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 H\"older 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.

翻译：我们考虑从本地差异隐私框架内匿名数据估算回归函数的问题。 我们提议对回归函数进行新的分割估计,得出H\'olders类超常预测风险的趋同率,并证明匹配的下限。 与现有文献相比,在设计分布方面不需要额外的假设,而无需匿名。