasets while enforcing strong privacy guarantees for sensitive attributes.
Authors
Nicolas Ruiz
Abstract
This paper derives an exact attenuation formula for multivariate cross-moments under differential privacy achieved through randomized response. From a proposed alternative formulation of randomization matrices compliant with differential privacy guarantees we show that, under attribute-level randomization and where the randomization of the whole distribution is characterized by Kronecker products, any cross-moment of the anonymized dataset involving distinct attributes is equal to the original cross-moment multiplied by attenuation parameters, themselves determined by the part of the overall privacy budget allocated to each attribute. This characterization enables explicit and transparent controls of multivariate relationships preservations in differential privacy through privacy budget allocation. A simple numerical illustration demonstrates that identical total budgets can yield substantially different covariance-preservation profiles. The results also make the multiplicative loss of higher-order interactions explicit and thus can support mechanism design guided by analytical priorities.