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, and 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).
R. Speicher. (2009)cite arxiv:0911.0087Comment: 21 pages; my contribution for the Handbook on Random Matrix Theory, to be published by Oxford University Press.
J. Helton, T. Mai, and R. Speicher. (2015)cite arxiv:1511.05330Comment: We have undertaken a major revision, mainly for the sake of clarity and readability.
M. Raginsky, and I. Sason. (2012)cite arxiv:1212.4663Comment: Foundations and Trends in Communications and Information Theory, vol. 10, no 1-2, pp. 1-248, 2013. Second edition was published in October 2014. ISBN to printed book: 978-1-60198-906-2.
A. Gorban, and 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.
K. Kawaguchi, L. Kaelbling, and Y. Bengio. (2017)cite arxiv:1710.05468Comment: To appear in Mathematics of Deep Learning, Cambridge University Press. All previous results remain unchanged.