Nonparametric learning and Regularization

Several nonparametric methods in a regression model are presented. First, the most classical ones: piecewise polynomial estimators, estimation with Spline bases, kernel estimators and projection estimators on orthonormal bases (such as Fourier or wavelet bases). Since these methods suffer from the curse of dimensionality, we also present Generalized Additive Models and CART regression models. The main references for this course are the following books : • The elements of Statistical Learning by T. Hastie et al [2]. • Introduction to nonparametric statistics (2009) by A. Tsybakov [4] • Introduction to High-Dimensional Statistics by C. Giraud [1] • Concentration inequalities and model selection by P. Massart [3]