This paper considers minimax and adaptive transfer learning for nonparametric classification under the posterior drift model with distributed differential privacy constraints. Our study is conducted within a heterogeneous framework, encompassing diverse sample sizes, varying privacy parameters, and data heterogeneity across different servers. We first establish the minimax misclassification rate, precisely characterizing the effects of privacy constraints, source samples, and target samples on classification accuracy. The results reveal interesting phase transition phenomena and highlight the intricate trade-offs between preserving privacy and achieving classification accuracy. We then develop a data-driven adaptive classifier that achieves the optimal rate within a logarithmic factor across a large collection of parameter spaces while satisfying the same set of differential privacy constraints. Simulation studies and real-world data applications further elucidate the theoretical analysis with numerical results.

翻译：本文研究分布式差分隐私约束下基于后验漂移模型的非参数分类问题中的最小最大与自适应迁移学习。我们的研究在异构框架下展开，涵盖不同服务器间多样化的样本量、变化的隐私参数以及数据异质性。首先，我们建立了最小最大误分类率，精确刻画了隐私约束、源域样本与目标域样本对分类准确性的影响。研究结果揭示了有趣的相变现象，并凸显了隐私保护与分类准确性之间复杂的权衡关系。随后，我们提出了一种数据驱动的自适应分类器，该分类器在满足相同差分隐私约束的同时，能在广泛参数空间集合中以对数因子达到最优收敛速率。仿真研究与实际数据应用进一步通过数值结果验证了理论分析。