  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.
