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arXiv · 2206.00114

On rate optimal private regression under local differential privacy

László Györfi·Martin Kroll
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Abstract

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 H\"older 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contrast to the existing literature on the problem the so-called strong density assumption on the design distribution is obsolete.

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László Györfi, Martin Kroll. 2022-05-31. On rate optimal private regression under local differential privacy. https://arxiv.org/abs/2206.00114

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