Additive Nonparametric Regression with Spatial and Network Objects
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.
Related
- Recursive moment updates for scalable Bayesian nonparametric regression
- Choosing the penalty in nonparametric regression: short and long-range dependence
- A multi-predictor nonparametric local linear generalized Poisson regression model for overdispersed count data.
- Nonparametric Regression with Measurement Error in Banach Spaces
- Nonparametric Regression on the Circle with Applications to Climate and Environmental Science
BibTeX
@misc{guhaniyogi2026additive,
title = {{Additive Nonparametric Regression with Spatial and Network Objects}},
author = {Rajarshi Guhaniyogi and Pritam Dey and Krishnendu Chandra and Aaron Scheffler and Bani K. Mallick},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26867},
eprint = {2609.26867},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26867},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Additive Nonparametric Regression with Spatial and Network Objects
AU - Rajarshi Guhaniyogi
AU - Pritam Dey
AU - Krishnendu Chandra
AU - Aaron Scheffler
AU - Bani K. Mallick
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26867
UR - https://arxiv.org/abs/2609.26867
AB - 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.
ER -