Differentially Private Spatial Decompositions (1103.5170v3)

Abstract: Differential privacy has recently emerged as the de facto standard for private data release. This makes it possible to provide strong theoretical guarantees on the privacy and utility of released data. While it is well-known how to release data based on counts and simple functions under this guarantee, it remains to provide general purpose techniques to release different kinds of data. In this paper, we focus on spatial data such as locations and more generally any data that can be indexed by a tree structure. Directly applying existing differential privacy methods to this type of data simply generates noise. Instead, we introduce a new class of "private spatial decompositions": these adapt standard spatial indexing methods such as quadtrees and kd-trees to provide a private description of the data distribution. Equipping such structures with differential privacy requires several steps to ensure that they provide meaningful privacy guarantees. Various primitives, such as choosing splitting points and describing the distribution of points within a region, must be done privately, and the guarantees of the different building blocks composed to provide an overall guarantee. Consequently, we expose the design space for private spatial decompositions, and analyze some key examples. Our experimental study demonstrates that it is possible to build such decompositions efficiently, and use them to answer a variety of queries privately with high accuracy.

• The paper introduces a framework that adapts spatial tree structures with differential privacy by carefully calibrating noise and optimizing node splits.
• It employs non-uniform noise allocation and post‐processing techniques, reducing query error by up to an order of magnitude.
• Experimental evaluations on real and synthetic datasets show significant improvements in balancing privacy and query accuracy over previous methods.

Analyzing Differentially Private Spatial Decompositions

The paper "Differentially Private Spatial Decompositions" by Cormode et al. addresses the challenge of releasing spatial data in a manner that preserves individual privacy while still being useful for various queries. Differential privacy, a rigorous framework for privacy-preserving data analysis, is leveraged to ensure that data output does not significantly differ based on the presence or absence of an individual.

Contributions

The primary contribution of the paper lies in the development of a framework for differentially private spatial decompositions (PSDs). These structures adapt classical spatial indexing methods, such as quadtrees and kd-trees, to ensure differential privacy. The transformation requires careful consideration of several components, such as:

• Split Selection: Ensuring that node splitting decisions in tree structures do not reveal sensitive information.
• Parameter Calibration: Introducing geometric noise allocation and post-processing techniques to optimize utility and privacy.
• Design Space Exploration: Examining various configurations of PSDs to balance query accuracy and computational efficiency.

Key Techniques and Results

1. Non-Uniform Noise Allocation: The paper proposes setting noise parameters in a geometric progression, increasing from root to leaves, which significantly improves query accuracy while maintaining privacy guarantees.
2. Post-Processing to Minimize Query Variance: By optimizing the use of noisy counts through post-processing, the researchers demonstrate a method to improve query accuracy. This technique generalizes beyond uniform noise settings and is shown to reduce query error by up to an order of magnitude in experiments.
3. Private Median Computation: Several techniques for private median calculation are evaluated, such as smooth sensitivity and the exponential mechanism, to balance privacy noise and tree structure quality. Empirical comparisons reveal that the exponential mechanism often provides the most accurate median selection for data-dependent trees.
4. Practical Implementations and Evaluation: Through experimental validation on both real and synthetic datasets, the paper demonstrates that their proposed methods outperform previous approaches significantly, achieving lower relative errors in query responses.

Implications and Future Directions

The development of PSDs has significant implications in privacy-preserving data analysis, especially for domains that rely on frequent spatial queries, such as urban planning and resource distribution. This work highlights the importance of rigorous privacy evaluations while suggesting practical methods for enhancing utility.

Looking forward, this research opens paths for several speculative investigations, including extending the framework to handle high-dimensional data more effectively and adapting the techniques for real-time scenarios where data is continuously updated.

Theoretical enhancements in differential privacy might also catalyze further practical improvements, enabling even tighter privacy budgets while maintaining desirable data utility. Indeed, the balance between computational efficiency and accuracy will continue to be a pivotal concern in advancing PSD research.