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

arXiv: https://arxiv.org/abs/2602.16436 · HTML: https://mlsanity.com/paper/2602.16436/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 27 references that are in the map.
- First posted on arXiv 18 Feb 2026.

## Builds on (most cited first, 8 of 8)

- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Membership Inference Attacks on Machine Learning: A Survey](https://mlsanity.com/paper/2103.07853/) (2021)
- [Minimax Optimal Procedures for Locally Private Estimation](https://mlsanity.com/paper/1604.02390/) (2016)
- [Unified Optimal Analysis of the (Stochastic) Gradient Method](https://mlsanity.com/paper/1907.04232/) (2019)
- [Empirical Risk Minimization in Non-interactive Local Differential Privacy: Efficiency and High Dimensional Case](https://mlsanity.com/paper/1802.04085/) (2018)
- [Collect at Once, Use Effectively: Making Non-interactive Locally Private Learning Possible](https://mlsanity.com/paper/1706.03316/) (2017)
- [Noninteractive Locally Private Learning of Linear Models via Polynomial Approximations](https://mlsanity.com/paper/1812.06825/) (2018)
- [Minimax Excess Risk of First-Order Methods for Statistical Learning with Data-Dependent Oracles](https://mlsanity.com/paper/2307.04679/) (2023)

## Abstract (arXiv)

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 O(1/n), with n the number of examples. We empirically validate IWP-SGD on binary classification tasks using synthetic and real-world datasets.