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

• URL: http://arxiv.org/abs/2602.16436v1
• Date: Wed, 18 Feb 2026 13:13:43 GMT
• Title: Learning with Locally Private Examples by Inverse Weierstrass Private Stochastic Gradient Descent
• Authors: Jean Dufraiche, Paul Mangold, Michaël Perrot, Marc Tommasi,
• Abstract summary: We use the Weierstrass transform to characterize this bias in binary classification.<n>We build a novel gradient descent algorithm called Inverse Weierstrass Private SGD.<n>We empirically validate IWP-SGD on binary classification tasks using synthetic and real-world datasets.
• Score: 9.706390554730126
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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