Title: Federated Learning of Quantile Inference under Local Differential Privacy
Primary area: alignment, fairness, safety, privacy, and societal considerations
Keywords: Confidence interval; Federated learning; Local differential privacy; Quantile; Self-normalization

Abstract: In this paper, we investigate federated learning for quantile inference under local differential privacy (LDP). We propose an estimator based on local stochastic gradient descent (SGD), whose local gradients are perturbed via a randomized mechanism with global parameters, making the procedure tolerant of communication and storage constraints without compromising statistical efficiency. Although the quantile loss and its corresponding gradient do not satisfy standard smoothness conditions typically assumed in existing literature, we establish asymptotic normality for our estimator as well as a functional central limit theorem. The proposed method accommodates data heterogeneity and allows each server to operate with an individual privacy budget. Furthermore, we construct confidence intervals for the target value through a self‐normalization approach, thereby circumventing the need to estimate additional nuisance parameters. Extensive numerical experiments and real data application validate the theoretical guarantees of the proposed methodology.

TL;DR: We consider the statistical inference of federated learning for quantile loss via local stochastic gradient decent under local differential privacy