Title: Cross-validation model assessment for modular networks

Abstract: Model assessment of the stochastic block model is a crucial step in identification of modular structures in networks. Although this has typically been done according to the principle that a parsimonious model with a large marginal likelihood or a short description length should be selected, another principle is that a model with a small prediction error should be selected. We show that the leave-one-out cross-validation estimate of the prediction error can be efficiently obtained using belief propagation for sparse networks. Furthermore, the relations among the objectives for model assessment enable us to determine the exact cause of overfitting.