Utility-Privacy Tradeoff in Databases: An Information-theoretic Approach (1102.3751v4)

Abstract: Ensuring the usefulness of electronic data sources while providing necessary privacy guarantees is an important unsolved problem. This problem drives the need for an analytical framework that can quantify the safety of personally identifiable information (privacy) while still providing a quantifable benefit (utility) to multiple legitimate information consumers. This paper presents an information-theoretic framework that promises an analytical model guaranteeing tight bounds of how much utility is possible for a given level of privacy and vice-versa. Specific contributions include: i) stochastic data models for both categorical and numerical data; ii) utility-privacy tradeoff regions and the encoding (sanization) schemes achieving them for both classes and their practical relevance; and iii) modeling of prior knowledge at the user and/or data source and optimal encoding schemes for both cases.

• The paper presents a rigorous framework that quantifies the tradeoff between data utility and privacy using rate-distortion theory and equivocation measures.
• It models numerical and categorical data through distortion metrics and mutual information to define feasible utility-privacy regions.
• The study proposes practical encoding schemes based on quantization techniques to achieve an optimal balance between preserving data utility and ensuring privacy.

An Information-Theoretic Framework for Utility-Privacy Tradeoffs in Databases

The paper explores an analytical approach to balancing data utility and privacy using information-theory in database systems. The authors, Lalitha Sankar, S. Raj Rajagopalan, and H. Vincent Poor, provide a rigorous framework that addresses how much utility can be achieved for a particular degree of privacy protection and vice versa. The use of information-theoretic tools, particularly rate-distortion theory and equivocation, grounds the analysis in a technical domain focused on quantifying the relationship between data usefulness and the risk of privacy loss.

The key contributions of this research can be described as follows:

1. Stochastic Data Models: The paper proposes models for both numerical and categorical data where data utility is formalized using distortion metrics, while privacy is characterized by information leakage, measured via mutual information or equivocation.
2. Utility-Privacy Tradeoff Regions: The paper develops what it calls the U-P tradeoff region, which comprises of all feasible combinations of utility (quantified as distortion) and privacy (quantified as equivocation). The characteristic tradeoff is achieved by employing rate-distortion theory with an additional privacy constraint, formulated as the conditional entropy of private attributes.
3. Encoding Schemes: Specific schemes for encoding or sanitizing data are suggested, which achieve these tradeoff regions. The paper utilizes quantization techniques, which are aligned with rate-distortion principles, to handle the transformation of data into sanitized forms that balance privacy and utility most effectively.

The theoretical underpinning of this research posits that for datasets, particularly when modeled as sequences or vectors of random variables, there exists an inherent utility in making data available while simultaneously ensuring privacy through methods like data sanitization. The research shows that encoding schemes based on rate-distortion theory can be adapted to include privacy constraints by considering both utility and privacy in terms of statistical distributions associated with data attributes.

One of the paper's striking features is its treatment of the data as i.i.d. generated by a source with a specific joint probability distribution, and the authors thoroughly analyze the implications of this assumption. This allows the analytical developments and encoding schemes to be leveraged across varying applications and datasets, given the assumption holds.

Illustrative examples like categorical databases using a generalized Hamming distortion, and numerical databases with Gaussian-distributed attributes, showcase practical applications of these principles. Furthermore, robust solutions are proposed to prevent information leakage, focusing on the suppression and distortion of data to maintain privacy amidst reliable utility.

In practice, the paper suggests that information-theoretic privacy frameworks are a viable and necessary avenue for addressing modern data security concerns in databases. Concepts such as quantize-and-bin for encoding databases reveal pathways that future developments can build upon, particularly as databases become increasingly integrated across sectors dealing with sensitive information.

Theoretical implications suggest that the balancing act between privacy and utility can indeed be quantified, allowing database engineers and information theorists to implement mathematical guarantees around data privacy. Future research could delve into areas not covered by this work, such as non-identically distributed data sources, adaptive data models, and more practical algorithms to simplify the adaptation of these theories into real-world systems, all of which would likely benefit from the foundational work elucidated in this paper.