Building uncertainty-aware mathematical models based on evidence from datasets using grammatical evolution optimization techniques: the case of the obesity dynamics

Abstract

This paper introduces a methodology to build mathematical models based on evidence and data sets, considering data and model uncertainty. We study the evolution of obesity in the population, being obesity a consequence of the transmission of unhealthy lifestyle habits and behavioral patterns influenced by social networks (family, friends, peers, etc.). We propose a three-step methodology. First, we create a synthetic data set based on a previous model with real data. Then, we search for dynamic models based on difference equations that best fit the dynamics described by the dataset and their uncertainty (uncertainty-aware). To do this, we use a dynamic structured grammatical evolution algorithm (an algorithm that builds possible models) on which we have defined a grammar (set of possible expressions that can be part of the model). The definition of appropriate grammar is crucial because it allows us to build models that do not contradict the knowledge of the phenomenon studied. However, the data may suggest introducing new terms that indicate the influence of unknown factors. Finally, from among all the models obtained, we will algorithmically search for a selection of them that best describes the uncertainty of the data. This methodology can be applied to various scenarios with available datasets and a limited understanding of the phenomenon. It aims to generate models that not only achieve precision but also incorporate terms that correspond to identifiable processes, which can be explained within the context of the study problem.