When using k-fold cross-validation, what happens to the size of the training set as k increases?

In k-fold cross-validation, the dataset is divided into k equally sized subsets or "folds." The model is trained on k-1 of these folds and validated on the remaining fold. This process is repeated k times, with each fold serving as the validation set once.

As the value of k increases, the size of the training set actually changes in a specific way. For example, with k equal to a smaller number, fewer folds mean that fewer data points are left out during each training iteration, so the majority of the dataset can be used for training each time. However, as k approaches the total number of data points in the dataset (for instance, in the case of leave-one-out cross-validation where k equals the number of observations), each training set will contain almost all of the data except for one observation per fold.

Therefore, as k increases, while the size of the training set approaches the full dataset, it doesn't increase in the sense of simply having more data available; rather, it means you're using more of the data to train than to validate on each cycle of cross-validation. The growth in k means a more comprehensive use of the dataset for training, making the training set size effectively maximize with respect to the available data.