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. Dreyfus, C. Rasmussen, N. Apkarian, и M. Tabach. INDRUM 2018, (2018)"The complexity of knowledge flow in the classroom, even based on this one class session, is far greater than one might imagine. ".
D. Spikol, и J. Eliasson. The 6th IEEE International Conference on Wireless, Mobile, and Ubiquitous Technologies in Education, стр. 137--141. IEEE, (2010)
M. Carlson, M. Oehrtman, и P. Thompson. Making the Connection: Research and Practice in Undergraduate Mathematics, Mathematical Association of America, Washington, DC, (2008)
A. Waraich. ITiCSE '04: Proceedings of the 9th annual SIGCSE conference on Innovation and technology in computer science education, стр. 97-101. New York, NY, USA, ACM, (2004)
C. Bergsten. Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education, 2, стр. 153-160. Prague, Czech Republic July 16-21, (2006)
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3-8(мая 1968)Systematization is a great virtue of mathematics, and if possible, the student has to learn this virtue, too. But then I mean the activity of systematizing, not its result. Its result is a system, a beautiful closed system, closed, with no entrance and no exit. In its highest perfection it can even be handled by a machine. But for what can be performed by machines, we need no humans. What humans have to learn is not mathematics as a closed system, but rather as an activity, the process of mathematizing reality and if possible even that of mathematizing mathematics..