Generalized linear models with low rank effects for network data

Networks are a useful representation for data on connections between units of interests, but the observed connections are often noisy and/or include missing values. One common approach to network analysis is to treat the network as a realization from a random graph model, and estimate the underlying edge probability matrix, which is sometimes referred to as network denoising. Here we propose a generalized linear model with low rank effects to model network edges. This model can be applied to various types of networks, including directed and undirected, binary and weighted, and it can naturally utilize additional information such as node and/or edge covariates. We develop an efficient projected gradient ascent algorithm to fit the model, establish asymptotic consistency, and demonstrate empirical performance of the method on both simulated and real networks.