This course will give a detailed introduction to learning theory with a focus on the classification problem. It will be shown how to obtain (pobabilistic) bounds on the generalization error for certain types of algorithms. The main themes will be: * probabilistic inequalities and concentration inequalities * union bounds, chaining * measuring the size of a function class, Vapnik Chervonenkis dimension, shattering dimension and Rademacher averages * classification with real-valued functions Some knowledge of probability theory would be helpful but not required since the main tools will be introduced.
T. Banica, S. Curran, und R. Speicher. (2009)cite arxiv:0907.3314Comment: Published in at http://dx.doi.org/10.1214/10-AOP619 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org).
A. Gorban, und I. Tyukin. (2018)cite arxiv:1801.03421Comment: Accepted for publication in Philosophical Transactions of the Royal Society A, 2018. Comprises of 17 pages and 4 figures.