# Consistencies and inconsistencies between model selection and link prediction in networks

## TL;DR

This paper investigates the relationship between model selection based on plausibility and link prediction accuracy in networks, revealing cases of inconsistency and the risks of overfitting when optimizing predictive performance.

## Contribution

It demonstrates that model plausibility and predictive accuracy can diverge, and shows the benefits of averaging over multiple models rather than selecting a single most plausible one.

## Key findings

- In most cases, model plausibility and predictive performance align.
- Instances exist where the most plausible model is not the most predictive.
- Averaging over multiple models can improve predictive performance.

## Abstract

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.