Global and individualized community detection in inhomogeneous multilayer networks

In network applications, it has become increasingly common to obtain datasets in the form of multiple networks observed on same set subjects, where each is obtained a related but different experiment condition or application scenario. Such can be modeled by multilayer layer separate itself while layers are associated and share some information. The present paper studies community detection stylized yet informative inhomogeneous model. our model, generated stochastic block models, structures which (random) perturbations global structure connecting probabilities not related. Focusing symmetric two case, we establish minimax rates for both estimation individualized layerwise structures. Both have sharp exponents. addition, provide an efficient algorithm that simultaneously asymptotic optimal tasks under mild conditions. depend parity number most layers, phenomenon caused inhomogeneity across layers. method extended handle potentially asymmetric cases. We demonstrate its effectiveness simulated examples real multimodal single-cell dataset.