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.
A. Boffet and S. Rocca Serra. “Identification of spatial structures within urban blocks for town characterisation,” in Proceedings of the 20th International Cartographic Conference, Beijing, China, 2001 (CD-ROM).
S. Chen, E. Dobriban, and J. Lee. (2019)cite arxiv:1907.10905Comment: Changed title. Added results on overparametrized 2-layer nets. Added error bars to experiments. Numerous other minor improvements.