New Inference Methods For Multiway Functional Data and Multilayer Network Data

点击翻译按钮获取中文摘要

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.