This set of lectures will complement the statistical learning theory course and focus on recent advances in the domain of classification. 1- PAC Bayesian bounds: a simple derivation, comparison with Rademacher averages.
2 - Local Rademacher complexity with classification loss, Talagrand's inequality. Tsybakov noise conditions.
3 - Properties of loss functions for classification (influence on approximation and estimation, relationship with noise conditions).
4 - Applications to SVM - Estimation and approximation properties, role of eigenvalues of the Gram matrix.