V-fold penalization: an alternative to V-fold cross-validation
Sylvain Arlot
In: Oberwolfach Reports Mathematisches Forschungsinstitut Oberwolfach Report , 4 (4). (2007) European Mathematical Society , Zurich .

Abstract

One of the most widely used model selection techniques is V-fold cross-validation. We study some of its properties from the non-asymptotic viewpoint, in particular with the goal of choosing the optimal V. Then, following Efron's resampling heuristics (Efron, 1979), we propose to use a V-fold resampling scheme to define a new penalization procedure, called V-fold penalization. In a regression framework with heteroscedastic noise, we prove a non-asymptotic oracle inequality with constant almost one, implying asymptotic optimality. A simulation study finally shows that V-fold penalties outperform V-fold cross-validation and Mallows' penalties in several heteroscedastic cases.

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