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Cross-validated average: metrics mean or ensembling probabilities?

Data Science Asked on March 30, 2021

Let’s say I have 5 models cross-validated via leave-one-out strategy. I have the predictions and scores of each model.

Now, it’s time to calculate the average for the set of 5 models – am I supposed to:

  • add up the 5 losses and divide them by 5?
  • Or average their probabilities for each prediction and use the average probability to calculate new metrics like an ensemble/ forest?

2 Answers

A standard way to provide the performance of each model would be:

  • providing, for each split, the value of the chosen metric (accuracy, roc_auc, etc) on the train and test sets (on your case, your one-out sample), something like this (in this case with 2 models): enter image description here

  • as a final model performance (for each one of the 5 models), a mean metric value together with its standard deviation for the test sets is a way to inform about the model quality and its robustness, something like (preferably for the test set):

enter image description here

You have more detail on how to automatically get this done via scikit-learn, and in this answer and this one.

By the way, consider using another strategy as stratified k-fold, in case you have a lot of samples, as leave-one-out would be very costly.

Answered by German C M on March 30, 2021

There are multiple popular ways to ensemble models. Averaging, majority voting, selecting the one with the highest probability, learn a new model based on these 5 numbers are amongst the many methods available. Check also the Bayes optimal classifier which 'averages' these probabilities in a Bayes way: https://en.wikipedia.org/wiki/Ensemble_learning#Bayes_optimal_classifier

Answered by LuckyLuke on March 30, 2021

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