📏 Micro AUROC

Micro AUROC#

AUROC pooled across classes by aggregating individual decisions first; weights every sample equally.

Important

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What it is#

AUROC (Area Under the ROC Curve) is, for a binary task, the probability that the model scores a randomly chosen positive higher than a randomly chosen negative — a threshold-free measure of ranking ability. Micro AUROC is one of the two standard ways to extend that single number to \(K\) classes.

The multiclass problem#

With \(K\) classes there is no single ROC curve. Two aggregation strategies dominate:

Macro AUROC — compute a one-vs-rest AUROC per class, then average them with equal weight.
Micro AUROC — pool every one-vs-rest binary decision across all classes into one big set, then compute a single AUROC.

How micro works#

Flatten all per-class one-vs-rest scores and labels into a single pool, count true and false positives globally, and evaluate AUROC as if it were one binary problem:

\[\text{AUROC}_{\text{micro}} = \text{AUROC}\!\left(\textstyle\bigcup_{i=1}^{K}\text{positives}_i,\; \bigcup_{i=1}^{K}\text{negatives}_i\right).\]

Because counts are pooled, frequent classes dominate the result.

Worked example#

Three classes with one-vs-rest scores AUROC(A)=0.90, AUROC(B)=0.70, AUROC(C)=0.60:

Macro AUROC \(= (0.90 + 0.70 + 0.60)/3 = 0.733\).
Micro AUROC pools predictions, so if class A has far more samples the micro value is pulled toward 0.90 — the majority class’s score.

When to use it (and the trap)#

Micro AUROC answers “how well does the model discriminate overall, per sample”. Its trap is imbalance: it can look excellent while rare classes are handled badly, because their few samples barely move the pooled total. Macro AUROC weights every class equally and exposes weak minorities. Report both.

In code#

from sklearn.metrics import roc_auc_score

# y_true: one-hot (n_samples, K); y_score: predicted probabilities (n_samples, K)
micro = roc_auc_score(y_true, y_score, average="micro", multi_class="ovr")
macro = roc_auc_score(y_true, y_score, average="macro", multi_class="ovr")

Theme: Classification & Averaging Metrics · All terminology

Hint

Mind map — connected ideas

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

Hint

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 AUROC (Macro-Averaged AUROC) · Macro Averaging · Macro F1