Formal Privacy for Complex Data Objects

这项研究项目将开发保护隐私和共享大型、复杂和高度结构化的数据和模型的统计方法。这些类型的数据通常在金融、纵向研究、可穿戴设备研究、医学成像和电子健康记录中遇到。复杂的数据对保护受试者的隐私提出了巨大的挑战，同时使数据公开将促进科学理解和政策制定。该项目将对统计数据隐私及其所依赖的领域，如统计学和计算机科学，作出重大的理论和方法贡献。现在，大公司和政府机构正在采用正式的隐私工具来共享数据摘要。这项研究将证明，即使是大型的复杂结构，如人脸，如果得到适当的利用，也可以成为私人结构。将要开发的方法将在社会、行为和经济科学、医学研究和工业中得到应用。研究人员将指导一名博士后研究员，以及研究生和本科生。这个跨学科的研究项目将在统计披露限制、差异隐私和功能数据分析方面改进方法，以开发正式的隐私工具。这些工具在大数据时代至关重要。该项目将集中于三个目标：(1)为无限维线性空间中的物体，特别是功能和表面开发隐私工具。这些工具将包括非高斯扰动、指数机制，以及对函数主成分和回归的特别关注，因为它们在函数数据分析中占有重要地位；(2)开发可描述为黎曼流形的非线性空间中对象的建模和共享的隐私机制。当处理3D图像、形状、协方差矩阵或大规模时空数据时，这样的数据自然产生。流形结构将被用来开发扰动方法，特别是高斯方法，以产生具有更大统计实用性的代表性清洁估计和数据；(3)为来自无限维线性空间或非线性流形的样本开发合成数据机制。合成数据对于加快科学进步，同时保持数据隐私正变得越来越关键。然而，产生适当地模仿这里描述的复杂结构的合成数据仍然是一个主要的开放问题。这个项目代表了利用非线性空间来增加由此产生的净化估计和数据的效用的一些首创工作。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This research project will develop statistical methodology for preserving privacy and sharing of large, complex, and highly structured data and models. These types of data are commonly encountered in finance, longitudinal studies, wearable device studies, medical imaging, and electronic health records. Complex data present substantial challenges for preserving subjects' privacy while making data that will advance scientific understanding and policy making publicly available. The project will make major theoretical and methodological contributions to statistical data privacy and to the fields it relies on, such as statistics and computer science. Formal privacy tools now are being adopted by major companies and government agencies for sharing data summaries. This research will demonstrate how even large complex structures, such as human faces, can be made private if that structure is properly exploited. The methods to be developed will have applications in the social, behavioral, and economic sciences, medical research, and industry. The investigators will mentor a post-doctoral researcher, as well as graduate and undergraduate students. Open-source software packages will be developed and made publicly available.This interdisciplinary research project will improve upon methods in statistical disclosure limitation, differential privacy, and functional data analysis to develop formal privacy tools. These tools are essential in the era of big data. The project will focus on three aims: (1) Development of privacy tools for objects in infinite-dimensional linear spaces, especially functions and surfaces. These tools will include non-Gaussian perturbations, exponential mechanisms, and a special focus on functional principal components and regression, given their prominence in functional data analysis; (2) Development of privacy mechanisms for modeling and sharing of objects in nonlinear spaces that can be described as Riemannian manifolds. Such data arises naturally when working with 3D images, shapes, covariance matrices, or large scale spatio-temporal data. The manifold structure will be used to develop perturbation methods, especially Gaussian, that produce representative sanitized estimates and data with greater statistical utility; (3) Development of synthetic data mechanisms for samples from infinite dimensional linear spaces or nonlinear manifolds. Synthetic data are becoming increasingly critical for expediting scientific progress while maintaining data privacy. However, producing synthetic data that properly mimics the complex structures described here remains a major open problem. This project represents some of the first work that exploits nonlinear spaces to increase the utility of the resulting sanitized estimates and data.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.