How does repeated k-fold cross validation identify model instability? In these threads 1,2,3, cbeleites mentions that in a single k-fold cross validation you cannot tell whether the variance is  caused by model instability or using a different test set. Hence, one can perform repeated k-fold to get a measure of model instability.
My question is:

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*Model stability can be thought of as getting the same predictions for a fixed set of test data as you train your model on slightly different data. How does repeated k-fold cross validation provide a measure of this as your training and test data is still random as you repeat it? You are training on different data, but your test data is also different, so the relationship between the two is not clear to me. Does anyone have a simple and intuitive explanation for this?


The meaning of 'model stability' is open to interpretation. An application of control theoretic stability for statistical models are not well established, at least there is no single definition out there. However, the repeated k-fold CV can be used for nonparametric way of finding generalisation performance as an interval estimate, as single CV would be a point estimate.
