New statistical methods for functional and array-valued brain imaging data: joint modelling and statistical machine learning perspectives

该提案开发了新的统计方法，用于灵活分析功能/阵列值的脑成像数据，目的是提供一个通用框架，用于利用嵌入在脑成像数据中的有价值的信息，通过贝叶斯分层建模及其与统计机器学习方法的集成来解释或预测给定的结果。具体而言，提出了以下具体目标： 在目标1中，提出了一类新的贝叶斯增长混合模型，用于纵向结果数据，该模型将功能/阵列值脑成像数据作为预测因子。这一目标的主要焦点是利用混合建模来识别未观察到的纵向轨迹模式子组（即，潜在类），并开发一系列功能/张量回归模型，以适应脑成像数据作为协变量，以预测纵向轨迹的潜在类成员。 在目标2中，提出了一种统一的贝叶斯建模方法来联合分析功能/阵列值脑成像数据和横截面结果数据。重点是灵活建模的大脑成像数据，以捕捉信息的潜在数据特征，并使用提取的潜在特征的结果的同时预测。 在目标3中，通过与支持向量机（SVM）学习框架相结合，扩展了目标1和目标2中的贝叶斯层次模型。 虽然在脑成像数据中识别高信息/预测特征的问题的动机，提出的方法创新广泛适用于许多不同的情况下，涉及功能数据和数组值的数据与复杂的空间相关性，例如，遗传研究。拟议的研究还将推进高素质人才（5名硕士生，2名博士生和1名博士后研究员）的培训，以分析高维复杂数据。

This proposal develops novel statistical methodologies for flexible analysis of functional/array-valued brain imaging data, with the aim of providing a general framework for utilizing valuable information embedded in the brain imaging data to explain or predict a given outcome through Bayesian hierarchical modelling and its integration with statistical machine learning methods. In particular, the following specific aims are proposed: In aim 1, a new class of Bayesian Growth Mixture Models for longitudinal outcome data that accommodate functional/array-valued brain imaging data as predictors is proposed. The main focus of this aim is to utilize mixture modelling to identify unobserved longitudinal trajectory pattern subgroups (i.e., latent classes), and develop a series of functional/tensor regression models to accommodate brain imaging data as covariates to predict the latent class memberships of longitudinal trajectories. In aim 2, a unified Bayesian modelling approach to joint analysis of functional/array-valued brain imaging data and cross-sectional outcome data is proposed. The focus is on flexible modelling of brain imaging data to capture informative latent data features, and simultaneous prediction of the outcome using the extracted latent features. In aim 3, the Bayesian hierarchical models in Aim 1 and 2 are extended by integrating with the Support Vector Machine (SVM) learning framework. Although motivated by the problems of identifying highly informative/predictive features in the brain imaging data, the methodological innovations proposed are widely applicable to a number of different contexts that involve functional data and array-valued data with complex spatial correlation, for example, genetic studies. The proposed research will also advance training of highly qualified personnel (5 MSc students, 2 PhD students and 1 postdoc research fellow) to analyze high-dimensional complex data.