# Strongly universally consistent nonparametric regression and classification with privatised data

arXiv: https://arxiv.org/abs/2011.00216 · HTML: https://mlsanity.com/paper/2011.00216/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2020.

## Built on by (most cited first, 8 of 8)

- [Optimal Federated Learning for Nonparametric Regression with Heterogeneous Distributed Differential Privacy Constraints](https://mlsanity.com/paper/2406.06755/) (2024)
- [Locally Private Estimation with Public Features](https://mlsanity.com/paper/2405.13481/) (2024)
- [Learning with User-Level Local Differential Privacy](https://mlsanity.com/paper/2405.17079/) (2024)
- [About the Cost of Central Privacy in Density Estimation](https://mlsanity.com/paper/2306.14535/) (2023)
- [On Rate-Optimal Partitioning Classification from Observable and from Privatised Data](https://mlsanity.com/paper/2312.14889/) (2023)
- [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)
- [On public and private binary classification with metric space valued predictors](https://mlsanity.com/paper/2605.31184/) (2026)

## Abstract (arXiv)

In this paper we revisit the classical problem of nonparametric regression, but impose local differential privacy constraints. Under such constraints, the raw data (X1,Y1),ldots,(Xn,Yn), taking values in ℝd × ℝ, cannot be directly observed, and all estimators are functions of the randomised output from a suitable privacy mechanism. The statistician is free to choose the form of the privacy mechanism, and here we add Laplace distributed noise to a discretisation of the location of a feature vector Xi and to the value of its response variable Yi. Based on this randomised data, we design a novel estimator of the regression function, which can be viewed as a privatised version of the well-studied partitioning regression estimator. The main result is that the estimator is strongly universally consistent. Our methods and analysis also give rise to a strongly universally consistent binary classification rule for locally differentially private data.