On Rate Optimal Private Regression Under Local Differential Privacy
László Györfi, Martin Kroll · Statistica Sinica · 2023
We consider the problem of estimating a regression function from anonymized data in the framework of local differential privacy.We propose a novel partitioning estimate of the regression function, derive a rate of convergence for the excess prediction risk over Hölder classes, and prove a matching lower bound.In contrast to the existing literature on the problem the so-called strong density assumption on the design distribution is obsolete.