Consistencies and inconsistencies between model selection and link prediction in networks
This work addresses a key methodological issue in network science for researchers, highlighting inconsistencies that can affect model reliability and predictive accuracy, though it is incremental in nature.
The study investigates the relationship between model selection based on posterior probability and link prediction performance in network analysis, finding that while these criteria are often consistent, there are cases where the most plausible model is not the most predictive, leading to overfitting, and that averaging over less plausible models can improve predictive performance.
A principled approach to understand network structures is to formulate generative models. Given a collection of models, however, an outstanding key task is to determine which one provides a more accurate description of the network at hand, discounting statistical fluctuations. This problem can be approached using two principled criteria that at first may seem equivalent: selecting the most plausible model in terms of its posterior probability; or selecting the model with the highest predictive performance in terms of identifying missing links. Here we show that while these two approaches yield consistent results in most of cases, there are also notable instances where they do not, that is, where the most plausible model is not the most predictive. We show that in the latter case the improvement of predictive performance can in fact lead to overfitting both in artificial and empirical settings. Furthermore, we show that, in general, the predictive performance is higher when we average over collections of models that are individually less plausible, than when we consider only the single most plausible model.