Mathematical Models of Brain Connectivity and Behavior | Niharika S. D’Souza @IBM Research, Almaden

Abstract: The study of networks is very relevant to modern day data-science, as we gain a lot of insight into otherwise mysterious phenomena. One such complex network is the human brain. Recently, there has been a lot of interest in understanding how regions in the brain communicate with each other and how these communication patterns
influence our behavior and health. This sets us up for an important, yet really challenging question in healthcare: of how to represent these interactions and relate them to meaningful diagnostics.
For the first part of my talk, I will develop a joint network optimization framework to predict clinical severity from resting state fMRI data. This model is based on two coupled terms: a generative matrix factorization and a discriminative regression framework. One of the main novelties lies in jointly optimizing the representation learning and prediction task, which is key to the generalization onto unseen examples. Building onto this framework, I will then introduce an extension of these general principles to
incorporate multimodal information from Diffusion Tensor Imaging (DTI) and dynamic functional connectivity (rs-fMRI). At a high level, our generative matrix factorization now estimates a time-varying functional decomposition guided by anatomical connections in a graph regularization setting. We couple this representation with a deep network
to predict multidimensional clinical characterizations. This deep network consists of an LSTM to model temporal-attention based dynamics of scan evolution and an ANN for prediction.
For the second part, I will focus on end-to-end geometric frameworks which are designed to exploit the complementarity between functional and structural connectomes. The first of these models is a matrix autoencoder designed to explicitly capture the underlying data geometry within functional connectivity. This is coupled with a manifold alignment model that maps from function to structure and a deep network that maps to phenotypic information. We demonstrate that the model reliably recovers structural connectivity patterns across individuals, while robustly extracting predictive yet interpretable brain biomarkers. Lastly, we move away from decomposition based models and instead treat the brain as a multimodal graph. Our novel Multimodal Graph Convolutional Network (M-GCN) is designed to capture topological properties of brain functional
and structural connectivity via carefully designed graph filtering operations. Overall, this provides improved phenotypic prediction performance.
Holistically, these models help us develop a more comprehensive picture of brain connectivity and behavior. Overall, these frameworks make minimal assumptions and can potentially find a broad range of applications outside of the medical realm.
Reach out to the author - @SdNiharika