A nested heuristic for parameter tuning in Support Vector Machines

The default approach for tuning the parameters of a Support Vector Machine (SVM) is a grid search in the parameter space. Different metaheuristics have been recently proposed as a more efficient alternative, but they have only shown to be useful in models with a low number of parameters. Complex models, involving many parameters, can be seen as extensions of simpler and easy-to-tune models, yielding a nested sequence of models of increasing complexity. In this paper we propose an algorithm which successfully exploits this nested property, with two main advantages versus the state of the art. First, our framework is general enough to allow one to address, with the very same method, several popular SVM parameter models encountered in the literature. Second, as algorithmic requirements we only need either an SVM library or any routine for the minimization of convex quadratic functions under linear constraints. In the computational study, we address Multiple Kernel Learning tuning problems for which grid search clearly would be infeasible, while our classification accuracy is comparable to that of ad hoc model-dependent benchmark tuning methods.