[FAQ]Why can a numerical feature have ROC AUC below 0.5, and why can we invert it? #478

Course

machine-learning-zoomcamp

Question

Why can a numerical feature have a ROC AUC below 0.5, and why can we invert the feature when using AUC for feature importance?

Answer

An AUC below 0.5 does not necessarily mean that the feature contains no useful information.

It can mean that the feature is related to the target in the opposite direction. For example, higher values of the feature may be associated with the negative class instead of the positive class.

When we use a single numerical feature as a prediction score, we can reverse its direction:

if auc < 0.5:
auc = roc_auc_score(y_train, -df_train[feature])

Negating the feature reverses its ranking. This allows us to measure how strongly the feature separates the two classes regardless of whether the relationship is positive or negative.

So, in this context, an AUC below 0.5 may indicate useful predictive information with an inverse relationship to the target.

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