# Optimal Locally Private Nonparametric Classification with Public Data

arXiv: https://arxiv.org/abs/2311.11369 · HTML: https://mlsanity.com/paper/2311.11369/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 78 references that are in the map.
- First posted on arXiv 19 Nov 2023.

## Builds on (most cited first, 8 of 8)

- [A survey on domain adaptation theory: learning bounds and theoretical guarantees](https://mlsanity.com/paper/2004.11829/) (2020)
- [Position: Considerations for Differentially Private Learning with Large-Scale Public Pretraining](https://mlsanity.com/paper/2212.06470/) (2022)
- [Training Production Language Models without Memorizing User Data](https://mlsanity.com/paper/2009.10031/) (2020)
- [Privacy Loss in Apple's Implementation of Differential Privacy on MacOS 10.12](https://mlsanity.com/paper/1709.02753/) (2017)
- [Selective Pre-training for Private Fine-tuning](https://mlsanity.com/paper/2305.13865/) (2023)
- [Choosing Public Datasets for Private Machine Learning via Gradient Subspace Distance](https://mlsanity.com/paper/2303.01256/) (2023)
- [Classification under local differential privacy](https://mlsanity.com/paper/1912.04629/) (2019)
- [Optimal Differentially Private Model Training with Public Data](https://mlsanity.com/paper/2306.15056/) (2023)

## Built on by (most cited first, 7 of 7)

- [Minimax And Adaptive Transfer Learning for Nonparametric Classification under Distributed Differential Privacy Constraints](https://mlsanity.com/paper/2406.20088/) (2024)
- [Locally Private Estimation with Public Features](https://mlsanity.com/paper/2405.13481/) (2024)
- [Mitigating Privacy-Utility Trade-off in Decentralized Federated Learning via f-Differential Privacy](https://mlsanity.com/paper/2510.19934/) (2025)
- [Better Locally Private Sparse Estimation Given Multiple Samples Per User](https://mlsanity.com/paper/2408.04313/) (2024)
- [Locally Private Nonparametric Contextual Multi-armed Bandits](https://mlsanity.com/paper/2503.08098/) (2025)
- [PrAda-GAN: A Private Adaptive Generative Adversarial Network with Bayes Network Structure](https://mlsanity.com/paper/2511.07997/) (2025)
- [Classification Under Local Differential Privacy with Model Reversal and Model Averaging](https://mlsanity.com/paper/2602.05797/) (2026)

## Abstract (arXiv)

In this work, we investigate the problem of public data assisted non-interactive Local Differentially Private (LDP) learning with a focus on non-parametric classification. Under the posterior drift assumption, we for the first time derive the mini-max optimal convergence rate with LDP constraint. Then, we present a novel approach, the locally differentially private classification tree, which attains the mini-max optimal convergence rate. Furthermore, we design a data-driven pruning procedure that avoids parameter tuning and provides a fast converging estimator. Comprehensive experiments conducted on synthetic and real data sets show the superior performance of our proposed methods. Both our theoretical and experimental findings demonstrate the effectiveness of public data compared to private data, which leads to practical suggestions for prioritizing non-private data collection.