[Paper Review] Differentially Private Hierarchical Group Size Estimation.

Yu-Hsuan Kuo, Cho-Chun Chiu+3 more|arXiv (Cornell University)|Apr 2, 2018

Privacy-Preserving Technologies in Data12 references3 citations

TL;DR

This paper introduces a differentially private solution for estimating household sizes across hierarchical geographic levels—national, state, and county—while ensuring individual privacy. It proposes a consistent estimation framework that maintains accuracy and coherence across all levels of the hierarchy using advanced noise calibration and hierarchical constraints.

ABSTRACT

Consider the problem of estimating, for every integer j, the number of households with j people in them, while protecting the privacy of individuals. Add in a geographical component, so that the household size distribution can be compared at the national, state, and county levels. This is an instance of the private hierarchical group size estimation problem, in which each group is associated with a size and a hierarchical attribute. In this paper, we introduce this problem, along with appropriate error metrics and propose a differentially private solution that generates group size estimates that are consistent across all levels of the hierarchy.

Motivation & Objective

• To address the challenge of estimating household sizes at multiple geographic levels while preserving individual privacy.
• To define a formal problem setting for hierarchical group size estimation with differential privacy guarantees.
• To develop a method that ensures consistent estimates across all levels of the hierarchy, avoiding inconsistencies common in independent estimation.
• To introduce appropriate error metrics tailored to hierarchical private estimation.
• To demonstrate that the proposed method achieves strong privacy guarantees without sacrificing estimation accuracy.

Proposed method

• The method formulates the hierarchical group size estimation problem as a constrained optimization task under differential privacy.
• It applies calibrated noise to group size counts at each level of the hierarchy to ensure (ε, δ)-differential privacy.
• The solution enforces consistency constraints across levels, ensuring that county-level estimates sum to state-level estimates, and so on up the hierarchy.
• It uses a hierarchical decomposition of the data to propagate privacy budgets efficiently across levels.
• The approach integrates a post-processing step that enforces non-negativity and sum consistency across hierarchical levels.
• It leverages a noise distribution that accounts for the hierarchical structure to minimize error while preserving privacy.

Experimental results

Research questions

• RQ1 How can we estimate household sizes at multiple geographic levels while preserving individual privacy?
• RQ2 What error metrics are most appropriate for evaluating hierarchical private group size estimation?
• RQ3 How can we ensure consistency between estimates at different levels of the hierarchy under differential privacy?
• RQ4 What is the trade-off between privacy budget allocation and estimation accuracy across hierarchical levels?
• RQ5 Can a differentially private method produce estimates that are both accurate and consistent across national, state, and county levels?

Key findings

• The proposed method achieves (ε, δ)-differential privacy across all levels of the hierarchy.
• The estimates are consistent across all levels, with county-level counts summing exactly to state-level counts and so on.
• The method maintains strong accuracy, with error bounded by the noise calibration and hierarchical constraints.
• The approach outperforms independent estimation methods by reducing inconsistency and error propagation.
• The privacy budget is allocated efficiently across levels, preserving utility while ensuring strong privacy guarantees.
• The framework is generalizable to other hierarchical group size estimation problems beyond household data.