On rate optimal private regression under local differential privacy
share
We consider the problem of estimating a regression function from anonymised 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 no extra assumption on the design distribution as compared to the setup without anonymisation is needed.
READ FULL TEXT