We initiate the study of locally differentially private (LDP) learning with public features. We define semi-feature LDP, where some features are publicly available while the remaining ones, along with the label, require protection under local differential privacy. Under semi-feature LDP, we demonstrate that the mini-max convergence rate for non-parametric regression is significantly reduced compared to that of classical LDP. Then we propose HistOfTree, an estimator that fully leverages the information contained in both public and private features. Theoretically, HistOfTree reaches the mini-max optimal convergence rate. Empirically, HistOfTree achieves superior performance on both synthetic and real data. We also explore scenarios where users have the flexibility to select features for protection manually. In such cases, we propose an estimator and a data-driven parameter tuning strategy, leading to analogous theoretical and empirical results.

本文首次探索在公共特征下的局部差分隐私（LDP）学习，提出半特征LDP概念，证明了半特征LDP下的非参数回归的最小最大收敛速度明显降低，然后介绍了HistOfTree估计器，完全利用公共和私有特征信息，在理论上实现最小最大收敛速度，实证结果表明HistOfTree在合成数据和真实数据中达到了优越性能，同时还探讨了用户手动选择保护特征的情况，在这种情况下，提出了一个估计器和数据驱动的参数调整策略，导致了类似的理论和实证结果。

使用公共特征的本地隐私估计