  Modeling the behavior of coupled networks is challenging due to their
intricate dynamics. For example in neuroscience, it is of critical importance
to understand the relationship between the functional neural processes and
anatomical connectivities. Modern neuroimaging techniques allow us to
separately measure functional connectivity through fMRI imaging and the
underlying white matter wiring through diffusion imaging. Previous studies have
shown that structural edges in brain networks improve the inference of
functional edges and vice versa. In this paper, we investigate the idea of
coupled networks through an optimization framework by focusing on interactions
between structural edges and functional edges of brain networks. We consider
both types of edges as observed instances of random variables that represent
different underlying network processes. The proposed framework does not depend
on Gaussian assumptions and achieves a more robust performance on general data
compared with existing approaches. To incorporate existing domain knowledge
into such studies, we propose a novel formulation to place hard network
constraints on the noise term while estimating interactions. This not only
leads to a cleaner way of applying network constraints but also provides a more
scalable solution when network connectivity is sparse. We validate our method
on multishell diffusion and task-evoked fMRI datasets from the Human Connectome
Project, leading to both important insights on structural backbones that
support various types of task activities as well as general solutions to the
study of coupled networks.
