K-Fold Cross Validation

Produce the index splits for k-fold cross validation.

Divide range(n) into k contiguous folds without shuffling. Each fold takes a turn as the validation set while the other k - 1 folds form the training set.

When n is not divisible by k the folds cannot all be the same size. Use the standard convention: the first n % k folds get one extra element. For n = 10 and k = 3 that gives sizes 4, 3, 3.

Return a list of k tuples (train_indices, test_indices), each an integer np.ndarray, with the folds in order and the indices inside each array ascending.

Cross validation exists because a single train/test split is a noisy estimate of performance. Averaging over k folds uses every sample for validation exactly once.

Function signature

def k_fold_indices(n, k):

Example

Input

k_fold_indices(6, 3)

Output

[(array([2, 3, 4, 5]), array([0, 1])),
 (array([0, 1, 4, 5]), array([2, 3])),
 (array([0, 1, 2, 3]), array([4, 5]))]

Reasoning

6 splits evenly into 3 folds of 2. Each fold is the test set once, in order, and the other four indices are the training set.

Constraints and notes

• Do not shuffle. The folds are contiguous.
• The first n % k folds get one extra element.
• Indices in each array are ascending.