Privacy Amplification for Synthetic data using Range Restriction

TL;DR

This paper proposes a new range restricted privacy standard that enhances synthetic data privacy by incorporating owner beliefs about data ranges, improving privacy guarantees while maintaining data utility.

Contribution

It introduces a novel class of range restricted formal privacy standards that condition on owner beliefs, and adapts the risk-weighted pseudo posterior mechanism for stronger privacy guarantees.

Findings

Range restricted standards protect specific data subsets.

The method improves privacy guarantees with minimal utility loss.

Two approaches to incorporate owner beliefs into privacy mechanism.

Abstract

We introduce a new class of range restricted formal data privacy standards that condition on owner beliefs about sensitive data ranges. By incorporating this additional information, we can provide a stronger privacy guarantee (e.g. an amplification). The range restricted formal privacy standards protect only a subset (or ball) of data values and exclude ranges (or balls) believed to be already publicly known. The privacy standards are designed for the risk-weighted pseudo posterior (model) mechanism (PPM) used to generate synthetic data under an asymptotic Differential (aDP) privacy guarantee. The PPM downweights the likelihood contribution for each record proportionally to its disclosure risk. The PPM is adapted under inclusion of beliefs by adjusting the risk-weighted pseudo likelihood. We introduce two alternative adjustments. The first expresses data owner knowledge of the sensitive range as a probability, $\lambda$, that a datum value drawn from the underlying generating distribution lies outside the ball or subspace of values that are sensitive. The portion of each datum likelihood contribution deemed sensitive is then $(1-\lambda) \leq 1$ and is the only portion of the likelihood subject to risk down-weighting. The second adjustment encodes knowledge as the difference in probability masses $P(R) \leq 1$ between the edges of the sensitive range, $R$. We use the resulting conditional (pseudo) likelihood for a sensitive record, which boosts its worst case tail values away from 0. We compare privacy and utility properties for the PPM under the aDP and range restricted privacy standards.