Privacy-Preserving Bayesian Inference: Foundations and Extensions

本课题为利用差分私有数据进行贝叶斯统计推断提供了理论基础和计算方法。差分隐私是一种数学框架，它允许以这样一种方式发布潜在的敏感数据，即保护个人记录的机密性，而不会过度牺牲其对统计分析的总体有用性。随着大规模数据集的爆炸式增长，我们的社会正在努力解决隐私问题，差异隐私的发明提供了一种解决方案，可以在不阻碍公共知识积累的情况下保护个人人口统计和生物信息。美国人口普查局正式将差别隐私作为2020年人口普查的信息披露避免方法。预计在不久的将来，其他数据收集者和策展人也会效仿。本项目回应了对新的统计理论和方法的迫切需求，以适当地理解和有效地分析不同的私人数据。该项目将扩大可供研究人员使用的工具，并在尊重个人隐私的同时，为创建一个信息更灵通、更透明的社会做出贡献。PI将使用不精确的概率结构（包括度量区间和连贯的上下概率度量）研究微分隐私定义的理论公式。在贝叶斯上下文中，这样的公式提供了模型的鲁棒似然概念，并允许计算基于任意先验规范的差分私有数据的后验量的界限。PI还提出了差分私有近似贝叶斯计算（ABC）算法，这是一种嘈杂的ABC算法，在给定受任意加性噪声影响的差分私有观测值的情况下提供精确的后验推理。该算法允许从具有难处理似然的大规模贝叶斯模型中进行差分私有推理。该项目将鲁棒贝叶斯和广义贝叶斯的经典理论与统计隐私的新文献联系起来，并基于保护隐私的数据发布派生出实际实现。该项目将及时为分析人员和研究人员提供为不同私人投入量身定制的推理方法，这些方法在理论上是合理的，在计算上是有效的。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。

This project provides a theoretical foundation and computational methodologies to conduct Bayesian statistical inference using differentially private data. Differential privacy is a mathematical framework that allows the release of potentially sensitive data in such a way that protects the confidentiality of individual records without unduly sacrificing its overall usefulness for statistical analysis. As our society today grapples with the privacy implications that accompany the exploding growth of large-scale datasets, the invention of differential privacy provides a solution to protect personal demographic and biological information without deterring the accumulation of public knowledge. The U.S. Census Bureau has officially adopted differential privacy as the disclosure avoidance method for the 2020 Census. Other data collectors and curators are expected to follow suit in the near future. This project answers the pressing need for new statistical theory and methods to appropriately understand and efficiently analyze differentially private data. The project will expand the repertoire of tools available to researchers, and contribute to the cause of creating a better informed and more transparent society while respecting individual privacy. The PI will work on a theoretical formulation of the definitions of differential privacy using imprecise probability constructions, including interval of measures and coherent upper-lower probability measures. In the Bayesian context, such a formulation delivers a robust-likelihood conception of the model and allows for the computation of bounds on posterior quantities based on differentially private data for arbitrary prior specifications. The PI also proposes the differentially private approximate Bayesian computation (ABC) algorithm, a noisy ABC algorithm that delivers exact posterior inference given differentially private observations subject to arbitrary additive noise. The algorithm permits differentially private inference from large-scale Bayesian models with intractable likelihoods. The project bridges the classic theories of robust Bayes and generalized Bayes, with the novel literature on statistical privacy, and derives practical implementations based on privacy-preserving data releases. The project will supply analysts and researchers in a timely fashion with inferential methodologies tailored for differentially private input that are both theoretically sound and computationally efficient.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.