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contrast to the existing literature on the problem the so-called strong density assumption on the design distribution is obsolete.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。我们提出了一种新颖的基于分区的回归函数估计方法，推导了在赫尔德类上超额预测风险的收敛速度，并证明了匹配的下界。与现有文献不同，我们摒弃了对设计分布的所谓强密度假设。