A PAC-Bayesian approach to adaptive classification
This is meant to be a self-contained presentation of adaptive classification seen from the PAC-Bayesian point of view. Although most of the results are original, some review materials about the VC dimension and support vector machines are also included. This study falls in the field of statistical learning theory, where complex data have to be analyzed from a limited amount of informations, drawn from a finite sample. It relies on non asymptotic deviation inequalities, where the complexity of models is captured through the use of prior measures. The main improvements brought here are more localized bounds and the use of exchangeable prior distributions. Interesting consequences are drawn for the generalization properties of support vector machines and the design of new classification algorithms. 2000 Mathematics Subject Classification: 62H30, 68T05, 62B10.