We now review k$-$fold cross validation:

$($a$)$ Explain how k$-$fold cross validation is implemented.

$($b$)$ What are the advantages and disadvantages of k$-$fold cross validation relative to $($i$)$

the validation set approach and $($ii$)$ LOOCV?

Please provide detailed explanation and rationale to parts $($a$)$ and $($b$).$