📏 Macro AUROC (Macro-Averaged AUROC)

Macro AUROC (Macro-Averaged AUROC)#

The mean of per-class AUROC values, weighting every class equally regardless of size.

Important

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What it is#

AUROC measures ranking ability for a binary task — the probability a random positive outscores a random negative, ranging from 0.5 (chance) to 1.0 (perfect). Since ROC is inherently binary, a \(K\)-class model is scored by reducing it with one-vs-rest (OvR) (or one-vs-one). Macro AUROC averages the per-class OvR AUROCs with equal weight:

\[\text{AUROC}_{\text{macro}} = \frac{1}{K} \sum_{i=1}^{K} \text{AUROC}(\text{class}_i \;\text{vs}\; \text{rest}).\]

Because every class counts the same, a rare class the model handles badly drags the score down just as much as a common one.

Macro vs micro#

Macro gives equal weight per class, so it is sensitive to minority-class performance. Micro pools all OvR decisions into one global AUROC and is therefore dominated by majority classes. They answer different questions — fairness across classes vs overall sample-level discrimination — so reporting both is good practice. The scale matches binary AUROC in every case.

Worked example#

Three classes with AUROC(A vs rest)=0.85, AUROC(B vs rest)=0.72, AUROC(C vs rest)=0.65:

\[\text{AUROC}_{\text{macro}} = \frac{0.85 + 0.72 + 0.65}{3} = 0.74.\]

If C is rare but poorly separated, macro AUROC reflects it; micro might not.

Pitfalls and edge cases#

Undefined per-class AUROC — if a class has no positive (or no negative) samples in the evaluation set, its OvR AUROC is undefined and breaks the average; guard against empty classes.
Equal weighting cuts both ways — a single tiny, hard class can dominate the headline number; inspect the per-class AUROCs, not just the mean.
Weighted variant — averaging the per-class AUROCs by class frequency gives a middle ground between macro and micro.

In code#

from sklearn.metrics import roc_auc_score

macro = roc_auc_score(y_true, y_score, multi_class="ovr", average="macro")
per_class = roc_auc_score(y_true, y_score, multi_class="ovr", average=None)

Theme: Classification & Averaging Metrics · All terminology

Hint

Mind map — connected ideas

Micro AUROC · One-vs-Rest (OvR) AUROC · Macro F1 · Macro Recall

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More in Classification & Averaging Metrics

Accuracy · AUC (Area Under the Curve) · Average Precision (AP) · Binary Classification · Classification Probability · Discriminatory Power · F1-score · Gini Coefficient · Harmonic Mean · Log Loss (also called Logarithmic Loss or Cross-Entropy Loss) · Macro AUC · Macro Averaging · Macro F1 · Macro Precision