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.
M. Butz, P. Stalph, and P. Lanzi. GECCO '08: Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation, page 1365--1372. New York, NY, USA, ACM, (2008)
M. Trapp, T. Glander, H. Buchholz, and J. Döllner. Proceedings of the 12th International Conference on IEEE Information Visualization, page 356--361. IEEE Computer Society Press, (July 2008)
L. Lee. Approaches to algebra: perspectives for research and teaching, Kluwer Academic Publishers, p 102
… it is much of a challenge to demonstrate that functions, modelling, and problem solving are all types of generalizing activities, that algebra and indeed all of mathematics is about generalizing patterns.
p 103
The history of the science of algebra is the story of the growth of a technique for representing of finite patterns.
The notion of the importance of pattern is as old as civilization. Every art is founded on the study of patterns.
Mathematics is the most powerful technique for the understanding of pattern, and for the analysis of the relationships of patterns.(1996)
M. Liquiere. Proceedings of the 15th International Conference on Conceptual Structures (ICCS 2007), volume 4604 of Lecture Notes in Artificial Intelligence, page 333-346. Berlin, Heidelberg, Springer-Verlag, (July 2007)
M. Dao, M. Huchard, M. Hacene, C. Roume, and P. Valtchev. Proceedings of the 12th International Conference on Conceptual Structures (ICCS 2004), volume 3127 of Lecture Notes in Computer Science, page 346-360. Springer, (2004)