Genetic algorithms as tool for statistical analysis of high-dimensional data structures

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In regression, the goal is to find a function that accurately reflects reality while minimizing data noise and ensuring interpretability. A popular method for estimating the underlying function is the additive model, often fitted using B-splines, which facilitate direct calculation of estimators. However, using too many B-splines can lead to overfitting, resulting in overly complex functions that closely follow the observed data. To address this, a penalization approach with smoothing parameters is employed. This thesis introduces the use of genetic algorithms for optimizing these smoothing parameters, a method not commonly applied in statistics. Genetic algorithms operate on the principle that better-adapted individuals prevail under equal conditions. Additionally, datasets frequently contain numerous relevant and irrelevant explanatory variables, necessitating effective variable selection methods to narrow down to relevant subsets. We propose a simultaneous approach to variable selection and smoothing parameter optimization using genetic algorithms, integrating both processes through a strategic combination of techniques. This innovative approach aims to enhance the accuracy and interpretability of regression models while addressing the complexities of variable selection.