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Modeling the behavior of coupled networks is challenging due to theirintricate dynamics. For example in neuroscience, it is of critical importanceto understand the relationship between the functional neural processes andanatomical connectivities. Modern neuroimaging techniques allow us toseparately measure functional connectivity through fMRI imaging and theunderlying white matter wiring through diffusion imaging. Previous studies haveshown that structural edges in brain networks improve the inference offunctional edges and vice versa. In this paper, we investigate the idea ofcoupled networks through an optimization framework by focusing on interactionsbetween structural edges and functional edges of brain networks. We considerboth types of edges as observed instances of random variables that representdifferent underlying network processes. The proposed framework does not dependon Gaussian assumptions and achieves a more robust performance on general datacompared with existing approaches. To incorporate existing domain knowledgeinto such studies, we propose a novel formulation to place hard networkconstraints on the noise term while estimating interactions. This not onlyleads to a cleaner way of applying network constraints but also provides a morescalable solution when network connectivity is sparse. We validate our methodon multishell diffusion and task-evoked fMRI datasets from the Human ConnectomeProject, leading to both important insights on structural backbones thatsupport various types of task activities as well as general solutions to thestudy of coupled networks.

Learning Interpretable Models for Coupled Networks Under Domain Constraints