PriPL-Tree: Accurate Range Query for Arbitrary Distribution under Local Differential Privacy

TL;DR

PriPL-Tree is a new data structure that improves the accuracy of range queries under Local Differential Privacy by modeling arbitrary data distributions with hierarchical trees and adaptive grids.

Contribution

It introduces PriPL-Tree, a novel hierarchical data structure combining piecewise linear functions and adaptive grids for accurate range queries under LDP.

Findings

Outperforms existing solutions in accuracy on real datasets

Effectively models arbitrary data distributions with few line segments

Extends to multi-dimensional data with adaptive grid partitioning

Abstract

Answering range queries in the context of Local Differential Privacy (LDP) is a widely studied problem in Online Analytical Processing (OLAP). Existing LDP solutions all assume a uniform data distribution within each domain partition, which may not align with real-world scenarios where data distribution is varied, resulting in inaccurate estimates. To address this problem, we introduce PriPL-Tree, a novel data structure that combines hierarchical tree structures with piecewise linear (PL) functions to answer range queries for arbitrary distributions. PriPL-Tree precisely models the underlying data distribution with a few line segments, leading to more accurate results for range queries. Furthermore, we extend it to multi-dimensional cases with novel data-aware adaptive grids. These grids leverage the insights from marginal distributions obtained through PriPL-Trees to partition the grids adaptively, adapting the density of underlying distributions. Our extensive experiments on both real and synthetic datasets demonstrate the effectiveness and superiority of PriPL-Tree over state-of-the-art solutions in answering range queries across arbitrary data distributions.