Learning with Locally Private Examples by Inverse Weierstrass Private Stochastic Gradient Descent

Fuente: arXiv
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Main Authors: Dufraiche, Jean, Mangold, Paul, Perrot, Michaël, Tommasi, Marc
Format: Preprint
Published: 2026
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author Dufraiche, Jean
Mangold, Paul
Perrot, Michaël
Tommasi, Marc
author_facet Dufraiche, Jean
Mangold, Paul
Perrot, Michaël
Tommasi, Marc
contents Releasing data once and for all under noninteractive Local Differential Privacy (LDP) enables complete data reusability, but the resulting noise may create bias in subsequent analyses. In this work, we leverage the Weierstrass transform to characterize this bias in binary classification. We prove that inverting this transform leads to a bias-correction method to compute unbiased estimates of nonlinear functions on examples released under LDP. We then build a novel stochastic gradient descent algorithm called Inverse Weierstrass Private SGD (IWP-SGD). It converges to the true population risk minimizer at a rate of $\mathcal{O}(1/n)$, with $n$ the number of examples. We empirically validate IWP-SGD on binary classification tasks using synthetic and real-world datasets.
format Preprint
id arxiv_https___arxiv_org_abs_2602_16436
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Learning with Locally Private Examples by Inverse Weierstrass Private Stochastic Gradient Descent
Dufraiche, Jean
Mangold, Paul
Perrot, Michaël
Tommasi, Marc
Machine Learning
Cryptography and Security
Releasing data once and for all under noninteractive Local Differential Privacy (LDP) enables complete data reusability, but the resulting noise may create bias in subsequent analyses. In this work, we leverage the Weierstrass transform to characterize this bias in binary classification. We prove that inverting this transform leads to a bias-correction method to compute unbiased estimates of nonlinear functions on examples released under LDP. We then build a novel stochastic gradient descent algorithm called Inverse Weierstrass Private SGD (IWP-SGD). It converges to the true population risk minimizer at a rate of $\mathcal{O}(1/n)$, with $n$ the number of examples. We empirically validate IWP-SGD on binary classification tasks using synthetic and real-world datasets.
title Learning with Locally Private Examples by Inverse Weierstrass Private Stochastic Gradient Descent
topic Machine Learning
Cryptography and Security
url https://arxiv.org/abs/2602.16436