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

This paper extends $\mathtt{\text{InfTDA}}$, 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.