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📝 FAQ UPDATE

Course: machine-learning-zoomcamp
Section: module-4 (The proposal is directly about ROC AUC behavior for numerical features in classification, which fits Module 4’s coverage of ROC curves and ROC AUC.)
Related Issue: #478

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?

Decision Rationale

Existing FAQs explain how to use AUC as a score and mention inverting when auc < 0.5, but they don’t explicitly explain why AUC can be below 0.5 (opposite-direction relationship) and how/why negation changes ranking for feature importance.

Placement Details

• Section ID: module-4
• Sort Order: 30
• Document ID: 866f5d58d2

⚠️ Warnings

• This will effectively merge into the existing Module 4 AUC/feature-score FAQ (document_id 866f5d58d2), adding the missing ‘why < 0.5’ explanation.

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🤖 Generated by FAQ Bot

Closes #478

[saeidsoheily]

A numerical feature can have ROC AUC below 0.5 when its relationship with the target is reversed: lower feature values tend to correspond to the positive class (y=1), rather than higher values.

This does not necessarily mean the feature is useless. It may be a strong predictor in the opposite direction.

When evaluating a numerical feature directly using roc_auc_score(), we treat its values as prediction scores.

ROC AUC measures how well those scores rank positive examples above negative examples.

• AUC = 1.0: Positive examples consistently have higher values.
• AUC = 0.5: No ranking discrimination.
• AUC below 0.5: Negative examples tend to have higher values.
• AUC = 0.0: Perfect ranking in the opposite direction.

In Module 4, we can use ROC AUC to evaluate the predictive strength of individual numerical features.

from sklearn.metrics import roc_auc_score

for feature in numerical:
    auc = roc_auc_score(df_train.y, df_train[feature])

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

    print(f"{feature:30s} AUC = {auc:.3f}")

Alternatively, since negation reverses AUC:

for feature in numerical:
    auc = roc_auc_score(df_train.y, df_train[feature])
    auc = max(auc, 1 - auc)

    print(f"{feature:30s} AUC = {auc:.3f}")

This produces a direction-independent AUC between 0.5 and 1.0.

In simple words; Negating a feature does not add information or make the underlying feature more predictive. It simply reverses which direction counts as a higher score.

Also, single-feature AUC is only one measure of feature importance. It does not capture interactions, redundancy between features, or how much a feature improves a multivariate model.