Preferential Latent Space Models for Networks with Textual Edges

Music City Center 

Many real-world networks contain rich textual information in the edges, such as email networks where an edge between two nodes is an email exchange. The useful textual information carried in the edges is often discarded in most network analyses, resulting in an incomplete view of the relationships between nodes. In this work, we represent each text document as a generalized multi-layer network, and introduce a new and flexible preferential latent space network model that can capture how node-layer preferences directly modulate edge probabilities. We establish identifiability conditions for the proposed model and tackle model estimation with a computationally efficient projected gradient descent algorithm. We further derive the non-asymptotic error bound of the estimator from each step of the algorithm. The efficacy of our proposed method is demonstrated through simulations and an analysis of the Enron email network.

latent space model

multi-layer network

non-convex optimization 

IMS