PrivTree: A Differentially Private Algorithm for Hierarchical Decompositions (1601.03229v2)

Abstract: Given a set D of tuples defined on a domain Omega, we study differentially private algorithms for constructing a histogram over Omega to approximate the tuple distribution in D. Existing solutions for the problem mostly adopt a hierarchical decomposition approach, which recursively splits Omega into sub-domains and computes a noisy tuple count for each sub-domain, until all noisy counts are below a certain threshold. This approach, however, requires that we (i) impose a limit h on the recursion depth in the splitting of Omega and (ii) set the noise in each count to be proportional to h. This leads to inferior data utility due to the following dilemma: if we use a small h, then the resulting histogram would be too coarse-grained to provide an accurate approximation of data distribution; meanwhile, a large h would yield a fine-grained histogram, but its quality would be severely degraded by the increased amount of noise in the tuple counts. To remedy the deficiency of existing solutions, we present PrivTree, a histogram construction algorithm that also applies hierarchical decomposition but features a crucial (and somewhat surprising) improvement: when deciding whether or not to split a sub-domain, the amount of noise required in the corresponding tuple count is independent of the recursive depth. This enables PrivTree to adaptively generate high-quality histograms without even asking for a pre-defined threshold on the depth of sub-domain splitting. As concrete examples, we demonstrate an application of PrivTree in modelling spatial data, and show that it can also be extended to handle sequence data (where the decision in sub-domain splitting is not based on tuple counts but a more sophisticated measure). Our experiments on a variety of real datasets show that PrivTree significantly outperforms the states of the art in terms of data utility.

• The paper introduces PrivTree, a differential privacy algorithm that decouples noise magnitude from recursion depth in hierarchical decompositions, offering constant noise for fine-grained data utility.
• PrivTree employs a novel biased count mechanism and Laplace noise addition to balance noise impact and enable robust sub-domain decision making.
• Experimental validation shows PrivTree outperforms existing methods on real spatial and sequence datasets, proving its efficiency and adaptability.

Overview of PrivTree: A Differentially Private Algorithm for Hierarchical Decompositions

The paper "PrivTree: A Differentially Private Algorithm for Hierarchical Decompositions" presents a novel approach to constructing differentially private histograms over multi-dimensional data domains. This research addresses the critical issue of a predefined recursion depth, denoted as $h$, which impacts the granularity and privacy guarantees of hierarchical decomposition-based algorithms. PrivTree eliminates this dependency on $h$ and introduces a more flexible and effective mechanism for data privacy.

Summary of Findings

At the core of PrivTree is a mechanism leveraging properties of the Laplace distribution to control noise levels independently of recursion depth $h$. The traditional approach, which dictates that noise magnitude is proportional to $h$, results in a trade-off between resolution and privacy. PrivTree circumvents this challenge by using a novel biased count and noise addition strategy, enabling fine-grained decompositions with constant noise magnitude irrespective of $h$. This advancement is particularly impactful for handling skewed data distributions, where previous heuristic methods were insufficient.

The paper demonstrates PrivTree's applicability across both spatial and sequence data, showcasing its flexibility through extensive experimentation on real-world datasets. The results indicate that PrivTree consistently outperforms existing state-of-the-art techniques in terms of data utility, making bold claims about its efficiency advantages and adaptability.

Technical Contributions

1. Decoupling Noise Levels from Recursion Depth: PrivTree introduces a constant noise addition strategy, using a novel analysis based on Laplace noise characteristics. This method ensures different levels of granularity without violating differential privacy constraints.
2. Biased Count Mechanism: The paper develops a technique where node counts are adjusted by a decaying factor related to their depth, effectively balancing the potential impact of noise on sub-domain decision making.
3. Application Across Domains:
   • Spatial Data: PrivTree generates private spatial decompositions using adaptable quadtree structures to efficiently process range count queries, overcoming limitations of previous hierarchical methods.
   • Sequence Data: Extensions of PrivTree to Markov models for sequence data allow for improved handling of complex prediction tasks and sequence generation.
4. Extensive Experimental Validation: The authors present a thorough performance evaluation on various real datasets, substantiating their claims of superior data utility and proving PrivTree's efficacy across diverse query types and workloads.

Implications and Future Work

The implications of this research are broad. PrivTree offers a scalable and privacy-resilient solution for multi-dimensional data analysis, with immediate applications in areas requiring fine-grained histograms and data distributions under privacy constraints. Moreover, the mechanisms introduced, specifically the unbiased count approach, have potential in optimizing other privacy-preserving tasks beyond hierarchical decompositions.

Future work could explore more complex data topologies, extend the PrivTree mechanism to operate with user-defined privacy budgets, and further integrate machine learning models that require adaptive data decomposition schemes. Additionally, the paper opens avenues for refining sensitivity calculations in differential privacy implementations to minimize information leakage while maximizing data utility.

Overall, "PrivTree: A Differentially Private Algorithm for Hierarchical Decompositions" advances the state of differential privacy by presenting a robust method for hierarchical data partitioning, effectively addressing long-standing challenges in data granularity and privacy assurance.