Additive Nonparametric Regression with Spatial and Network Objects

2026-09-22

AI Summary

本文针对多模态神经影像数据的整合与预测问题，提出了一种基于高斯过程先验的加性非参数回归框架，以处理t-fMRI和s-MRI图像，并通过ABCD研究的数据进行了验证。

Abstract

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.

Problem

• task-based brain activation
• cortical metrics
• brain connectivity
• hierarchical Bayesian modeling
• joint priors

Innovation

• additive nonparametric regression
• Gaussian process priors
• functional data
• multi-modal neuroimaging
• hierarchical Bayesian modeling