THE ROC THRESHOLD AUDIT
Difficulty: Medium Tags: Classification, Evaluation Metrics, Thresholding
Story
A fraud team chooses a decision threshold from predicted probabilities. The monitoring job must count true positives, false positives, true negatives, and false negatives without treating a score equal to the threshold inconsistently.
The Math
Predict positive iff p_i >= tau. For binary label y_i, compute TP,
FP, TN, FN. Then:
precision = TP / (TP + FP)
recall = TP / (TP + FN)
If a denominator is zero, define that metric as 0.
Input Format
probs (length n), labels (length n, 0/1), tau.
Output Format
(TP, FP, TN, FN), then (precision, recall) to 6 decimal places.
Constraints
1 <= n <= 10^5,0 <= p_i, tau <= 1,y_iin{0, 1}.- Time limit: 1.0 second.
Example
Input
probs = [0.5, 0.2, 0.9, 0.7], labels = [1, 0, 1, 0], tau = 0.5
Output
2 1 1 0
0.666667 1.000000
Explanation: A score exactly equal to tau (0.5) counts as a predicted
positive, so the first example is a true positive.
Keywords
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