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Volume 19 Issue 3

PHDStream: Private Hierarchical Decomposition for Streaming Synthetic data

Girish Kumar^(a),(*), Thomas Strohmer^(a), Roman Vershynin^(b)

Transactions on Data Privacy 19:3 (2026) 111 - 147

Abstract, PDF

(a) Department of Mathematics, University of California, Davis, CA 95616 USA.

(b) Department of Mathematics, University of California, Irvine, CA 92697 USA.

e-mail:gkum @ucdavis.edu; @; @

Abstract

Much of the research in differential privacy has focused on offline applications with the assumption that all data is available at once. These methods cannot be applied to streams without violating the privacy guarantees or resulting in poor utility. We propose PHDStream, an algorithm for differentially private synthetic streaming data generation, especially curated towards spatial datasets. Our framework uses popular differentially private mechanisms as subroutines such as hierarchical decomposition (using PrivTree) and stream-bit-counter (using binary tree mechanism). Furthermore, we provide a general framework for online selective counting among a collection of queries, which forms a basis for many tasks such as query answering and synthetic data generation. Our algorithm comes with provable differential privacy guarantees, and its utility is verified on both real-world and simulated datasets.

^* Corresponding author.