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.

翻译：我们首次研究了具有公共特征的本地差分隐私（LDP）学习。我们定义了半特征LDP，其中部分特征是公开可用的，而其余特征以及标签需要在本地差分隐私下进行保护。在半特征LDP下，我们证明了非参数回归的极小极大收敛率相较于经典LDP显著降低。随后，我们提出了HistOfTree，一种能够充分利用公共和私有特征中所含信息的估计器。理论上，HistOfTree达到了极小极大最优收敛率。实证上，HistOfTree在合成数据和真实数据上均表现出优越的性能。我们还探讨了用户可以灵活手动选择特征进行保护的情景。在此类情况下，我们提出了一种估计器及一种数据驱动的参数调优策略，从而得出了类似的理论和实证结果。