On rate optimal private regression under local differential privacy

05/31/2022

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by   László Györfi, et al.

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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.