In Leave-One-Out Cross-Validation (LOOCV), if a dataset has $$n$$ observations, the model is trained on $$n-1$$ data points and a prediction is made on the single left-out observation. This process is repeated $$n$$ times so that each data point is used as the validation set exactly once. The model's overall performance is evaluated by averaging the performance across all $$n$$ predictions.

Leave-One-Out Cross-Validation

To perform $$K$$-fold cross-validation on a dataset with $$n$$ observations, the training set is separated into $$K$$ sets by randomly sampling $$n/K$$ observations from the dataset into each fold. The model of interest is then trained on $$K-1$$ folds and validated on the left-out fold; that is, once the model is trained, we use it to make predictions on the group that was left out of training. This process repeats $$K$$ times. To evaluate the model's overall performance, we calculate the average validation error across all $$K$$ tests. $$K$$-fold cross-validation provides a robust estimate of the empirical testing error of a model and is particularly useful for selecting model designs and adjusting hyperparameters.

K-Fold Cross-Validation

Stratified folds each contain a proportion of classes that matches the overal dataset. Now, all cclasses will be fairly represented in the test set.

Stratified Cross-Validation

Which of the following is true of cross-validation?

A validation dataset (or validation set) is a separate partition of data used to assess the quality of a machine learning model's solution. After training a model iteratively on the training data, its predictive performance is evaluated on this distinct validation dataset to measure how well it has learned the underlying patterns. This evaluation is critical for automatically tuning hyperparameters without relying on the training set, ensuring the model generalizes appropriately to unseen data.

Validation Dataset

Cross-validation methods differ in the bias and variance of their estimated test error. A validation-set approach trains on a relatively small subset of the data and may therefore overestimate test error. Leave-one-out cross-validation trains each model on $$n-1$$ observations, producing an approximately unbiased estimate, but its estimates tend to have higher variance. In $$K$$-fold cross-validation, each model is trained on $$(K-1)n/K$$ observations, so values such as $$K=5$$ or $$K=10$$ generally provide an intermediate bias with lower variance than leave-one-out cross-validation.

Bias–Variance Tradeoff Among Cross-Validation Methods

1. Validation set
2. Leave-One-Out Cross-Validation
3. k-fold Cross-Validation

University of Michigan - Ann Arbor

Divides the training set into two parts - a training set and a validation set (also known as the “holdout set”). A model is made to fit the training set, and then the validation set is used to test the accuracy of the model because the model is blind to it. This gives an estimate of the test error of the model and can be useful in determining the best model from a series of models using different hyperparameters.

Cross-Validation for resampling

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, pp. 3-7). New York: springer.

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