Statistical Properties of Privacy-Preserving Algorithms: Optimality, Adaptivity, and Stability

大规模数据分析的日益普及引发了对隐私的担忧。搜索引擎、社交网络平台和医疗机构等数据管理员收集的大量数据包含有关个人的潜在敏感信息。随着数据驱动技术的迅速出现，尊重个人隐私变得越来越重要。一个核心问题是：如何构建隐私保护算法来保护个人隐私，同时又不会在很大程度上牺牲效用？该项目旨在开发严格的工具和方法来分析隐私保护算法。本课题的研究目标是发展隐私保护算法的统计理论和应用。具体而言，技术目标包括：(1)参数模型中隐私保护算法的统计最优性；(2)非参数回归中隐私保护算法的统计最优性和自适应性，重点研究了随机森林算法；(3)隐私保护算法的稳定性及其在后选择推理中的应用和深度神经网络的对抗鲁棒性。新的理论理解不仅将阐明当前的隐私保护方法，而且还将导致稳定和对抗鲁棒算法的新方法发展。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The increasing popularity of large-scale data analysis raises privacy concerns. The tremendous amount of data collected by data curators such as search engines, social network platforms, and medical institutions contain potentially sensitive information about individuals. With the rapid emergence of data-driven technologies, it has been increasingly important to respect the privacy of individuals. A central question is: how to build privacy-preserving algorithms to protect individual privacy without sacrificing the utility in a large degree? This project aims to develop rigorous tools and methodologies to analyze privacy-preserving algorithms. The research objective of this project is to develop statistical theories and applications of privacy-preserving algorithms. In particular, the technical goals include (1) the statistical optimality of privacy-preserving algorithms in parametric models; (2) the statistical optimality and adaptivity of privacy-preserving algorithms in nonparametric regression, with focus on random forests algorithms, and; (3) the stability of privacy-preserving algorithms with applications to post-selection inference and adversarial robustness of deep neural networks. The new theoretical understandings will not only shed light on current privacy-preserving methodologies but also lead to new methodological developments of stable and adversarially robust algorithms.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.