In this report we show that the-tube size in Support Vector Machine (SVM) for regression is 2= p 1 + jjwjj 2. By using this result we show that, in the case all the data points are inside the-tube, minimizing jjwjj 2 in SVM for regression is equivalent to maximizing the distance between the approximating hyperplane and the farest points in the training set. Moreover, in the most general setting...

In spline regression models, the smoothness of the tted model depends on the knots via their location and how many knots there are. An alternative to knot selection is to keep all the knots, but to restrict their in uence on the tted model, that is, to constrain the values of these coe cients which correspond to the spline basis functions. For example, we can bound the squared L2 norm by some c...

In this report we show some consequences of the work done by Pontil et al. in 1]. In particular we show that in the same hypotheses of the theorem proved in their paper, the optimal approximating hyperplane f R found by SVM regression classiies the data. This means that y i f R (x i) > 0 for points which live externally to the margin between the two classes or points which live internally to th...