The deviation between chronological age and biological age is a well-recognized biomarker associated with cognitive decline and neurodegeneration. Age-related and pathology-driven changes to brain structure are captured by various neuroimaging modalities. These datasets are characterized by high dimensionality as well as collinearity, hence applications of graph neural networks in neuroimaging research routinely use sample covariance matrices as graphs. We have recently studied covariance neural networks (VNNs) that operate on sample covariance matrices using the architecture derived from graph convolutional networks, and we showed VNNs enjoy significant advantages over traditional data analysis approaches. In this paper, we demonstrate the utility of VNNs in inferring brain age using cortical thickness data. Furthermore, our results show that VNNs exhibit multi-scale and multi-site transferability for inferring brain age. In the context of brain age in Alzheimer’s disease (AD), our experiments show that i) VNN outputs are interpretable as brain age predicted using VNNs is significantly elevated as compared to the chronological age for AD with respect to healthy subjects for different datasets; and ii) VNNs can be transferable, i.e., VNNs trained on one dataset can be transferred to another dataset with different dimensionality without retraining for brain age prediction.

In computational neuroscience, there has been an increased interest in developing machine learning algorithms that leverage brain imaging data to provide estimates of "brain age" for an individual. Importantly, the discordance between brain age and chronological age (referred to as "brain age gap") can capture accelerated aging due to adverse health conditions and therefore, can reflect increased vulnerability towards neurological disease or cognitive impairments. However, widespread adoption of brain age for clinical decision support has been hindered due to lack of transparency and methodological justifications in most existing brain age prediction algorithms. In this paper, we leverage coVariance neural networks (VNN) to propose an explanation-driven and anatomically interpretable framework for brain age prediction using cortical thickness features. Specifically, our brain age prediction framework extends beyond the coarse metric of brain age gap in Alzheimer’s disease (AD) and we make two important observations: (i) VNNs can assign anatomical interpretability to elevated brain age gap in AD by identifying contributing brain regions, (ii) the interpretability offered by VNNs is contingent on their ability to exploit specific eigenvectors of the anatomical covariance matrix. Together, these observations facilitate an explainable and anatomically interpretable perspective to the task of brain age prediction.

Graph neural networks (GNN) are an effective framework that exploit inter-relationships within graph-structured data for learning. Principal component analysis (PCA) involves the projection of data on the eigenspace of the covariance matrix and draws similarities with the graph convolutional filters in GNNs. Motivated by this observation, we study a GNN architecture, called coVariance neural network (VNN), that operates on sample covariance matrices as graphs. We theoretically establish the stability of VNNs to perturbations in the covariance matrix, thus, implying an advantage over standard PCA-based data analysis approaches that are prone to instability due to principal components associated with close eigenvalues. Our experiments on real-world datasets validate our theoretical results and show that VNN performance is indeed more stable than PCA-based statistical approaches. Moreover, our experiments on multi-resolution datasets also demonstrate that VNNs are amenable to transferability of performance over covariance matrices of different dimensions; a feature that is infeasible for PCA-based approaches.