InfTDA: A Simple TopDown Mechanism for Hierarchical Differentially Private Counting Queries

TL;DR

This paper generalizes the InfTDA mechanism to handle any dataset with categorical features, providing differentially private synthetic data that accurately answers hierarchical queries, extending prior work on mobility datasets.

Contribution

It introduces a versatile, differentially private algorithm for hierarchical query answering applicable to various datasets, building on the TopDown mechanism from the 2020 US Census.

Findings

Produces synthetic datasets with bounded error for hierarchical queries

Extends InfTDA to general datasets with categorical features

Builds on and generalizes the TopDown mechanism

Abstract

This paper extends $\texttt{InfTDA}$, a mechanism proposed in (Boninsegna, Silvestri, PETS 2025) for mobility datasets with origin and destination trips, in a general setting. The algorithm presented in this paper works for any dataset of $d$ categorical features and produces a differentially private synthetic dataset that answers all hierarchical queries, a special case of marginals, each with bounded maximum absolute error. The algorithm builds upon the TopDown mechanism developed for the 2020 US Census.