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.
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