On rate optimal private regression under local differential privacy

TL;DR

This paper introduces a new method for private regression estimation under local differential privacy, achieving optimal convergence rates without requiring strong density assumptions on the data distribution.

Contribution

It proposes a novel partitioning estimator for regression under local differential privacy and establishes matching upper and lower bounds for the convergence rate.

Findings

Achieves rate optimality in private regression estimation.

Removes the need for strong density assumptions on the design distribution.

Provides theoretical guarantees with matching lower bounds.

Abstract

We consider the problem of estimating a regression function from anonymized data in the framework of local differential privacy. We propose a novel partitioning estimate of the regression function, derive a rate of convergence for the excess prediction risk over H\"older classes, and prove a matching lower bound. In contrast to the existing literature on the problem the so-called strong density assumption on the design distribution is obsolete.