Precision

Formula

\[ \operatorname{Precision} = \frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FP}} \]

Parameters

• \(\mathrm{TP}\): true positives
• \(\mathrm{FP}\): false positives

What it means

Of the predicted positives, how many are actually positive.

What it's used for

• Estimating how many predicted positives are correct.
• Tuning thresholds when false positives are costly.

Key properties

• Sensitive to false positives
• Trades off with recall via the decision threshold

Common gotchas

• Undefined if \(\mathrm{TP}+\mathrm{FP}=0\) (no predicted positives).
• Macro vs micro averaging differ for imbalanced data.

Example

If \(\mathrm{TP}=30\) and \(\mathrm{FP}=10\), \(\mathrm{Precision}=30/(30+10)=0.75\).

How to Compute (Pseudocode)

Input: confusion-matrix counts
Output: precision

compute the required numerator/denominator from TP, FP, FN, TN
if denominator == 0:
  return undefined (or use a task-specific convention)
return numerator / denominator

Complexity

• Time: \(O(1)\) once confusion-matrix counts are available
• Space: \(O(1)\)
• Assumptions: Binary classification formula shown; computing the confusion matrix itself is typically \(O(n)\)

See also

• Recall