K-Fold CV works by randomly partitioning your data into k (fairly) equal partitions. If your data were evenly balanced across classes like [0,1,0,1,0,1,0,1,0,1], randomly sampling with (or without replacement) will give you approximately equal sample sizes of 0 and 1.

However, if your data is more like[0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0] where one class over represents the data, k-fold cv without weighted sampling would give you erroneous results.

If you use ordinary k-fold CV without adjusting sampling weights from uniform sampling, then you'd obtain something like

k = 5

y = [0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0]

splits = np.array_split(y, k)

for i in range(k):

print(np.mean(splits[i]))

Result

where there are clearly splits without useful representation of both classes.

The point of k-fold CV is to train/test a model across all subsets of data, while at each trial leaving out 1 subset and training on k-1 subsets.

In this scenario, you'd want to use split by strata. In the above data set, there are 27 0s and 5 1s. If you'd like to compute k=5 CV, it wouldn't be reasonable to split the strata of 1 into 5 subsets. A better solution is to split it into k < 5 subsets, such as 2. The strata of 0s can remain with k=5 splits since it's much larger. Then while training, you'd have a simple product of 2 x 5 from the data set. Here is some code to illustrate

from itertools import product

for strata, iterable in groupby(y):

data = np.array(list(iterable))

if strata == 0:

zeros = np.array_split(data, 5)

else:

ones = np.array_split(data, 2)

cv_splits = list(product(zeros, ones))

print(cv_splits)

m = len(cv_splits)

for i in range(2):

for j in range(5):

data = np.concatenate((ones[-i+1], zeros[-j+1]))

print("Leave out ONES split {}, and Leave out ZEROS split {}".format(i,j))

print("train on: ", data)

print("test on: ", np.concatenate((ones[i], zeros[j])))

Leave out ONES split 0, and Leave out ZEROS split 0

train on: [1 1 0 0 0 0 0 0]

test on: [1 1 1 0 0 0 0 0 0]

Leave out ONES split 0, and Leave out ZEROS split 1

train on: [1 1 0 0 0 0 0 0]

...

Leave out ONES split 1, and Leave out ZEROS split 4

train on: [1 1 1 0 0 0 0 0]

test on: [1 1 0 0 0 0 0]

This method can accomplish splitting the data into partitions where all partitions are eventually left out for testing. It should be noted that not all statistical learning methods allow for weighting, so adjusting methods like CV is essential to account for sampling proportions.

- Reference: James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning: With applications in R.