Choice of V for V-Fold Cross-Validation in Least-Squares Density Estimation - Inria - Institut national de recherche en sciences et technologies du numérique
Preprints, Working Papers, ... Year : 2015

Choice of V for V-Fold Cross-Validation in Least-Squares Density Estimation

Abstract

This paper studies V-fold cross-validation for model selection in least-squares density estimation. The goal is to provide theoretical grounds for choosing V in order to minimize the least-squares loss of the selected estimator. We first prove a non-asymptotic oracle inequality for V-fold cross-validation and its bias-corrected version (V-fold penalization). In particular, this result implies that V-fold penalization is asymptotically optimal in the nonparametric case. Then, we compute the variance of V-fold cross-validation and related criteria, as well as the variance of key quantities for model selection performance. We show that these variances depend on V like 1+4/(V-1), at least in some particular cases, suggesting that the performance increases much from V=2 to V=5 or 10, and then is almost constant. Overall, this can explain the common advice to take V=5---at least in our setting and when the computational power is limited---, as supported by some simulation experiments. An oracle inequality and exact formulas for the variance are also proved for Monte-Carlo cross-validation, also known as repeated cross-validation, where the parameter V is replaced by the number B of random splits of the data.
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Dates and versions

hal-00743931 , version 1 (22-10-2012)
hal-00743931 , version 2 (17-07-2014)
hal-00743931 , version 3 (09-10-2015)

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Sylvain Arlot, Matthieu Lerasle. Choice of V for V-Fold Cross-Validation in Least-Squares Density Estimation. 2015. ⟨hal-00743931v3⟩
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