From the Information Bottleneck to the Privacy Funnel (1402.1774v5)

Abstract: We focus on the privacy-utility trade-off encountered by users who wish to disclose some information to an analyst, that is correlated with their private data, in the hope of receiving some utility. We rely on a general privacy statistical inference framework, under which data is transformed before it is disclosed, according to a probabilistic privacy mapping. We show that when the log-loss is introduced in this framework in both the privacy metric and the distortion metric, the privacy leakage and the utility constraint can be reduced to the mutual information between private data and disclosed data, and between non-private data and disclosed data respectively. We justify the relevance and generality of the privacy metric under the log-loss by proving that the inference threat under any bounded cost function can be upper-bounded by an explicit function of the mutual information between private data and disclosed data. We then show that the privacy-utility tradeoff under the log-loss can be cast as the non-convex Privacy Funnel optimization, and we leverage its connection to the Information Bottleneck, to provide a greedy algorithm that is locally optimal. We evaluate its performance on the US census dataset.

• The paper demonstrates that applying log-loss transforms privacy leakage into mutual information evaluation, linking privacy and utility effectively.
• The paper reformulates the privacy-utility challenge as a Privacy Funnel optimization to minimize leakage while preserving data utility.
• The paper develops a greedy algorithm to address the non-convex optimization, providing practical solutions for privacy-preserving data sharing.

An Expert Overview of "From the Information Bottleneck to the Privacy Funnel"

The paper "From the Information Bottleneck to the Privacy Funnel" explores the privacy-utility trade-off in the context of data sharing. Specifically, it addresses the challenges faced by individuals looking to share non-private data with an analyst, while keeping their private data secure. The researchers align their framework with the information-theoretic concepts, notably building on the Information Bottleneck method to introduce the Privacy Funnel optimization.

Key Contributions and Methodology

The paper's significant contribution lies in its unique application of the log-loss metric in both privacy and utility evaluation. By employing the log-loss, the authors effectively reduce the complex privacy leakage and utility constraints to evaluations of mutual information. This approach allows a nuanced balance between privacy protection and utility maximization in shared data.

1. Privacy Metric Under Log-Loss: The authors argue for the relevance of the log-loss by demonstrating that privacy leakage can be assessed using the mutual information $I(S; Y)$, where $S$ is private data and $Y$ is data disclosed after a probabilistic transformation. They provide mathematical justifications that show the general applicability of this measure, establishing upper bounds on inference threats under various bounded cost functions.
2. Privacy-Utility Trade-off Optimization: Leveraging the above insights, the authors reformulate the privacy-utility trade-off as the Privacy Funnel optimization. This formulation is analogous but opposite to the Information Bottleneck method; it seeks to minimize privacy leakage for a given level of data disclosure.
3. Algorithm Development: Given that the Privacy Funnel poses a non-convex problem, the authors propose a greedy algorithm informed by strategies developed for the Information Bottleneck. This algorithm iteratively seeks locally optimal solutions, effectively managing the balance between privacy and utility for real-world data applications.

Implications and Performance Evaluation

The research has practical implications for designing privacy-preserving data sharing mechanisms, particularly in scenarios where the integrity of non-private data must be maintained for utility purposes while minimizing leakage of sensitive private information. This work enables a statistically sound approach to design privacy mappings that optimize a trade-off scenario crucial for many data-driven industries.

The effectiveness of the proposed methodology is demonstrated using the US 1994 Census dataset. The paper illustrates the range of feasible $I(S; Y)$ for given $I(X; Y)$, showcasing how carefully designed mappings can achieve the minimal privacy leakage for a set disclosure level.

Future Directions

Future exploration could extend this framework to incorporate more dynamic privacy-utility criteria and explore the impact of varying probabilistic transformations across diverse datasets and application domains. Additionally, addressing the inherent non-convexity of the problem via advanced optimization techniques or machine learning approaches might yield further practical insights and new pathways for privacy-preserving data analytics.

This paper provides an essential bridge between theoretical information metrics and practical data privacy challenges, establishing a foundation upon which further advances in privacy-preserving technology can be developed. Its integration of information-theoretic methodologies renders it a substantial contribution to both the academic and practical landscapes of data privacy and utility management.