Abstract

The foundations of Support Vector Machines (SVM) have been developed by Vapnik and are gaining popularity due to many attractive features, and promising empirical performance. The formulation embodies the traditional Empirical Risk Minimisation (ERM) principle, and the Structural Risk Minimisation (SRM) principle.
SVM were developed to solve classification problems, but recently they have been extended to the domain of regression problems.
This course will be an introduction to statitical learning theory and will then focus on specific algorithms (linear and non linear) that have been developed to solve classification and regression problems, with a particular emphasis on Support vector machines and their kernel generalisation. Here are the specific topics that will be addressed:
1. Basic notions in statitical learning
2. Empirical and Structural risk minimasation
3. Empirical processes, upper bounds for the risk and VC dimension
4. Support vector machines
5. Kernels and reproducing kernel hilbert spaces.
6. Kernel SVM and their applications