Before revision:  Hierarchical variational inference is employed to jointly detect and typologize block-structures as local signals or global noise. These principles are incorporated into novel community detection algorithm called Stochastic Block (with) Ambient Noise Model(SBANM) for multilayer weighted networks.
After revision:  Hierarchical variational inference is employed to jointly detect and typologize blocks as signal or noise. We call this model for multilayer weighted networks the Stochastic Block (with) Ambient Noise Model(SBANM) for multilayer weighted networks.