Kernel Methods and Applications
Feliks Nüske
Additional information / Pre-requisites
This lecture/lab course is suitable for Master students of Mathematics, Computer Science or Computational Sciences.
Comments
Reproducing kernels provide a powerful modelling and approximation framework, which have been widely applied to problems in science and technology. Rooted in functional analysis and approximation theory, kernels lead to a theoretical framework of surprising mathematical elegance on one hand, and to simple and robust algorithms on the other hand. In this course, we will learn about both theory and applications of kernel methods. Practical coding exercises will accompany the course.
Theoretical Concepts
- concepts from functional analysis
- introduction to reproducing kernel Hilbert spaces; fundamental properties
- examples
- Mercer integral operator and feature representation
- density and regularity properties of reproducing kernel Hilbert spaces; relation to Fourier transform
- error analysis and statistical learning theory
Applications
- support vector machine
- kernel PCA
- canonical correlation analysis and analysis of dynamical systems
- solution of partial differential equations
13 Class schedule
Regular appointments