Learning with Locally Private Examples by Inverse Weierstrass Private Stochastic Gradient Descent
This work addresses bias correction for data reuse in LDP, which is an incremental improvement for privacy-preserving machine learning.
The paper tackles bias in binary classification under noninteractive Local Differential Privacy (LDP) by using the Weierstrass transform to characterize and correct this bias, resulting in the Inverse Weierstrass Private SGD (IWP-SGD) algorithm that converges to the true population risk minimizer at a rate of O(1/n).
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.