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contrast to the existing literature on the problem the so-called strong density assumption on the design distribution is obsolete.

翻译：我们考虑在局部差分隐私框架下，从匿名数据中估计回归函数的问题。我们提出了一个新颖的回归函数分割估计，推导了在H\"older类中超额预测风险的收敛速率，并证明了相匹配的下限。与现有文献研究相比，在设计分布上的所谓强密度假设是过时的。