Predictability as a Fine-Grained Measure for Privacy

2026-06-18

AI Summary

Traditional differential privacy, relying on worst-case assumptions, often overestimates privacy loss under specific adversary models, leading to unnecessary utility degradation. This work proposes a predictability-based, fine-grained privacy framework that quantifies privacy leakage as the incremental gain in an adversary’s ability to predict sensitive information after observing the algorithm’s output, explicitly incorporating the adversary’s prior knowledge and the query family. For the first time, privacy is measured via predictive gain, offering a complementary and more nuanced metric to differential privacy, with variants derived under specific conditions. Leveraging generalized method-of-moments analysis, the paper characterizes asymptotic predictability for stationary ergodic mixing processes and designs a predictability-calibrated perturbation mechanism for empirical risk minimization. Theoretically, it reveals an intrinsic connection between predictability and mutual-information-based differential privacy, enabling precise privacy control tailored to specific sensitive attributes and adversary models, while remaining compatible with standard differential privacy guarantees.

Abstract

Differential privacy (DP) ensures rigorous individual-level privacy guarantees against even the most knowledgeable attackers, but its worst-case nature can impose a costly privacy-accuracy tradeoff. We introduce privacy via predictability, a fine-grained framework that explicitly incorporates the attacker's core knowledge, a compromised portion of the dataset generated by a stochastic process, and a specified family of queries. Predictability measures privacy leakage as the incremental gain in an attacker's ability to predict sensitive information about unknown individuals after observing the algorithm's output, beyond what can already be inferred from the compromised data. We show that predictability and DP are generally incomparable: each can be small while the other is large. However, in the worst-case regime where all but one individual is compromised, and all binary queries are considered sensitive, predictability implies mutual-information DP. More generally, predictability provides a finer-grained privacy metric tailored to specific sensitive information and specific attacker models. We introduce a general framework, using the generalized method of moments (GMM), to analyze asymptotic predictability when the compromised data is generated by a stationary, ergodic, mixing process. Using this analysis, we derive a predictability-calibrated output perturbation scheme for ERM. Our approach is complementary to DP and can be used alongside DP to provide fine-grained privacy control.

Problem

• privacy
• predictability
• differential privacy
• attacker model
• privacy leakage

Innovation

• predictability
• differential privacy
• generalized method of moments
• privacy leakage
• output perturbation