Before revision:  In weighted multilayer noisy networks , a natural hierarchy is induced by the assumption of all but one block being under the `umbrella' of signal , while a single block is classified as exhibiting the same characteristics as interstitial interactions and subsumed into ambient noise. We use hierarchical variational inference to jointly detect block-structures and differentiate the communities' local signals from global noise.
After revision:  In weighted multilayer noisy networks , a natural hierarchy is induced by the assumption of all but one block being under the `umbrella' of signal , while a single block is classified as ambient noise, which behaves identically as interactions across differing blocks. Hierarchical variational inference is employed to jointly detect block-structures and differentiate the communities' local signals from global noise.