In-sample model selection for Support Vector Machines

In-sample model selection for Support Vector Machines is a promising approach that allows using the training set both for learning the classifier and tuning its hyperparameters. This is a welcome improvement respect to out-of-sample methods, like cross-validation, which require to remove some samples from the training set and use them only for model selection purposes. Unfortunately, in-sample methods require a precise control of the classifier function space, which can be achieved only through an unconventional SVM formulation, based on Ivanov regularization. We prove in this work that, even in this case, it is possible to exploit well-known Quadratic Programming solvers like, for example, Sequential Minimal Optimization, so improving the applicability of the in-sample approach.