  We introduce a novel model for multilayer weighted networks that accounts for
global noise in addition to local signals. The model is similar to a multilayer
stochastic blockmodel (SBM), but the key difference is that between-block
interactions independent across layers are common for the whole system, which
we call ambient noise. A single block is also characterized by these fixed
ambient parameters to represent members that do not belong anywhere else. This
approach allows simultaneous clustering and typologizing of blocks into signal
or noise in order to better understand their roles in the overall system, which
is not accounted for by existing Blockmodels. We employ a novel application of
hierarchical variational inference to jointly detect and differentiate types of
blocks. We call this model for multilayer weighted networks the Stochastic
Block (with) Ambient Noise Model (SBANM) and develop an associated community
detection algorithm. We apply this method to subjects in the Philadelphia
Neurodevelopmental Cohort to discover communities of subjects with co-occurrent
psychopathologies in relation to psychosis.
