V-fold cross-validation improved: V-fold penalization
| dc.creator | Arlot, Sylvain | |
| dc.date | 2008-02-05 | |
| dc.date | 2008-02-07 | |
| dc.date.accessioned | 2026-07-07T09:18:57Z | |
| dc.date.available | 2026-07-07T09:18:57Z | |
| dc.description | We study the efficiency of V-fold cross-validation (VFCV) for model selection from the non-asymptotic viewpoint, and suggest an improvement on it, which we call ``V-fold penalization''. Considering a particular (though simple) regression problem, we prove that VFCV with a bounded V is suboptimal for model selection, because it ``overpenalizes'' all the more that V is large. Hence, asymptotic optimality requires V to go to infinity. However, when the signal-to-noise ratio is low, it appears that overpenalizing is necessary, so that the optimal V is not always the larger one, despite of the variability issue. This is confirmed by some simulated data. In order to improve on the prediction performance of VFCV, we define a new model selection procedure, called ``V-fold penalization'' (penVF). It is a V-fold subsampling version of Efron's bootstrap penalties, so that it has the same computational cost as VFCV, while being more flexible. In a heteroscedastic regression framework, assuming the models to have a particular structure, we prove that penVF satisfies a non-asymptotic oracle inequality with a leading constant that tends to 1 when the sample size goes to infinity. In particular, this implies adaptivity to the smoothness of the regression function, even with a highly heteroscedastic noise. Moreover, it is easy to overpenalize with penVF, independently from the V parameter. A simulation study shows that this results in a significant improvement on VFCV in non-asymptotic situations. | |
| dc.description | 40 pages, plus a separate technical appendix | |
| dc.identifier | https://arxiv.org/abs/0802.0566 | |
| dc.identifier | http://arxiv.org/abs/0802.0566 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154215 | |
| dc.subject | Statistics Theory | |
| dc.subject | Machine Learning | |
| dc.subject | 62G09 (Primary); 62G08, 62M20 (Secondary) | |
| dc.title | V-fold cross-validation improved: V-fold penalization | |
| dc.type | text |