View source for Precision-Recall Curve

= Precision-Recall Curve =

The '''Precision-Recall Curve''' (PR Curve) is a graphical representation used to evaluate the performance of binary classification models, especially on '''imbalanced datasets''' where the positive class is rare.

It plots '''Precision''' (y-axis) against '''Recall''' (x-axis) for different classification thresholds.

== Why Use Precision-Recall Curve? ==

In many real-world problems like fraud detection, disease diagnosis, or spam filtering, the positive class is much less frequent than the negative class. Traditional metrics like [[ROC Curve]] or [[Accuracy]] can be misleading in such cases.

The Precision-Recall curve focuses on the performance of the positive class, showing how precision and recall change as the classification threshold varies.

== Definitions ==

* '''Precision''' measures the proportion of correctly predicted positive observations to all predicted positives:

:<math> \text{Precision} = \frac{TP}{TP + FP} </math>

* '''Recall''' (Sensitivity) measures the proportion of correctly predicted positive observations to all actual positives:

:<math> \text{Recall} = \frac{TP}{TP + FN} </math>

Where:

* TP = True Positives  
* FP = False Positives  
* FN = False Negatives

== How to Interpret the Curve ==

- The top-right corner (Precision=1, Recall=1) represents perfect classification.  
- A high area under the PR curve indicates both high precision and recall.  
- The curve helps to select the best threshold by balancing false positives and false negatives.

== Area Under the Precision-Recall Curve (AUPRC) ==

Similar to ROC AUC, the '''Area Under the Precision-Recall Curve''' (AUPRC) summarizes the model’s ability to balance precision and recall.

* Higher AUPRC means better model performance on the positive class.
* Unlike ROC AUC, AUPRC is more informative with highly skewed data.

== Example ==

Imagine a spam detection system:

- At a low threshold, many emails are classified as spam (high recall) but many legitimate emails are incorrectly flagged (low precision).
- At a high threshold, only very confident spam emails are flagged (high precision) but some spam emails go undetected (low recall).
- The PR curve shows how precision and recall trade off as the threshold changes.

== Precision-Recall Curve vs ROC Curve ==

{| class="wikitable"
! Aspect
! Precision-Recall Curve
! ROC Curve
|-
| Best used when
| Positive class is rare / imbalanced
| Classes are balanced or costs similar
|-
| Focus
| Performance on positive class
| Trade-off between TPR and FPR (sensitivity and specificity)
|-
| Interpretation
| Emphasizes false positives impact on precision
| Emphasizes false positives rate relative to negatives
|}

== Related Pages ==

* [[Precision]]
* [[Recall]]
* [[F1 Score]]
* [[ROC Curve]]
* [[Confusion Matrix]]
* [[Imbalanced Data]]

== SEO Keywords ==

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[[Category:Artificial Intelligence]]