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Model selection is a crucial issue in machine-learning and a wide variety ofpenalisation methods (with possibly data dependent complexity penalties) haverecently been introduced for this purpose. However their empirical performanceis generally not well documented in the literature. It is the goal of thispaper to investigate to which extent such recent techniques can be successfullyused for the tuning of both the regularisation and kernel parameters in supportvector regression (SVR) and the complexity measure in regression trees (CART).This task is traditionally solved via V-fold cross-validation (VFCV), whichgives efficient results for a reasonable computational cost. A disadvantagehowever of VFCV is that the procedure is known to provide an asymptoticallysuboptimal risk estimate as the number of examples tends to infinity. Recently,a penalisation procedure called V-fold penalisation has been proposed toimprove on VFCV, supported by theoretical arguments. Here we report on anextensive set of experiments comparing V-fold penalisation and VFCV forSVR/CART calibration on several benchmark datasets. We highlight cases in whichVFCV and V-fold penalisation provide poor estimates of the risk respectivelyand introduce a modified penalisation technique to reduce the estimation error.

An Empirical Comparison of V-fold Penalisation and Cross Validation for Model Selection in Distribution-Free Regression