Privacy-Preserving Bayesian Inference: Foundations and Extensions

该项目为利用不同的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。差别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，而不过度牺牲其对统计分析的整体有用性。随着当今社会努力应对大规模数据集爆炸式增长带来的隐私影响，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和生物信息。美国人口普查局已正式采用差别隐私作为2020年人口普查的信息披露避免方法。其他数据收集者和馆长预计将在不久的将来效仿。这个项目满足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。该项目将扩大研究人员可用工具的范围，并有助于创建一个更知情、更透明的社会，同时尊重个人隐私。PI将使用不精确的概率构造，包括度量区间和一致的上下概率度量，致力于差分隐私定义的理论公式。在贝叶斯背景下，这样的公式提供了模型的稳健似然概念，并允许基于任意先验规范的差分私有数据来计算后验量的界。PI还提出了差分私有近似贝叶斯计算(ABC)算法，这是一种噪声较大的ABC算法，可以提供精确的后验推断，给出受任意加性噪声影响的差分私有观测数据。该算法允许从具有难以处理的可能性的大规模贝叶斯模型进行差分私有推理。该项目将稳健贝叶斯和广义贝叶斯的经典理论与关于统计隐私的新文献联系起来，并基于隐私保护数据发布得出实际实现。该项目将及时为分析师和研究人员提供为不同私人输入量身定做的推理方法，这些方法在理论上是合理的，在计算上也是有效的。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 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.