Learnability of latent position network models

The latent position model is a well known model for social network analysis which has also found application in other fields, such as analysis of marketing and e-commerce data. In such applications, the data sets are increasingly massive and only partially observed, giving rise to the possibility of overfitting by the model. Using tools from statistical learning theory, we bound the VC dimension of the latent position model, leading to bounds on the overfit of the model. We find that the overfit can decay to zero with increasing network size even if only a vanishing fraction of the total network is observed. However, the amount of observed data on a per-node basis should increase with the size of the graph.