Privacy Against Statistical Inference (1210.2123v1)

Abstract: We propose a general statistical inference framework to capture the privacy threat incurred by a user that releases data to a passive but curious adversary, given utility constraints. We show that applying this general framework to the setting where the adversary uses the self-information cost function naturally leads to a non-asymptotic information-theoretic approach for characterizing the best achievable privacy subject to utility constraints. Based on these results we introduce two privacy metrics, namely average information leakage and maximum information leakage. We prove that under both metrics the resulting design problem of finding the optimal mapping from the user's data to a privacy-preserving output can be cast as a modified rate-distortion problem which, in turn, can be formulated as a convex program. Finally, we compare our framework with differential privacy.

• The paper presents a novel statistical inference model that optimizes the privacy-utility trade-off by minimizing an adversary’s information gain.
• It introduces average and maximum information leakage metrics derived via self-information cost functions and convex optimization techniques.
• The study demonstrates that differential privacy may not fully restrict information leakage, advocating for more robust, information-theoretic privacy measures.

Analysis of "Privacy Against Statistical Inference"

The paper "Privacy Against Statistical Inference" by Flávio du Pin Calmon and Nadia Fawaz presents a comprehensive framework for assessing privacy threats in the context of statistical inference, with a particular focus on the privacy-utility trade-off. The authors introduce two novel privacy metrics—average information leakage and maximum information leakage—and thoroughly compare these with the widely-discussed differential privacy model.

Central Contributions

The paper’s contributions can be summarized as follows:

1. Statistical Inference Framework: The authors propose a statistical model that evaluates privacy risks as an inference cost gained by an adversary. This model offers an optimized privacy-utility trade-off by defining the problem as an optimization task, minimizing the cost gain subjected to predetermined utility constraints.
2. Application of Self-Information Cost Function: By applying the self-information cost function, the work naturally extends to defining average and maximum information leakage metrics. The derivation of these metrics corresponds to solving a modified rate-distortion problem, which can further be expressed as a convex optimization task.
3. Comparison with Differential Privacy: It is demonstrated that differential privacy does not necessarily confine average or maximum information leakage. By introducing the concept of information privacy, the authors establish its superiority over differential privacy in limiting information leakage.

Detailed Insights

Application of Rate-Distortion Theory

The mathematical innovation in this paper is its use of information-theoretic tools, particularly those reminiscent of rate-distortion theory. By conceptualizing privacy-preserving mappings as solutions to a convex optimization problem, the paper positions itself at a confluence of information theory and privacy-preserving computation. This theory provides both theoretical grounding and practical computational techniques, allowing the formulation of efficient algorithms using convex solvers.

Metrics of Privacy

The introduction of average and maximum information leakage metrics marks a significant conceptual advancement. Average information leakage is computed using mutual information metrics, ensuring minimal gain in an adversary's knowledge upon observing the released data. It is particularly insightful how this metric is rooted in KL-divergence, which signifies the "distance" between prior and posterior distributions.

The maximum information leakage metric further investigates the scenarios of maximum vulnerability, delimiting the highest conceivable data leak. The refinement to convex programs forms a robust mathematical setup to tackle such data security problems efficiently.

Implications and Future Directions

By presenting an approach that quantifies privacy threats in terms of the adversary's gain in information, this paper facilitates the design of more secure data systems. These systems not only adhere to utility constraints but also minimize privacy breaches in statistical terms. The theoretical implications have far-reaching potential, encouraging a re-examination of existing privacy standards and suggesting modifications that incorporate the information leakage metrics detailed in this paper.

Future research could explore other cost functions within this framework to address specific domain requirements, further benchmarking against differential privacy to refine privacy metrics. The real-world implementation of these models could involve developing tools to automatically identify optimal privacy mappings in industry settings, enhancing both data security and utility.

Conclusion

In summary, "Privacy Against Statistical Inference" introduces a robust approach to quantifying privacy threats, challenging traditional concepts like differential privacy with a method grounded in statistical inference and information theory. By offering a practical, algorithmic way to optimize the privacy-utility balance, this research lays foundational work for future investigations into more sophisticated and secure data privacy mechanisms.