# Additive Nonparametric Regression with Spatial and Network Objects

arXiv: https://arxiv.org/abs/2609.26867 · HTML: https://mlsanity.com/paper/2609.26867/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 55 references that are in the map.
- First posted on arXiv 22 Sep 2026.

## Builds on (most cited first, 12 of 12)

- [Convolutional Gaussian Processes](https://mlsanity.com/paper/1709.01894/) (2017)
- [An Introduction to Image Synthesis with Generative Adversarial Nets](https://mlsanity.com/paper/1803.04469/) (2018)
- [Bayesian Tensor Regression](https://mlsanity.com/paper/1509.06490/) (2015)
- [Scalar-on-Image Regression via the Soft-Thresholded Gaussian Process](https://mlsanity.com/paper/1604.03192/) (2016)
- [Efficient Estimation for Random Dot Product Graphs via a One-step Procedure](https://mlsanity.com/paper/1910.04333/) (2019)
- [Bayesian Regression with Undirected Network Predictors with an Application to Brain Connectome Data](https://mlsanity.com/paper/1803.10655/) (2018)
- [A tensor based varying-coefficient model for multi-modal neuroimaging data analysis](https://mlsanity.com/paper/2303.16443/) (2023)
- [Latent Subgroup Identification in Image-on-scalar Regression](https://mlsanity.com/paper/2307.00129/) (2023)
- [Bayesian Image-on-Image Regression via Deep Kernel Learning based Gaussian Processes](https://mlsanity.com/paper/2311.05649/) (2023)
- [Large Multi-scale Spatial Kriging Using Tree Shrinkage Priors](https://mlsanity.com/paper/1803.11331/) (2018)
- [Spatial shrinkage via the product independent Gaussian process prior](https://mlsanity.com/paper/1805.03240/) (2018)
- [Multi-object Data Integration in the Study of Primary Progressive Aphasia](https://mlsanity.com/paper/2407.09542/) (2024)

## Abstract (arXiv)

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.