CIF: Small: Collaborative Research: Graphical Modeling of Multivariate Functional Data

CIF：小型：协作研究：多元函数数据的图形建模

• 批准号: 2102227
• 负责人: Lexin Li
• 金额: $ 24.96万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-07-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2102227&HistoricalAwards=false
• 关键词: CIF; Small; Collaborative; Research; Graphical; CIF; Small; Collaborative; Research; Graphical

Multivariate functional data, where continuous observations are sampled from multiple processes, are emerging in a wide range of scientific applications. A central problem in analyzing multivariate functional data is to understand the interdependency among the functions. This can be formulated as the problem of graphical modeling of multivariate functions. The majority of existing solutions, however, focus on random variables, and extension to random functions is far from trivial. This project is developing a class of novel statistical methods and associated theory for functional graphical modeling. This research is timely in that it responds to the growing demand for functional data analysis, and is expected to advance numerous biological and medical research areas, including the analyses of brain connectivity networks, gene regulatory networks, and protein-protein interaction networks. This project is studying three sets of problems: (1) nonparametric functional graphical modeling, which relaxes the Gaussian distribution or the linear structural assumptions, and avoids the curse of dimensionality and works for large graphs; (2) functional directed acyclic graphical modeling, which combines directed graph and functional graph, and offers a tractable solution for inferring directional dependency among multivariate functions; and (3) conditional and dynamic functional graphical modeling, which models graph that varies continuously with one or multiple external variables such as time. At the heart of its development is linear-operator-based statistical learning, which provides a highly flexible and efficient platform to handle massive and complex functional data. The accompanying estimation algorithms and asymptotic theory also make useful additions to the toolbox of multiple fields, including functional data analysis, network and graphical modeling, and statistical machine learning.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.

多元功能数据，其中连续观察是从多个过程中采样的，它正在广泛的科学应用中出现。分析多元功能数据的一个核心问题是了解功能之间的相互依赖性。这可以作为多元函数的图形建模问题进行表述。但是，大多数现有解决方案都集中在随机变量上，并且向随机函数扩展远非微不足道。该项目正在开发一类新型统计方法和功能图形建模的相关理论。这项研究是及时的，因为它响应了对功能数据分析的不断增长的需求，并有望推进许多生物学和医学研究领域，包括对脑连通性网络，基因调节网络和蛋白质 - 蛋白质相互作用网络的分析。该项目正在研究三组问题：（1）非参数功能图形建模，它放松了高斯分布或线性结构假设，并避免了维数的诅咒并适用于大图； （2）结合了有向图和功能图的功能性定向无环图形建模，并提供了一种可拖动的解决方案，用于推断多元函数之间的方向依赖性； （3）有条件和动态的功能图形建模，该模型图形与一个或多个外部变量（例如时间）连续变化。其开发的核心是基于线性操作员的统计学习，该学习提供了一个高度灵活，有效的平台来处理大规模且复杂的功能数据。随附的估计算法和渐近理论还为多个领域的工具箱提供了有用的补充，包括功能数据分析，网络和图形建模以及统计机器学习。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识智能和更广泛影响的评估来通过评估来获得支持的。