# Locally Private Estimation with Public Features

arXiv: https://arxiv.org/abs/2405.13481 · HTML: https://mlsanity.com/paper/2405.13481/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 48 references that are in the map.
- First posted on arXiv 22 May 2024.

## Builds on (most cited first, 15 of 15)

- [RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Response](https://mlsanity.com/paper/1407.6981/) (2014)
- [Deep Learning with Label Differential Privacy](https://mlsanity.com/paper/2102.06062/) (2021)
- [Minimax Optimal Procedures for Locally Private Estimation](https://mlsanity.com/paper/1604.02390/) (2016)
- [Discrete Distribution Estimation under Local Privacy](https://mlsanity.com/paper/1602.07387/) (2016)
- [Antipodes of Label Differential Privacy: PATE and ALIBI](https://mlsanity.com/paper/2106.03408/) (2021)
- [Dark Patterns after the GDPR: Scraping Consent Pop-ups and Demonstrating their Influence](https://mlsanity.com/paper/2001.02479/) (2020)
- [Regression with Label Differential Privacy](https://mlsanity.com/paper/2212.06074/) (2022)
- [GeoPointGAN: Synthetic Spatial Data with Local Label Differential Privacy](https://mlsanity.com/paper/2205.08886/) (2022)
- [Strongly universally consistent nonparametric regression and classification with privatised data](https://mlsanity.com/paper/2011.00216/) (2020)
- [Optimal Locally Private Nonparametric Classification with Public Data](https://mlsanity.com/paper/2311.11369/) (2023)
- [Private Learning with Public Features](https://mlsanity.com/paper/2310.15454/) (2023)
- [Optimal Unbiased Randomizers for Regression with Label Differential Privacy](https://mlsanity.com/paper/2312.05659/) (2023)
- [Training Differentially Private Ad Prediction Models with Semi-Sensitive Features](https://mlsanity.com/paper/2401.15246/) (2024)
- [Classification with Partially Private Features](https://mlsanity.com/paper/2312.07583/) (2023)
- [Private Matrix Factorization with Public Item Features](https://mlsanity.com/paper/2309.11516/) (2023)

## Built on by (most cited first, 3 of 3)

- [Better Locally Private Sparse Estimation Given Multiple Samples Per User](https://mlsanity.com/paper/2408.04313/) (2024)
- [On Theoretical Limits of Learning with Label Differential Privacy](https://mlsanity.com/paper/2502.14309/) (2025)
- [Locally Private Nonparametric Contextual Multi-armed Bandits](https://mlsanity.com/paper/2503.08098/) (2025)

## Abstract (arXiv)

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.