Minimax rate for multivariate data under componentwise local differential privacy constraints
Abstract
Our research analyses the trade-off between maintaining privacy and preserving statistical accuracy when dealing with multivariate data subject to componentwise local differential privacy (CLDP). Under CLDP, each component of the private data is released through a separate privacy channel. This allows for varying levels of privacy protection for different components or for the privatization of each component by different entities, each with their own distinct privacy policies. It also covers practical situations where it is impossible to privatize all components of the raw data jointly. We develop general techniques for establishing minimax bounds that quantify the statistical cost of privacy as a function of the privacy levels of the d components. The versatility and efficiency of these techniques are demonstrated through various statistical applications. Specifically, we examine nonparametric density estimation and joint moments estimation under CLDP, providing upper and lower bounds that match up to constant factors, along with an associated data-driven adaptive procedure. We also conduct a detailed analysis of the effective privacy level, exploring how information about a private characteristic of an individual may be inferred from the publicly visible characteristics of the same individual.
About the speaker
Chiara Amorino is currently an Assistant Professor in the Statistics Group at Universitat Pompeu Fabra in Barcelona, a position she has held since April 2024. In 2025, she was awarded the prestigious Ramón y Cajal Fellowship in Mathematics, a five-year individual grant from the Spanish Ministry of Economy, Industry and Competitiveness. Since 2024, she has also served as Chair of the Bernoulli Young Researchers Committee for Europe. Before joining UPF, she was a postdoctoral researcher at the University of Luxembourg in the group of Prof. Mark Podolskij. She earned her PhD in Mathematics from Université Paris-Saclay (LaMME) under the supervision of Prof. Arnaud Gloter, defending her thesis in July 2020. Her research interests include statistical inference for stochastic differential equations, interacting particle systems, Hawkes processes, fractional processes, and local differential privacy.