Cross-validation
Cross-validation
This text is a survey on cross-validation. We define all classical cross-validation procedures, and we study their properties for two different goals: estimating the risk of a given estimator, and selecting the best estimator among a given family. For the risk estimation problem, we compute the bias (which can also be corrected) and the variance of cross-validation methods. For estimator selection, we first provide a first-order analysis (based on expectations). Then, we explain how to take into account second-order terms (from variance computations, and by taking into account the usefulness of overpenalization). This allows, in the end, to provide some guidelines for choosing the best cross-validation method for a given learning problem.
in French
FOS: Computer and information sciences, model selection, bias-corrected cross-validation, estimator selection, leave-one-out, sélection d'estimateurs, Mathematics - Statistics Theory, Machine Learning (stat.ML), Statistics Theory (math.ST), cross-validation, V-fold cross-validation, Statistics - Machine Learning, overpenalization, FOS: Mathematics, risk estimation, sélection de modèles, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], V-fold penalization, [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH], estimation du risque, pénalisation V-fold, [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], leave-p-out, validation croisée V-fold, validation croisée corrigée, surpénalisation, validation croisée
FOS: Computer and information sciences, model selection, bias-corrected cross-validation, estimator selection, leave-one-out, sélection d'estimateurs, Mathematics - Statistics Theory, Machine Learning (stat.ML), Statistics Theory (math.ST), cross-validation, V-fold cross-validation, Statistics - Machine Learning, overpenalization, FOS: Mathematics, risk estimation, sélection de modèles, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], V-fold penalization, [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH], estimation du risque, pénalisation V-fold, [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], leave-p-out, validation croisée V-fold, validation croisée corrigée, surpénalisation, validation croisée
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