📏 Average Precision (AP)

Average Precision (AP)#

The area under the precision-recall curve summarising ranked retrieval.

Important

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What it is#

Average precision summarizes the entire precision–recall curve in one number — the mean of precision across recall levels, computed as precision weighted by the gain in recall at each threshold:

\[\text{AP} = \sum_{n} (R_n - R_{n-1})\,P_n.\]

It equals the area under the PR curve (PR-AUC / AUPRC).

Why it’s useful#

Because it sweeps all thresholds, AP needs no single cutoff, and because it is built from precision and recall it ignores true negatives — making it far more informative than ROC-AUC on imbalanced data where the positive class is rare.

Where it’s used#

AP is the standard score for ranking and detection; averaging it over classes or queries gives mean average precision (mAP), the headline metric in information retrieval and object detection.

Theme: Classification & Averaging Metrics · All terminology

Hint

Mind map — connected ideas

Precision–Recall AUC (PR-AUC) · F1-score · Precision (a.k.a. Positive Predictive Value, PPV) · ROC-AUC (Receiver Operating Characteristic – Area Under Curve, = AUROC) · Harmonic Mean · Macro Averaging

Hint

More in Classification & Averaging Metrics

Accuracy · AUC (Area Under the Curve) · 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 · Macro Precision