Mathematical Statistics II

The course presents modern methods and tools for nonparametric statistical learning theory. Topics include: (1) Kernel methods for density estimation and regression, analysis of overfitting/underfitting, undersmoothing/oversmoothing, model selection via cross validation; (2) Penalty methods for regression based on Reproducing Kernel Hilbert Spaces; (3) Classification and regression trees; (4) Aggregating classifiers including BAGGING, Random forest, and Boosting; (5) Projection pursuit and neural network approximations for regression and classification; (6) Deep learning including convolution networks and neural network transformers; (7) Rademacher complexity, VC-dimension, Covering number, and concentration inequalities; (8) Application of concentration inequalities to high-probability bounds for regression and classification; (9) Model selection via structural risk minimization. Prerequisites: APMA 2670