Adaptive Dependent Data Models via Graph-Informed Shrinkage and Sparsity

这一研究项目将推进相关数据的统计建模和计算策略。相依数据是广泛而重要的。许多社会经济、文化和政治数据是以空间区域单位衡量的，大多数经济数据是按时间顺序和相互依赖的，现代监测系统以近乎连续的分辨率记录社会、环境和经济暴露数据。然而，这种日益丰富的相关数据已经超过了针对这些数据的统计方法和算法的发展。该项目将开发新的统计工具，使研究人员能够从这些独立的数据中提取可靠的信息并做出决定。要开发的方法将受到以下领域具体、及时和重要问题的推动：地方选举和重新划分选区；通货膨胀建模和预测；经济、卫生和城市数据的空间模式提取；以及监测和暴露数据的建模。该项目将为本科生和研究生提供培训和指导，开发公开可用的软件和可视化工具，并展示地方、州和联邦政府的数据。该研究项目将开发新的统计工具，以充分捕获广泛的数据相关性，为海量数据集提供计算可伸缩性，并利用相关性结构进行更适应性和本地化的估计、不确定性量化和缺失数据的估算。未建模的依赖使得推断不是最优的或无效的，从而导致分析能力不足和错误的结论。此外，相依数据往往是高维的，具有很大的缺失性，这导致了重大的计算和统计挑战。在贝叶斯框架内，该项目将同时整合(I)信号模型中的依赖性以提供平滑和正则化，(Ii)伴随的收缩或稀疏性优先于增强的局部适应性，以及(Iii)用于可扩展后验推断的计算和数值策略。相关性将被编码为将观测单元链接在一起的图，所述观测单元例如用于时间排序或函数数据的连续观测、用于图像或点阵数据的相邻像素、以及用于空间数据的相邻面积单元，以及许多其他示例。这种基于图形的公式将为统一和推进一系列广泛的模型、收缩和稀疏先验以及相关数据的推理算法奠定基础。将开发的工具将针对各种设置进行定制，包括趋势估计和归因、收缩或稀疏先验、图形信息回归分析、因素模型和离散数据等。该奖项反映了NSF的法定使命，并已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 advance statistical modeling and computing strategies for dependent data. Dependent data are widespread and important. Many socioeconomic, cultural, and political data are measured on spatial areal units, most economic data are time-ordered and co-dependent, and modern monitoring systems record social, environmental, and economic exposure data at near-continuous resolutions. However, this growing abundance of dependent data has outpaced the development of statistical methods and algorithms for such data. The project will develop new statistical tools that will allow researchers to extract reliable information and make decisions from such dependent data. The methods to be developed will be motivated by specific, timely, and important problems in the following areas: local elections and redistricting; inflation modeling and forecasting; spatial pattern extraction for economic, health, and urban data; and modeling of monitoring and exposure data. The project will provide training and mentoring for undergraduate and graduate students, develop publicly available software and visualization tools, and showcase local, state, and federal government data.This research project will develop new statistical tools to adequately capture a broad array of data dependencies, provide computational scalability for massive datasets, and leverage the dependence structures for more adaptive and localized estimation, uncertainty quantification, and imputation of missing data. Unmodeled dependence renders inferences suboptimal or invalid, resulting in underpowered analyses and erroneous conclusions. In addition, dependent data are often high-dimensional with substantial missingness, leading to significant computational and statistical challenges. Within a Bayesian framework, the project will simultaneously integrate the dependence in (i) the model for the signal to provide smoothness and regularization, (ii) the accompanying shrinkage or sparsity prior for enhanced local adaptivity, and (iii) the computational and numerical strategies for scalable posterior inference. Dependence will be encoded as a graph that links together observational units, such as consecutive observations for time-ordered or functional data, adjacent pixels for image or lattice data, and neighboring areal units for spatial data, among many other examples. This graph-based formulation will lay the foundation to unify and advance a broad collection of models, shrinkage and sparsity priors, and inference algorithms for dependent data. The tools to be developed will be customized for a variety of settings, including trend estimation and imputation, shrinkage or sparsity priors, graph-informed regression analysis, factor models, and discrete data, among others.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.