Comparaison de différentes approches de l'évaluation supervisée

摘要

Instance selection for the nearest neighbor rule is a classical topic in statistical learning. Within the context of hypothesis selection, the characteristics of this problem is that: the set of hypotheses is structured and depends on the data. We thus propose specific nonparametric criteria. We aim at comparing sets of instances of varying size without introducing an extra parameter. Balancing approaches give tools to solve this problem. Three approaches are considered successively : the SRM (standing for Structural Risk Minimization) approach, the BIC (standing for Bayesian Information Criterion) approach end the MDL (standing for Minimum Description Length) approach. The exploration of each one leads to the definition of a regularized criterion. Each criterion permits the comparison of sets of instances of various size. Each criterion is nonparametric. We make use of real and synthetic datasets to prove the following point: the MDL criterion is finer than the BIC criterion which, in turn, is finer than the SRM criterion.