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

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.

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.

项目成果

Orthogonalized Kernel Debiased Machine Learning for Multimodal Data Analysis

• DOI: 10.1080/01621459.2021.2013851
• 发表时间: 2021-03
• 期刊: Journal of the American Statistical Association
• 影响因子: 3.7
• 作者: Xiaowu Dai;Lexin Li

Sliced Inverse Regression in Metric Spaces

• DOI: 10.5705/ss.202022.0097
• 发表时间: 2022-06
• 期刊: Statistica Sinica
• 影响因子: 1.4
• 作者: Joni Virta;Kuang‐Yao Lee;Lexin Li

Statistical Inference for High-Dimensional Vector Autoregression with Measurement Error

• DOI: 10.5705/ss.202021.0151
• 发表时间: 2020-09
• 期刊: Statistica Sinica
• 影响因子: 1.4
• 作者: Xiang Lyu;Jian Kang;Lexin Li

Sequential pathway inference for multimodal neuroimaging analysis

• DOI: 10.1002/sta4.433
• 发表时间: 2021-09
• 期刊: Stat
• 影响因子: 1.7
• 作者: Lexin Li;C. Shi;Tengfei Guo;W. Jagust

Nonparametric Functional Graphical Modeling Through Functional Additive Regression Operator

• DOI: 10.1080/01621459.2021.2006667
• 发表时间: 2021-11
• 期刊: Journal of the American Statistical Association
• 影响因子: 3.7
• 作者: Kuang‐Yao Lee;Lexin Li;Bing Li;Hongyu Zhao