Possible to use predict_proba without normalizing to 1?

Question

I'm using xgboost multi-class classifier to predict a collection of things likely to fail. I want to run that prediction, and report anything that the classifier identifies with probability > 75%. However if I use xgb.predict_proba(), the sum of the results in the array add up to 1. So, if there are a lot of things likely to fail, they will all have tiny percentages in the result array.

Looking at the predict_proba code, I can see where the array is getting normalized. However I can't figure out how to prevent this.

In the end, I think my code would look something like this (except with the pre-normalized probabilities):

probas = xgb.predict_proba(single_element_dataframe)

for class_name in xgb.classes_:
    class_index = np.where(xgb.classes_ == class_name)
    proba = probas[0][class_index]
    if proba > 0:
        print(f"{class_name}: {proba}")

Any ideas?

Answer 1

Currently you're doing multiclass classification: find the most likely among N classes. Each class $C$ probability indicates how likely class $C$ is for the instance as opposed to any other class. This is why the probabilities sum to 1: in this setting, there is only one "correct" class, so two classes cannot both have high probability.

Based on your description you should use multi-label classification: find all the classes that apply to the instances among N classes. In this case each class $C$ probability indicates how likely this instance has class $C$ as opposed to not having class $C$ (i.e. independently from any other class). Naturally the consequence is that the probabilities don't sum to one, since they are independent of each other.

Note: multi-label classification is exactly the same as training a binary model for every class independently.