Versatile differentially private learning for general loss functions
提出基于零膨胀对称多元拉普拉斯噪声的隐私机制，支持一般损失函数下的参数估计与统计推断，无需预先指定分析任务，适用于在线场景，并扩展了局部差分隐私框架。
This paper aims to provide a versatile privacy-preserving release mechanism along with a unified approach for subsequent parameter estimation and statistical inference. We propose a privacy mechanism based on zero-inflated symmetric multivariate Laplace (ZIL) noise, which requires no prior specification of subsequent analysis tasks, allows for general loss functions under minimal conditions, imposes no limit on the number of analyses, and is adaptable to increasing data volume in online scenarios. We derive the trade-off function for the proposed ZIL mechanism, which characterizes its privacy protection level. Furthermore, to formalize the local differential privacy (LDP) property of the ZIL mechanism, we extend the classical ε-LDP to a more general f-LDP framework. To address scenarios where only individual attribute values require protection, we propose attribute-level differential privacy (ADP) and its local version. Within the M-estimation framework, we introduce a novel doubly random (DR) corrected loss for the ZIL mechanism, which yields consistent and asymptotically normal M-estimates under differential privacy constraints. The proposed approach is computationally efficient and does not require numerical integration or differentiation for noisy data. It applies to a broad class of loss functions, including nonsmooth ones. Two alternative estimators for smooth loss are also proposed with asymptotic properties. The cost of privacy in terms of estimation efficiency for these three estimators is evaluated both theoretically and numerically.