ROC Curve Points

Compute the ROC curve points (TPR and FPR at each threshold).

Given true labels and predicted probabilities, compute the True Positive Rate (TPR) and False Positive Rate (FPR) at each unique threshold.

For each unique predicted probability (used as threshold, sorted descending), classify all predictions $\geq$ threshold as positive:

$TPR = \frac{TP}{TP + FN}, \quad FPR = \frac{FP}{FP + TN}$

Return a list of (fpr, tpr) tuples rounded to 4 decimal places, starting from (0, 0) when threshold is above the max prediction, ending at (1, 1) when threshold is 0.

Example:

Input:

y_true = [1, 0, 1, 0]
y_scores = [0.9, 0.4, 0.65, 0.3]

Output:

[(0.0, 0.0), (0.0, 0.5), (0.0, 1.0), (0.5, 1.0), (1.0, 1.0)]

Reasoning:

First, we sort the predicted probabilities in descending order and use them as thresholds: $[0.9, 0.65, 0.4, 0.3]$ .
Then, we calculate the TPR and FPR at each threshold:
- At threshold $0.9$ , only the first prediction is $\geq$ threshold, so $TP = 1$ , $FP = 0$ , $TN = 1$ , $FN = 1$ , resulting in $TPR = \frac{1}{1+1} = 0.5$ and $FPR = \frac{0}{0+1} = 0$ .
- At threshold $0.65$ , the first two predictions are $\geq$ threshold, so $TP = 2$ , $FP = 0$ , $TN = 1$ , $FN = 0$ , resulting in $TPR = \frac{2}{2+0} = 1$ and $FPR = \frac{0}{0+1} = 0$ .
- At threshold $0.4$ , the first three predictions are $\geq$ threshold, so $TP = 2$ , $FP = 1$ , $TN = 0$ , $FN = 0$ , resulting in $TPR = \frac{2}{2+0} = 1$ and $FPR = \frac{1}{1+0} = 0.5$ .
- At threshold $0$ , all predictions are $\geq$ threshold, so $TP = 2$ , $FP = 2$ , $TN = 0$ , $FN = 0$ , resulting in $TPR = \frac{2}{2+0} = 1$ and $FPR = \frac{2}{2+0} = 1$ .
The final output includes the starting point $(0, 0)$ when the threshold is above the max prediction and the calculated points, resulting in $[(0.0, 0.0), (0.0, 0.5), (0.0, 1.0), (0.5, 1.0), (1.0, 1.0)]$ .

Constraints:

y_true: list of 0s and 1s
y_scores: list of predicted probabilities
Return sorted list of (fpr, tpr) tuples from (0,0) to (1,1)
Round to 4 decimal places

Example:

Constraints:

Test Results