On rate optimal private regression under local differential privacy

2022/05/31 by László Györfi, Györfi, László, Martin H. Kroll +1
Computer Science · #FOS: Mathematics #Privacy-Preserving Technologies in Data #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2206.00114

openalex publication_date 2022/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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contrast to the existing literature on the problem the so-called strong density assumption on the design distribution is obsolete.

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