Alternative Definitions of Complexity for Practical Applications of Model Selection Criteria

Defining and quantifying complexity is one of the major challenges of modern science and contemporary societies. This task is particularly critical for model selection, which is aimed at properly identifying the most adequate equations to interpret the available data. The traditional solution of equating the complexity of the models to the number of their parameters is clearly unsatisfactory. Three alternative approaches are proposed in this work. The first one estimates the flexibility of the proposed models to quantify their potential to overfit. The second interprets complexity as lack of stability and is implemented by computing the variations in the predictions due to uncertainties in their parameters. The third alternative is focused on assessing the consistency of extrapolation of the candidate models. All the upgrades are easy to implement and typically outperform the traditional versions of model selection criteria and constitute a good set of alternatives to be deployed, depending on the priorities of the investigators and the characteristics of the application.