Concentrated Differential Privacy (1603.01887v2)

Abstract: We introduce Concentrated Differential Privacy, a relaxation of Differential Privacy enjoying better accuracy than both pure differential privacy and its popular "(epsilon,delta)" relaxation without compromising on cumulative privacy loss over multiple computations.

• The paper introduces Concentrated Differential Privacy (CDP) as a relaxation of traditional DP, focusing on subgaussian modeling of privacy loss.
• It demonstrates improved composition properties, showing that repeated analyses maintain tighter overall privacy guarantees with less noise accumulation.
• The framework provides nearly optimal group privacy bounds, paving the way for accurate large-scale data analytics and real-world applications.

Overview of Concentrated Differential Privacy

The paper "Concentrated Differential Privacy" authored by Cynthia Dwork and Guy N. Rothblum introduces a new framework for privacy, termed Concentrated Differential Privacy (CDP). CDP is proposed as a relaxation of traditional Differential Privacy (DP), aiming to improve the accuracy of data analyses without sacrificing cumulative privacy guarantees over multiple computations. This paper addresses key concerns with existing DP frameworks, particularly the tension between accuracy and privacy assurance, while maintaining rigorous mathematical guarantees.

Introduction to Differential Privacy and Relaxations

Differential Privacy has been a cornerstone in the field of privacy-preserving data analysis, offering robust mathematical guarantees. The pure form of differential privacy, as expressed by the parameter $$ of exceeding the loss bound, offering improved accuracy under certain conditions.

This work highlights the limitations of traditional DP under repeated queries, where cumulative privacy loss can lead to significant distortions in analysis results due to the noise added to safeguard privacy. While $(\epsilon,\delta)$-DP improves upon pure DP in individual query settings, it still poses challenges in compositions, as repeated analyses accumulate noise, impacting data utility.

Concentrated Differential Privacy: Definition and Attributes

Concentrated Differential Privacy introduces a paradigm where the privacy loss is modeled as a random variable. CDP focuses on the expected value of this variable and its concentration around its mean, establishing that it behaves subgaussian. An algorithm is considered $(\mu,\tau)$-CDP if the privacy loss has mean $\mu$ and the centered loss is subgaussian with standard deviation $\tau$. This approach provides a better handle on cumulative privacy loss, enabling the handling of numerous analyses by focusing on tight distribution over loss rather than strict boundaries.

Composition and Group Privacy

A critical contribution of the paper is the examination of CDP under composition. The authors show that CDP mechanisms maintain their privacy advantages when composing $k$ mechanisms, with resulting privacy characterized as $(k\mu, \sqrt{k}\tau)$-CDP. This echoes the properties of advanced composition theorems but with potentially less accuracy degradation due to noise.

Furthermore, CDP naturally extends to group privacy, ensuring protection even when analyzing data from groups within the datasets. The analysis shows that under reasonable assumptions, CDP mechanisms offer nearly tight bounds for group privacy, which are almost optimal and support large-scale real-world applications where group-level insights are essential.

Practical Implications and Future Directions

The introduction of CDP holds significant promise for more nuanced privacy-preserving data analysis frameworks, particularly in settings involving extensive queries or large-scale data aggregations. Its subgaussian bounding of privacy loss provides a detailed understanding of the worst-case scenarios, enabling analysts to make informed decisions balancing trade-offs between privacy and accuracy.

Moving forward, further work could explore more practical mechanisms under the CDP framework, beyond the Gaussian mechanism already analyzed in the paper. Additionally, exploring the applicability of CDP in areas requiring high-fidelity data analyses, such as healthcare analytics and real-time personalized recommendations, could demonstrate its tangible benefits.

Overall, the proposition of Concentrated Differential Privacy marks a pivotal advancement in understanding and applying differential privacy in a more flexible and accurate manner, paving the way for its broader acceptance and utility in AI and data science.