Adaptive Rates for Support Vector Machines

In this thesis, new oracle inequalities and (essentially) minmax optimal learning rates are established for support vector machines (SVMs) for least squares regression using Gaussian kernels. The same learning rates can be adaptively obtained by a simple data-dependent parameter selection method. Moreover, a localized SVM approach is developed and a general oracle inequality is derived. This oracle inequality is applied to least squares regression using Gaussian kernels and local learning rates are deduced that are essentially minmax optimal. A data-dependent parameter selection method for the local SVM approach is introduced and the same learning rates as before are achieved. Additionally, comparable results are obtained for conditional quantile regression.