Comparison of Cross-Validation Methods for Stochastic Block Models

We introduce a novel cross-validation method that we call latinCV and we compare this method to other model selection methods using data generated from a stochastic block model. Comparing latinCV to other cross-validation methods, we show that latinCV performs similarly to a method described in \cite{hoff2008modeling} and that latinCV has a significantly larger true model recovery accuracy than the NCV method of \cite{chen2014network}. We also show that the reason for this discrepancy is related to the larger variance of the NCV estimate. Comparing latinCV to alternative model selection methods, we show that latinCV performs better than information criteria AIC and BIC, as well as the community detection method infomap and a routine that attempts to maximize modularity. The simulation study in this paper includes a range of network sizes and generative parameters for the stochastic block model that allow us to examine the relationship between model selection accuracy and the size and complexity of the model. Overall, latinCV performs more accurate model selection, and avoids overfitting better than any of the other model selection methods considered.