具有空间和网络对象的加性非参数回归
Additive Nonparametric Regression with Spatial and Network Objects
- Texas A&M University（德克萨斯农工大学）
- Indiana University（印第安纳大学）
- University of California, San Francisco（加州大学旧金山分校）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文提出一种加性非参数回归框架，将t-fMRI和s-MRI视为函数型数据，用高斯过程先验建模网络和函数型预测因子的非线性效应，以预测脑激活图，并具有理论保证和实证验证。
中文摘要 AI 辅助
本文受青少年大脑认知发展（ABCD）研究中的影像应用启发，旨在利用结构MRI（s-MRI）的皮层指标和静息态fMRI（rs-fMRI）的脑连接数据，预测基于任务fMRI（t-fMRI）的任务激活脑图。分层贝叶斯建模非常适合整合多样化的影像数据并量化预测不确定性。然而，由于在设计能够捕捉不同影像模态之间结构和相互联系的联合先验方面存在挑战，加之计算复杂性和缺乏理论保证，该领域的进展有限。为解决这些挑战，本文引入一种新颖的回归框架，将t-fMRI和s-MRI图像视为函数型数据，在函数型响应上纳入网络和函数型预测因子的加性非线性效应。具体而言，我们对与函数型预测因子相关的系数采用高斯过程（GP）先验，以捕捉其与响应之间复杂的函数依赖关系。此外，为网络预测因子对响应函数的非线性节点效应分配一个GP先验。该方法在函数型响应预测准确性方面有理论结果支持，并通过模拟研究和ABCD研究的多模态神经影像数据分析进行了实证验证。
英文摘要
This article is motivated by an imaging application from the Adolescent Brain Cognitive Development (ABCD) study, aiming to predict task-based brain activation maps from t-fMRI using cortical metrics from structural MRI (s-MRI) and brain connectivity data from resting-state fMRI (rs-fMRI). Hierarchical Bayesian modeling is well-suited for integrating diverse imaging data and quantifying prediction uncertainty. However, progress in this field is limited due to challenges in designing joint priors that capture the structures and interconnections between different imaging modalities, along with computational complexity and lack of theoretical assurances. To address these challenges, the article introduces a novel regression framework that treats t-fMRI and s-MRI images as functional data, incorporating additive non-linear effects of both network and functional predictors on the functional response. Specifically, we employ Gaussian process (GP) priors on coefficients related to the functional predictors to capture their intricate functional dependencies with the response. Furthermore, a GP prior is assigned to encapsulate the non-linear nodal effects of the network predictor on the response function. The method is supported by theoretical results on predictive accuracy for the functional response, and is empirically validated through simulation studies and analysis of multi-modal neuroimaging data from the ABCD study.
