Types of Training vs Test Error for Random Forest Classification Algorithm (Assessing Variance)

Question

I have 2 questions that I would like to ascertain if possible (questions are bolded):

I've recently understood (I hope) the random forest classification algorithm, and have tried to apply it using sklearn on Python on a rather large dataset of pixels derived from satellite images (with the features being the different bands, and the labels being specific features that I outlined by myself, i.e., vegetation, cloud, etc). I then wanted to understand if the model was experiencing a variance problem, and so the first thought that came to my mind was to compare between the training and testing data.

Now this is where the confusion kicks in for me - I understand that there have been many different posts about:

1. How CV error should/should not be used compared to the out of bag (OOB) error
2. How by design, the training error of a random forest classifier is almost always ~0 (i.e., fitting my model on the training data and using it to predict on the same set of training data) - seems to be the case regardless of the tree depth

Regarding point 2, it seems that I can never compare my training and test error as the former will always be low, and so I decided to use the OOB error as my 'representative' training error for the entire model. I then realized that the OOB error might be a pseudo test error as it essentially tests trees on points that they did not specifically learn (in the case of bootstrapped trees), and so I defaulted to CV error being my new 'representative' training error for the entire model.

Looking back at the usage of CV error, I initially used it for hyperparameter tuning (e.g., max tree depth, number of trees, criterion type, etc), and so I was again doubting myself if I should use it as my official training error to be compared against my test error.

What makes this worse is its hard for me to validate what I think is true based on posts across the web because each answers only a small part and might contradict each other, and so would anyone kindly help me with my predicament on what to use as my official training error that will be compared to my test error?

My second question revolves around how the OOB error might be a pseudo test error based on datapoints not selected during bootstrapping. If that were true, would it be fair to say this does not hold if bootstrapping is disabled (the algorithm is technically still a random forest as features are still randomly subsampled for each tree, its just that the correlation between trees are probably higher)?

Thank you!!!!

Answer 1

Generally, you want to distinctly break a dataset into training, validation, and test. Training is data fed into the model, validation is to monitor progress of the model as it learns, and test data is to see how well your model is generalizing to unseen data. As you've discovered, depending on the application and the algorithm, you can mix-up training and validation data or even forgo validation data entirely. For random forest, if you want to forgo having a distinct validation set and just use OOB to monitor progress that is fine. If you have enough data, I think it still makes sense to have a distinct validation set. No matter what, you should still reserve some data for testing. Depending on your data, you may even need to be careful about how you split up the data (e.g. if there's unevenness in the labels).

As to your second point about comparing training and test sets, I think you may be confused. The test set is really all you care about. You can compare the two to see if you're overfitting, so that you can change hyperparameters to generalize more, but otherwise the whole point is that the test set is to the sole truthful evaluation. If you have a really small dataset, you may need to bootstrap a number of models with a CV scheme like stratified CV to generate a more accurate test evaluation.