Minimax And Adaptive Transfer Learning for Nonparametric Classification under Distributed Differential Privacy Constraints

TL;DR

This paper develops minimax and adaptive transfer learning methods for nonparametric classification under distributed differential privacy constraints, revealing phase transitions and trade-offs between privacy and accuracy.

Contribution

It establishes the minimax misclassification rate under privacy constraints and proposes an adaptive classifier that attains near-optimal rates across diverse settings.

Findings

Characterized the minimax misclassification rate considering privacy and data heterogeneity.

Discovered phase transition phenomena in privacy-accuracy trade-offs.

Proposed an adaptive classifier achieving near-optimal performance across parameter spaces.

Abstract

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.