New Inference Methods For Multiway Functional Data and Multilayer Network Data

多路功能数据和多层网络数据的新推理方法

• 批准号: 1612458
• 负责人: Kehui Chen
• 金额: $ 30.09万
• 依托单位: University of Pittsburgh
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-07-01 至 2019-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1612458&HistoricalAwards=false
• 关键词: New; Inference; Methods; Multiway; Functional

This project focuses on developing efficient models for multi-way functional data and multi-layer network data. Functional data refers to data recorded over a continuum, such as growth curves for many children. Examples of multi-way functional data include brain-imaging data measured over space and time, and data obtained from mobile tracking apps where daily activity profiles are recorded for a number of individuals over a period of many days. Despite the growing number of applications, the complex structure and high-dimensionality of the data pose significant challenges for statistical modeling and inference. The second part of the project focuses on multi-layer network data obtained from multi-modal and multi-task brain connectivity studies. A rigorous statistical framework for these network structures will be developed. In the long history of image processing and spatial-temporal analysis, many methods have relied on separability, the assumption that the covariance can be factorized as a product of a spatial covariance and a temporal covariance. Recent approaches for repeated functional data and multi-way functional data also invoke separability, either explicitly or implicitly, to achieve efficient dimension reduction. A new notion of weak separability, that includes covariance separability as a special case, will be introduced. Tests of weak separability will be developed, and principled answers to several open questions will be provided. In the second part of the project, generative models of multi-layer network data with community structures will be introduced. Least squares estimation of memberships will be studied from a novel relational k-means perspective, and theoretical justification provided under a statistical inference framework.

该项目着重于开发用于多路功能数据和多层网络数据的有效模型。 功能数据是指在连续体中记录的数据，例如许多儿童的生长曲线。 多路功能数据的示例包括在空间和时间上测量的大脑成像数据，以及从移动跟踪应用程序获得的数据，其中在许多天内记录了许多个体的日常活动概况。 尽管应用的数量越来越多，但数据的复杂结构和高维度对统计建模和推理构成了重大挑战。 该项目的第二部分重点是从多模式和多任务大脑连接性研究获得的多层网络数据。 将开发针对这些网络结构的严格统计框架。 在图像处理和时空分析的悠久历史中，许多方法都取决于可分离性，即可以将协方差作为空间协方差和时间协方差的乘积进行分配的假设。 重复的功能数据和多路功能数据的最新方法也明确或隐式地调用可分离性，以实现有效的尺寸降低。 将引入一个新的弱可分离性概念，其中包括协方差可分离性作为特殊情况。 将开发出较弱的可分离性测试，并将为几个开放问题提供原则答案。 在项目的第二部分中，将介绍具有社区结构的多层网络数据的生成模型。 最小二乘将从新颖的关系K-均值的角度研究成员资格，并在统计推断框架下提供的理论理由。