Deep Generative Modeling with Spatial and Network Images: An Explainable AI (XAI) Approach

TL;DR

This paper presents a two-stage image-on-image regression framework to model the RS-fMRI ALFF outcome $y_i( s_{v,j})$ as $y_i( s_{v,j}) = x_i( s_{v,j})^\top β( s_{v,j}) + h( g_i,v) + ε_i( s_{v,j})$, where spatially varying coefficients $β(·)$ and a nonlinear network effect $h(·)$ are learned from structural inputs $x_i(·)$ and a latent network representation $g_i,v$. The first stage estimates node-specific latent network effects; the second stage uses deep neural networks with dropout to capture nonlinear, spatially varying relationships and enables MC dropout-based uncertainty quantification, linking to deep Gaussian processes. The method achieves competitive predictive accuracy with faster computation and provides superior uncertainty quantification compared to Bayesian deep learning competitors such as BIRD-GP and BART, while offering interpretable inference for $β(·)$ and $h(·)$. Applied to ABCD data, the model reveals systematic associations between cortical features and ALFF across the brain, with a substantial share of ROI-level effects being confidently nonzero, and yields open-source Python software.

Abstract

This article addresses the challenge of modeling the amplitude of spatially indexed low frequency fluctuations (ALFF) in resting state functional MRI as a function of cortical structural features and a multi-task coactivation network in the Adolescent Brain Cognitive Development (ABCD) Study. It proposes a generative model that integrates effects of spatially-varying inputs and a network-valued input using deep neural networks to capture complex non-linear and spatial associations with the output. The method models spatial smoothness, accounts for subject heterogeneity and complex associations between network and spatial images at different scales, enables accurate inference of each images effect on the output image, and allows prediction with uncertainty quantification via Monte Carlo dropout, contributing to one of the first Explainable AI (XAI) frameworks for heterogeneous imaging data. The model is highly scalable to high-resolution data without the heavy pre-processing or summarization often required by Bayesian methods. Empirical results demonstrate its strong performance compared to existing statistical and deep learning methods. We applied the XAI model to the ABCD data which revealed associations between cortical features and ALFF throughout the entire brain. Our model performed comparably to existing methods in predictive accuracy but provided superior uncertainty quantification and faster computation, demonstrating its effectiveness for large-scale neuroimaging analysis. Open-source software in Python for XAI is available.

Figures (9)

• Figure 1: (a) The Destriuex atlas used to parcellate our motivating ABCD imaging data into 148 ROIs grouped by nodes defined by hemisphere (left, right) and lobes (frontal, parietal, occipital, insula, and limbic). (b) Outcome of interest: variance in the rs-fMRI BOLD time series (BOLDVAR) which is a proxy for amplitude of low frequency fluctuations (ALFF). (c) Structural predictor: cortical gray/white matter intensity contrast (GWMIC). (d) Structural predictor: cortical thickness (CT). (e) Network predictor: multi-task coactivation matrix representing brain coactivation across $12$ nodes in response to an array of cognitive tasks.
• Figure 2: Illustration for the XAI.
• Figure 3: Root mean squared error (RMSE) comparison between the proposed XAI method and GLM for estimating the spatially varying coefficients $\beta_1( {\boldsymbol s} )$ and $\beta_2( {\boldsymbol s} )$, and the network latent effect $h( {\boldsymbol g} )$ under Case 1 to Case 4. Boxplots show the distribution of RMSE across $100$ simulation replications. The inference on $\beta_1( {\boldsymbol s} ),\beta_2( {\boldsymbol s} ),h( {\boldsymbol g} )$ are not available for BART and BIRD-GP. The inference on $h( {\boldsymbol g} )$ is not available for GLM.
• Figure 4: Coverage and length of 95% predictive intervals averaged over replications for XAI, BIRD-GP and BART. They are not available for GLM. Results show near nominal coverage of XAI with smaller predictive intervals than BIRD-GP.
• Figure 5: Root mean squared error (RMSE) comparison between the proposed XAI method and GLM for estimating the spatially varying coefficients $\beta_1( {\boldsymbol s} )$ and $\beta_2( {\boldsymbol s} )$, and the network latent effect $h( {\boldsymbol g} )$ under Case 5 to Case 7. Boxplots show the distribution of RMSE across $100$ simulation replications. The inference on $\beta_1( {\boldsymbol s} ),\beta_2( {\boldsymbol s} ),h( {\boldsymbol g} )$ are not available for BART and BIRD-GP. The inference on $h( {\boldsymbol g} )$ is not available for GLM.