Modeling and estimating mixed memberships for overlapping unipartite un-weighted networks has been well studied in recent years. However, to our knowledge, there is no model for a more general case, the overlapping bipartite weighted networks. To close this gap, we introduce a novel model, the Bipartite Mixed Membership Distribution-Free (BiMMDF) model. Our model allows an adjacency matrix to follow any distribution as long as its expectation has a block structure related to node membership. In particular, BiMMDF can model overlapping bipartite signed networks and it is an extension of many previous models, including the popular mixed membership stochastic blcokmodels. An efficient algorithm with a theoretical guarantee of consistent estimation is applied to fit BiMMDF. We then obtain the separation conditions of BiMMDF for different distributions. Furthermore, we also consider missing edges for sparse networks. The advantage of BiMMDF is demonstrated in extensive synthetic networks and eight real-world networks.

翻译：近年来，对重叠单部分无加权网络的混合成员进行建模和估计已得到深入研究。然而，据我们所知，目前尚无针对更一般情况——即重叠二分加权网络——的模型。为弥补这一空白，我们提出了一种新模型——二分混合成员无分布（BiMMDF）模型。该模型允许邻接矩阵服从任意分布，只要其期望具有与节点成员相关的块结构。特别地，BiMMDF能够对重叠二分符号网络进行建模，并且是众多先前模型（包括流行的混合成员随机块模型）的扩展。我们采用一种具有一致估计理论保证的高效算法来拟合BiMMDF。随后，我们获得了不同分布下BiMMDF的分离条件。此外，我们还考虑了稀疏网络的缺失边问题。BiMMDF的优势在大量合成网络和八个真实世界网络中得到验证。