PrivTree: A Differentially Private Algorithm for Hierarchical Decompositions
Jun Zhang, Xiaokui Xiao, Xing Xie

TL;DR
PrivTree introduces a novel hierarchical decomposition algorithm for differentially private histograms that adaptively determines splits without fixed depth limits, significantly improving data utility over existing methods.
Contribution
It presents PrivTree, a hierarchical decomposition algorithm that decouples noise from recursion depth, enabling adaptive, high-quality histograms without pre-set depth constraints.
Findings
PrivTree outperforms existing methods in data utility on real datasets.
The algorithm effectively models spatial and sequence data.
It maintains differential privacy while providing accurate data representations.
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…
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Taxonomy
TopicsCryptography and Data Security · Privacy-Preserving Technologies in Data · Complexity and Algorithms in Graphs
