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In the case of a dichotomous classification, this means that each fold contains roughly the same proportions of the two types of class labels.In the holdout method, we randomly assign data points to two sets d.The advantage of this method over repeated random sub-sampling (see below) is that all observations are used for both training and validation, and each observation is used for validation exactly once. When k = n (the number of observations), the k-fold cross-validation is exactly the leave-one-out cross-validation.In stratified k-fold cross-validation, the folds are selected so that the mean response value is approximately equal in all the folds.

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Since in linear regression it is possible to directly compute the factor (n − p − 1)/(n p 1) by which the training MSE underestimates the validation MSE, cross-validation is not practically useful in that setting (however, cross-validation remains useful in the context of linear regression in that it can be used to select an optimally regularized cost function). logistic regression), there is no simple formula to make such an adjustment.This is called overfitting, and is particularly likely to happen when the size of the training data set is small, or when the number of parameters in the model is large.Cross-validation is a way to predict the fit of a model to a hypothetical validation set when an explicit validation set is not a model validation technique for assessing how the results of a statistical analysis will generalize to an independent data set.It is mainly used in settings where the goal is prediction, and one wants to estimate how accurately a predictive model will perform in practice.

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