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.
V. Papyan, J. Sulam, and M. Elad. (2017)cite arxiv:1707.06066Comment: This is the journal version of arXiv:1607.02005 and arXiv:1607.02009, accepted to IEEE Transactions on Signal Processing.