- Lecturer: Nihat Ay
- Prerequisites: Linear algebra, elementary probability theory and functional analysis (the relevant results for this course will be summarised).
This course will introduce into the theory of kernels and associated Hilbert spaces (reproducing kernel Hilbert spaces, RKHS), which play an important role within mathematical learning theory. In Statistical Learning Theory and the theory of Support Vector Machines (SVM), they provide efficient ways to formalise and control the generalisation ability of learning systems, based on the structural risk minimisation principle. A closely related inductive principle comes from regularisation theory. Here, learning is interpreted as an ill-posed inverse problem, where kernels define appropriate regularisers of the problem.