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Modeling and estimating mixed memberships for overlapping unipartiteun-weighted networks has been well studied in recent years. However, to ourknowledge, there is no model for a more general case, the overlapping bipartiteweighted networks. To close this gap, we introduce a novel model, the BipartiteMixed Membership Distribution-Free (BiMMDF) model. Our model allows anadjacency matrix to follow any distribution as long as its expectation has ablock structure related to node membership. In particular, BiMMDF can modeloverlapping bipartite signed networks and it is an extension of many previousmodels, including the popular mixed membership stochastic blcokmodels. Anefficient algorithm with a theoretical guarantee of consistent estimation isapplied to fit BiMMDF. We then obtain the separation conditions of BiMMDF fordifferent distributions. Furthermore, we also consider missing edges for sparsenetworks. The advantage of BiMMDF is demonstrated in extensive syntheticnetworks and eight real-world networks.

Bipartite Mixed Membership Distribution-Free Model. A novel model for community detection in overlapping bipartite weighted networks