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.
J. Negrea, M. Haghifam, G. Dziugaite, A. Khisti, and D. Roy. (2019)cite arxiv:1911.02151Comment: 23 pages, 1 figure. To appear in, Advances in Neural Information Processing Systems (33), 2019.
I. Sason, and S. Verdú. (2015)cite arxiv:1508.00335Comment: IEEE Trans. on Information Theory, vol. 62, no. 11, pp. 5973--6006, November 2016. This manuscript is identical to the journal paper, apart of some additional material which includes Sections III-C and IV-F, and three technical proofs.