Cross-Validation in R using vtreat Package - r

Question

Currently learning about cross validation through a course on DataCamp. They start the process by creating an n-fold cross validation plan. This is done with the kWayCrossValidation() function from the vtreat package. They call it as follows:
splitPlan <- kWayCrossValidation(nRows, nSplits, dframe, y)
Then, they suggest running a for loop as follows:
dframe$pred.cv <- 0
# k is the number of folds
# splitPlan is the cross validation plan
for(i in 1:k) {
# Get the ith split
split <- splitPlan[[i]]
# Build a model on the training data
# from this split
# (lm, in this case)
model <- lm(fmla, data = dframe[split$train,])
# make predictions on the
# application data from this split
dframe$pred.cv[split$app] <- predict(model, newdata = dframe[split$app,])
}
This results in a new column in the datafram with the predictions, per the last line of the above chunk of code.
My doubt is thus whether the predicted values on the data frame will be in fact averages of the 3 folds or if they will just be those of the 3rd run of the for loop?
Am I missing a detail here, or is this exactly what this code is doing, which would then defeat the purpose of the 3-fold cross validation or any-fold cross validation for that matter, as it will simply output the results of the last iteration? Shouldn't we be looking to output the average of all the folds, as laid out in the splitPlan?
Thank you.

Answer 1

I see there is confusion about the scope of K-fold cross-validation. The idea is not to average predictions over different folds, rather to average some measure of the prediction error, so to estimate test errors.
First of all, as you are new on SO, notice that you should always provide some data to work with. As in this case your question is not data-contingent, I just simulated some. Still, it is a good practice helping us helping you.
Check the following code, which slightly modifies what you have provided in the post:
library(vtreat)
# Simulating data.
set.seed(1986)
X = matrix(rnorm(2000, 0, 1), nrow = 1000, ncol = 2)
epsilon = matrix(rnorm(1000, 0, 0.01), nrow = 1000)
y = X[, 1] + X[, 2] + epsilon
dta = data.frame(X, y, pred.cv = NA)
# Folds.
nRows = dim(dta)[1]
nSplits = 3
splitPlan = kWayCrossValidation(nRows, nSplits)
# Fitting model on all folds but i-th.
for(i in 1:nSplits)
{
# Get the i-th split.
split = splitPlan[[i]]
# Build a model on the training data from this split.
model = lm(y ~ ., data = dta[split$train, -4])
# Make predictions on the application data from this split.
dta$pred.cv[split$app] = predict(model, newdata = dta[split$app, -4])
}
# Now compute an estimate of the test error using pred.cv.
mean((dta$y - dta$pred.cv)^2)
What the for loop does, is to fit a linear model on all folds but the i-th (i.e., on dta[split$train, -4]), and then it uses the fitted function to make predictions on the i-th fold (i.e., dta[split$app, -4]). At least, I am assuming that split$train and split$app serve such roles, as the documentation is really lacking (which usually is a bad sign). Notice I am revoming the 4-th column (dta$pred.cv) as it just pre-allocates memory in order to store all the predictions (it is not a feature!).
At each iteration, we are not filling the whole dta$pred.cv, but only a subset of that (corresponding to the rows of the i-th fold, stored each time in split$app). Thus, at the end that column just stores predictions from the K iteration.
The real rationale for cross-validation jumps in here. Let me introduce the concepts of training, validation, and test set. In data analysis, the ideal is to have such a huge data set so that we can divide it in three subsamples. The first one could then be used to train the algorithms (fitting models), the second to validate the models (tuning the models), the third to choose the best model in terms on some perfomance measure (usually mean-squared-error for regression, or MSE).
However, we often do not have all these data points (especially if you are an economist). Thus, we seek an estimator for the test MSE, so that the need for splitting data disappears. This is what K-fold cross-validation does: at once, each fold is treated as the test set, and the union of all the others as the training set. Then, we make predictions as in your code (in the loop), and save them. What you miss is the last line in the code I provided: the average of the MSE across folds. That provides us with as estimate of the test MSE, where we choose the model yielding the lowest value.
That being said, I never heard before of the vtreat package. If you are into data analysis, I suggest to have a look at the tidiyverse and the caret packages. As far as I know (and I see here on SO), they are widely used and super-well documented. May be worth learning them.