**Selection of kernel
parameters**

O. Chapelle, V. Vapnik, O. Bousquet and S. Mukherjee, Choosing Multiple Parameters for Support Vector Machines, Machine Learning, 46, 2002.

The code implements the following kernel methods:**classification**: SVM with an L2 penalization of the training errors,**regression**: kernel ridge regression / Gaussian process.

- leave-one-out error
- radius/margin bound (the radius is approximated by the variance)
- validation error (a subset of the training set is used for validation)
- negative evidence.

Here is the Matlab code along with an example. It uses a modified version of Carl Rasmussen's conjugate gradient optimizer minimize.m.

Learning a linear combination of kernels

A special case of this general framework is when the kernel parameters correspond to the coefficients in convex combination of base kernels, Here is some code to select these coefficients by Newton optimization of the variance/margin estimate. It makes use of svqp, a quadratic solver written by Leon Bottou. Details about the algorithm can be found in this paper. One can show that this is aFast leave-one-out error estimate

Matlab code for estimating the generalization performance of an SVM, as described in Chapter 3 of my PhD thesis