Caret - Repeated K-fold cross-validation vs Nested K-fold cross validation, repeated n-times

Question

The caret package is a brilliant R library for building multiple machine learning models, and has several functions for model building and evaluation. For parameter tuning and model training, the caret package offers ‘repeatedcv’ as one of the methods.

As a good practice, parameter tuning might be performed using nested K-fold cross validation which works as follows:

1. Partition the training set into ‘K’ subsets
2. In each iteration, take ‘K minus 1’ subsets for model training, and keep 1 subset (holdout set) for model testing.
3. Further partition the ‘K minus 1’ training set into ‘K’ subsets, and iteratively use the new ‘K minus 1’ subset and the ‘validation set’ for parameter tuning (grid search). The best parameter identified in this step is used to test on the holdout set in step 2.

On the other hand, I assume, the repeated K-fold cross-validation might repeat the step 1 and 2 repetitively as many times we choose to find model variance.

However, going through the algorithm in the caret manual it looks like the ‘repeatedcv’ method might perform nested K-fold cross validation as well, in addition to repeating cross validation.

My questions are:

1. Is my understating about the caret ‘repeatedcv’ method correct?
2. If not, could you please give an example of using nested K-fold cross validation, with ‘repeatedcv’ method using the caret package?

Edit:

Different cross validation strategies are explained and compared in this methodology article.

Krstajic D, Buturovic LJ, Leahy DE and Thomas S: Cross-validation pitfalls when selecting and assessing regression and classification models. Journal of Cheminformatics 2014 6(1):10. doi:10.1186/1758-2946-6-10

I am interested in “Algorithm 2: repeated stratified nested cross-validation” and “Algorithm 3: repeated grid-search cross-validation for variable selection and parameter tuning” using caret package.

Answer 1

There's nothing wrong with the (nested) algorithm presented, and in fact, it would likely perform well with decent robustness for the bias-variance problem on different data sets. You never said, however, that the reader should assume the features you were using are the most "optimal", so if that's unknown, there are some feature selection issues that must first be addressed.

FEATURE/PARAMETER SELECTION

A lesser biased approached is to never let the classifier/model come close to anything remotely related to feature/parameter selection, since you don't want the fox (classifier, model) to be the guard of the chickens (features, parameters). Your feature (parameter) selection method is a $wrapper$ - where feature selection is bundled inside iterative learning performed by the classifier/model. On the contrary, I always use a feature $filter$ that employs a different method which is far-removed from the classifier/model, as an attempt to minimize feature (parameter) selection bias. Look up wrapping vs filtering and selection bias during feature selection (G.J. McLachlan).

There is always a major feature selection problem, for which the solution is to invoke a method of object partitioning (folds), in which the objects are partitioned in to different sets. For example, simulate a data matrix with 100 rows and 100 columns, and then simulate a binary variate (0,1) in another column -- call this the grouping variable. Next, run t-tests on each column using the binary (0,1) variable as the grouping variable. Several of the 100 t-tests will be significant by chance alone; however, as soon as you split the data matrix into two folds $\mathcal{D}_1$ and $\mathcal{D}_2$, each of which has $n=50$, the number of significant tests drops down. Until you can solve this problem with your data by determining the optimal number of folds to use during parameter selection, your results may be suspect. So you'll need to establish some sort of bootstrap-bias method for evaluating predictive accuracy on the hold-out objects as a function of varying sample sizes used in each training fold, e.g., $\pi=0.1n, 0.2n, 0,3n, 0.4n, 0.5n$ (that is, increasing sample sizes used during learning) combined with a varying number of CV folds used, e.g., 2, 5, 10, etc.

OPTIMIZATION/MINIMIZATION

You seem to really be solving an optimization or minimization problem for function approximation e.g., $y=f(x_1, x_2, \ldots, x_j)$, where e.g. regression or a predictive model with parameters is used and $y$ is continuously-scaled. Given this, and given the need to minimize bias in your predictions (selection bias, bias-variance, information leakage from testing objects into training objects, etc.) you might look into use of employing CV during use of swarm intelligence methods, such as particle swarm optimization(PSO), ant colony optimization, etc. PSO (see Kennedy & Eberhart, 1995) adds parameters for social and cultural information exchange among particles as they fly through the parameter space during learning. Once you become familiar with swarm intelligence methods, you'll see that you can overcome a lot of biases in parameter determination. Lastly, I don't know if there is a random forest (RF, see Breiman, Journ. of Machine Learning) approach for function approximation, but if there is, use of RF for function approximation would alleviate 95% of the issues you are facing.