  There is growing interest in understanding how the structural
interconnections among brain regions change with the occurrence of neurological
diseases. Diffusion weighted MRI imaging has allowed researchers to
non-invasively estimate a network of structural cortical connections made by
white matter tracts, but current statistical methods for relating such networks
to the presence or absence of a disease cannot exploit this rich network
information. Standard practice considers each edge independently or summarizes
the network with a few simple features. We enable dramatic gains in biological
insight via a novel unifying methodology for inference on brain network
variations associated to the occurrence of neurological diseases. The key of
this approach is to define a probabilistic generative mechanism directly on the
space of network configurations via dependent mixtures of low-rank
factorizations, which efficiently exploit network information and allow the
probability mass function for the brain network-valued random variable to vary
flexibly across the group of patients characterized by a specific neurological
disease and the one comprising age-matched cognitively healthy individuals.
