A central direction of theoretical LDP research is to design mechanisms that provide better data utility under the same privacy guarantee. This dissertation focuses on the cental direction, advancing the design of LDP mechanisms and the analysis of data utility under LDP. Technically, it introduces correlated perturbation into LDP, establishes optimality of piecewise-based mechanisms, and makes a first step to quantify classifiers' utility under LDP-perturbed inputs.

本文关注神经网络验证方法中界限传播方法的精度问题。关于此问题，本文提出界限传播路径的概念，将各种界限传播方法扩展到其对应的多路径界限传播方法；此外，本文将多路径界限传播在 PyTorch 框架上并行化，开发了高效而易用的鲁棒性验证工具。